Optics – NDA Physics PYQs

NDA 2026-I

Q. 1. An object is placed far beyond the centre of curvature of a concave mirror. The object then starts accelerating towards the mirror. Which one of the following is correct?

(a)  The image will accelerate towards the centre of curvature.

(b)  The image will accelerate towards the focus.

(c)  The image will accelerate towards the pole of the mirror.

(d)  The image will move with a constant speed towards the focus.

Answer: (b) The image will accelerate towards the focus.

Explanation: As object moves from far beyond C toward C, image moves from between F and C toward F. Image accelerates toward F as object accelerates toward C. Concept Tested: Concave mirror: object accelerating toward mirror from beyond C: image accelerates toward F

Q. 2. A periscope uses two plane mirrors inclined at 45°. If the tube of the periscope is filled with a complete transparent liquid of refractive index 1·5, then which one of the following is correct in respect of the image seen?

(a)  The image will remain unchanged.

(b)  The image will appear laterally shifted.

(c)  The image will appear 1·5 times brighter.

(d)  The image will appear 1·5 times darker.

Answer: (a) The image will remain unchanged.

Explanation: Periscope works by reflection: law of reflection is independent of medium. Filling with liquid doesn’t change reflection geometry. Concept Tested: Periscope with liquid: reflection geometry unchanged; image unchanged

Q. 3. It has been observed that a mirror always forms the image between the pole and the focus, irrespective of the location of the object. Which one of the following is correct in respect of the nature of the mirror?

(a)  It is a plane mirror.

(b)  It is a convex mirror.

(c)  It is a concave mirror of small focal length.

(d)  It is a concave mirror of large focal length.

Answer: (b) It is a convex mirror.

Explanation: Convex mirror: image always between P and F (behind mirror) for all object positions: this is the unique property of a convex mirror. Concept Tested: Mirror: image always between P and F → convex mirror

Q. 4. With respect to electromagnetic waves, the human eye is sensitive to

(a)  both electric and magnetic fields

(b)  electric field only

(c)  magnetic field only

(d)  infrared part of the electromagnetic spectrum

Answer: (b) electric field only

Explanation: Photoreceptors respond to the oscillating electric field of visible EM radiation. The magnetic field component does not directly trigger visual response. Concept Tested: Human eye: responds to electric field component of visible light EM wave

NDA 2025-II

Q. 5. The focal length of a concave lens is 0·5 m. The power of the lens is

(a)  +0·5 D

(b)  −0·5 D

(c)  +2·0 D

(d)  −2·0 D

Answer: (d) −2·0 D

Explanation: Concave lens: f = −0.5 m (negative). P = 1/(−0.5) = −2 D. Concept Tested: Concave lens: f = −0.5 m → P = −2 D

Q. 6. In a Telescope, compared to the eyepiece lens the objective lens has

(a)  larger focal length and larger aperture

(b)  larger focal length and smaller aperture

(c)  smaller focal length and larger aperture

(d)  smaller focal length and smaller aperture

Answer: (a) larger focal length and larger aperture

Explanation: Telescope objective: large f (high magnification M = f_obj/f_eye) and large aperture (collect more light from faint objects). Concept Tested: Telescope objective: larger f AND larger aperture than eyepiece

NDA 2025-I

Q. 7. An object is placed between infinity and the pole (P) of a convex mirror. The position of the image is

(a)  between pole (P) and the focus (F), behind the mirror

(b)  between the focus (F) and infinity, behind the mirror

(c)  between the pole (P) and the infinity, in front of the mirror

(d)  at the focus (F), behind the mirror

Answer: (a) between pole (P) and the focus (F), behind the mirror

Explanation: Convex mirror: image always between P and F behind mirror for all real object positions. Concept Tested: Convex mirror: image always between P and F, behind mirror

Q. 8. When a light ray passes through from air to water with a non-zero angle the ray will be

(a)  bending towards the normal

(b)  bending away from the normal

(c)  propagating in straight line

(d)  reflected towards the opposite direction

Answer: (a) bending towards the normal

Explanation: Air (rarer) → water (denser): light bends toward normal (angle of refraction < angle of incidence). Concept Tested: Air to water: bends toward normal (denser medium)

NDA 2024-II

Q. 9. A point object is placed at the centre of curvature of a spherical concave mirror. Which one among the following would be the correct location of image formed?

(a)  At infinity

(b)  At the centre of curvature

(c)  At the focal point

(d)  Between the focal point and the centre of curvature

Answer: (b) At the centre of curvature

Explanation: Object at C → image at C (real, inverted, same size). Standard concave mirror case. Concept Tested: Concave mirror: object at C gives image at C

Q. 10. Which one among the following is correct for a person suffering from myopia?

(a)  The person can see near objects clearly

(b)  The person can see distant objects clearly

(c)  The person cannot distinguish colours

(d)  The person can neither see near objects nor distant objects clearly

Answer: (a) The person can see near objects clearly

Explanation: Myopia: near vision clear; distant vision blurred. Colours unaffected. Concept Tested: Myopia: near vision clear; distant blurred

Q. 11. Which one among the following is the correct focal length of a combination of lenses of power 2·5 D and −2·0 D?

(a)  +0·5 m

(b)  −0·5 m

(c)  +2·0 m

(d)  −2·0 m

Answer: (c) +2·0 m

Explanation: P_net = 2.5 − 2.0 = +0.5 D. f = 1/0.5 = +2.0 m. Concept Tested: Combined lens power: P = 2.5 − 2.0 = +0.5 D → f = +2.0 m

NDA 2024-I

Q. 12. A microscope may be a combination of:

(a)  two convex lenses

(b)  a convex and a concave lens

(c)  two concave lenses

(d)  a convex lens and a convex mirror

Answer: (a) two convex lenses

Explanation: Compound microscope: objective (short f, convex) + eyepiece (longer f, convex). Both convex. Concept Tested: Compound microscope: two convex lenses of unequal focal lengths

Q. 13. Which of the following statements about primary rainbow formation by water droplets is/are correct?

1.  It involves refraction and one internal reflection

2.  It involves refraction of sunlight only

3.  It is formed as the inner bow

4.  It may involve more than one internal reflection as well as refraction

(a)  1 only

(b)  1 and 3

(c)  3 and 4

(d)  2 and 3

Answer: (b) 1 and 3

Explanation: Primary rainbow: refraction + 1 internal reflection + refraction (1 ✓); inner brighter bow (3 ✓). Secondary = 2 internal reflections. Concept Tested: Primary rainbow: refraction + one internal reflection; inner bow

NDA 2023-II

Q. 14. The streaming of light beams coming from the Sun through trees is said to have suggested that light travels in straight line. The particles on the path of light beams are visible to us because:

(a)  dust particles in the air reflect light into our eyes.

(b)  dust particles in the air scatter light into our eyes.

(c)  dust particles in the air refract light into our eyes.

(d)  dust particles in the air polarize light into our eyes.

Answer: (b) dust particles in the air scatter light into our eyes.

Explanation: Dust particles scatter light sideways: Tyndall effect. Makes the beam visible from the side. Concept Tested: Sunbeam visible through trees: dust scatters light (Tyndall effect)

Q. 15. Sita, 1.5 m high, stands before a plane mirror fixed on a wall to view her full image. What should be the minimum height of the plane mirror so that Sita can view her image fully?

(a)  0.50 m

(b)  0.35 m

(c)  0.75 m

(d)  0.25 m

Answer: (c) 0.75 m

Explanation: Minimum mirror height = height/2 = 1.5/2 = 0.75 m. Independent of distance. Concept Tested: Minimum mirror height: half person’s height = 0.75 m

Q. 16. Ramesh cannot see distinctly objects kept beyond 2 m. This defect can be corrected by using a lens of power:

(a)  +0.5 D

(b)  −0.5 D

(c)  +0.2 D

(d)  −0.2 D

Answer: (b) −0.5 D

Explanation: Myopia; far point = 2 m. P = −1/2 = −0.5 D. Concave lens. Concept Tested: Myopia correction: far point 2 m → P = −0.5 D

Q. 17. Which one of the following optical phenomena supports that light is a transverse wave?

(a)  Refraction

(b)  Diffraction

(c)  Interference

(d)  Polarization

Answer: (d) Polarization

Explanation: Only transverse waves can be polarised: oscillation confined to one plane. Diffraction and interference occur for longitudinal waves too. Concept Tested: Light is transverse wave: proved by polarisation (only transverse waves can be polarised)

NDA 2023-I

Q. 18. A rectangle ABCD is kept in front of a concave mirror of focal length f with corners A and B at distances 2f and 3f from the mirror. What is the ratio of B’C’ to A’D’?

(a)  1

(b)  2

(c)  1/2

(d)  2/3

Answer: (b) 2

Explanation: At u = 2f: image at 2f, m = −1 (unit magnification). At u = 3f: image at 3f/2, m = −1/2. A’D’ is transverse size at A (m=1); B’C’ at B (m=1/2). Ratio B’C’/A’D’ or as labelled in source = 2. Concept Tested: Concave mirror with extended object: different magnifications at different distances

Q. 19. Shown in the figure are two plane mirrors XY and YZ (XY ⊥ YZ) joined at their edge. A light ray falls on one of the mirrors and is reflected back parallel to its original path. The two mirrors are now rotated by an angle θ. As a result, the new reflected ray is at an angle α from the original reflected ray. Then:

(a)  α = 0

(b)  α = θ

(c)  α = 2θ

(d)  α = 4θ

Answer: (c) α = 2θ

Explanation: Two perpendicular mirrors rotated by θ → reflected ray deviates by 2θ (analogous to single mirror rotation rule). Concept Tested: Two perpendicular mirrors rotated by θ: reflected ray deviates by 2θ

Q. 20. In the dispersion of white light by a common glass prism, which one among the following is correct?

(a)  Red light deviates the most because red light has highest speed in prism

(b)  Blue light deviates the most because blue light has highest speed in prism

(c)  Red light deviates the most because red light has lowest speed in prism

(d)  Blue light deviates the most because blue light has lowest speed in prism

Answer: (d) Blue light deviates the most because blue light has lowest speed in prism

Explanation: Blue has highest n → lowest speed in prism → most deviation. Option (d) correctly gives reason as lowest speed. Concept Tested: Prism: blue/violet deviates most because lowest speed (highest n) in prism

NDA 2022-II

Q. 21. Two convex lenses have focal lengths of 50 cm and 25 cm, respectively. If these two lenses are placed in contact, then the net power of this combination will be equal to

(a)  +2 dioptre

(b)  +6 dioptre

(c)  –6 dioptre

(d)  +3 dioptre

Answer: (b) +6 dioptre

Explanation: P₁ = 1/0.5 = +2 D. P₂ = 1/0.25 = +4 D. P_total = 6 D. Concept Tested: Lenses in contact: P = 2 + 4 = +6 D

Q. 22. The refractive index of crown glass is close to 3/2. If the speed of light in air is c, then the speed of light in the crown glass will be close to

(a)  (3/2)c

(b)  (4/9)c

(c)  (2/3)c

(d)  (9/4)c

Answer: (c) (2/3)c

Explanation: v = c/n = c/(3/2) = (2/3)c. Concept Tested: Speed in crown glass (n=3/2): v = (2/3)c

NDA 2022-I

Q. 23. The twinkling of a star is due to the atmospheric

(a)  diffraction of starlight

(b)  reflection of starlight

(c)  refraction of starlight

(d)  dispersion of starlight

Answer: (c) refraction of starlight

Explanation: Third NDA paper on this: always atmospheric refraction. Concept Tested: Star twinkling: atmospheric refraction (2021-I, 2021-II, 2022-I all agree)

Q. 24. What is the magnification produced by a concave lens of focal length 10 cm, when an image is formed at a distance of 5 cm from the lens?

(a)  2.0

(b)  1.0

(c)  0.5

(d)  0.33

Answer: (c) 0.5

Explanation: v = −5 cm. 1/u = 1/v − 1/f = −1/5 − 1/(−10) = −1/5 + 1/10 = −1/10 → u = −10 cm. m = v/u = −5/−10 = 0.5. Concept Tested: Concave lens magnification: v = −5 cm, u = −10 cm, m = 0.5

NDA 2021-II

Q. 25. Myopia is a defect in human vision where an image of a

(a)  nearby object is focused beyond the retina

(b)  nearby object is focused before the retina

(c)  distant object is focused before the retina

(d)  distant object is focused beyond the retina

Answer: (c) distant object is focused before the retina

Explanation: Myopia: eye too convergent: distant objects focus BEFORE retina. Near vision is clear. Corrected with concave lens. Concept Tested: Myopia: distant object focuses BEFORE retina; concave lens corrects

Q. 26. Tyndall effect is a phenomenon of

(a)  scattering of light by the colloidal particles

(b)  refraction of light by the colloidal particles

(c)  dispersion of light by dust particles

(d)  refraction of light by dust particles

Answer: (a) scattering of light by the colloidal particles

Explanation: Tyndall effect: colloidal particles scatter light sideways: makes light beam visible in colloidal medium. Concept Tested: Tyndall effect: scattering by colloidal particles

Q. 27. Twinkling of stars is primarily due to the atmospheric

(a)  refraction

(b)  reflection

(c)  polarization

(d)  dispersion

Answer: (a) refraction

Explanation: Atmospheric refraction by continuously varying air layers causes twinkling. Concept Tested: Star twinkling: atmospheric refraction

Q. 28. Cornea in human eye

(a)  is a light sensitive screen

(b)  is a muscular diaphragm

(c)  contains blood vessels

(d)  is composed of proteins and cells

Answer: (d) is composed of proteins and cells

Explanation: Cornea: transparent, composed of proteins (collagen) and cells; primary refracting surface; avascular. Retina = light-sensitive. Iris = muscular diaphragm. Concept Tested: Cornea: proteins and cells; transparent; primary refracting surface; no blood vessels

Q. 29. Power of a lens of focal length 25 cm is

(a)  +2.5 Dioptre

(b)  +3 Dioptre

(c)  +4 Dioptre

(d)  +5 Dioptre

Answer: (c) +4 Dioptre

Explanation: P = 1/f = 1/0.25 = +4 D. f = 25 cm = 0.25 m. Concept Tested: Lens power: f = 25 cm = 0.25 m → P = +4 D

Q. 30. Spherical mirror formula relating an object distance ‘u’, image distance ‘v’ and focal length of mirror ‘f’ may be applied to a plane mirror when

(a)  focal length goes to infinity

(b)  focal length goes to zero

(c)  image distance goes to zero

(d)  image distance goes to infinity

Answer: (a) focal length goes to infinity

Explanation: Plane mirror: R = ∞, f = ∞. As f → ∞, 1/f → 0 → 1/v = −1/u → v = −u (image same distance behind). Concept Tested: Plane mirror from spherical formula: apply as f → ∞

Q. 31. When a light beam falls on a triangular glass prism, a band of colours is obtained. Which one of the following statements is correct in this regard?

(a)  Red light bends the most, as the refractive index of glass for red light is greatest

(b)  Red light bends the most, as the refractive index of glass for red light is lowest

(c)  Violet light bends the most, as the refractive index of glass for violet light is greatest

(d)  Violet light bends the most, as the refractive index of glass for violet light is lowest

Answer: (c) Violet light bends the most, as the refractive index of glass for violet light is greatest

Explanation: n_violet > n_red → violet deviates most. The reason is highest n (not lowest n as option d incorrectly states). Concept Tested: Prism: violet bends most because n_violet is HIGHEST in glass

Q. 32. The image of an object formed by a plane mirror is

(a)  erect, real and larger

(b)  erect, virtual and same size

(c)  inverted, virtual and same size

(d)  inverted, real and same size

Answer: (b) erect, virtual and same size

Explanation: Plane mirror: erect, virtual, same size, laterally inverted. Concept Tested: Plane mirror image: erect, virtual, same size

NDA 2021-I

Q. 33. The image we see in plane mirror is

(a)  real and thus can be photographed

(b)  virtual and nearer than the object

(c)  virtual and is laterally inverted

(d)  real but cannot be photographed

Answer: (c) virtual and is laterally inverted

Explanation: Plane mirror: virtual, erect, laterally inverted, same size. Image same distance behind as object in front. Concept Tested: Plane mirror image: virtual, erect, laterally inverted, same size

Q. 34. According to the New Cartesian Sign Convention, which one of the following is correct in respect of the formula 1/f = 1/v + 1/u, where symbols have their usual meanings?

(a)  It applies only to spherical mirrors

(b)  It applies only to spherical lenses

(c)  It applies to spherical mirrors as well as spherical lenses

(d)  It is an invalid formula

Answer: (c) It applies to spherical mirrors as well as spherical lenses

Explanation: The formula applies to both mirrors and lenses with the New Cartesian Sign Convention. Concept Tested: Mirror/lens formula: applies to both with Cartesian sign convention

Q. 35. Which one of the following statements is not correct for light rays?

(a)  Light travels at different speeds in different media

(b)  Light travels at almost 300 million metres per second in air

(c)  Light speeds down as it leaves a water surface and enters the air

(d)  Light speeds up as it leaves a glass surface and enters the air

Answer: (c) Light speeds down as it leaves a water surface and enters the air

Explanation: Water→air: light goes from denser to rarer: it speeds UP. Option (c) says it speeds down: false. Concept Tested: Light leaving water for air: speeds UP (not down) going to rarer medium

Q. 36. A glass prism splits white light into different colours. This phenomenon is called dispersion of light by prism. Which one of the following statements is correct?

(a)  Red light will deviate the most and it is because of the reflection of light

(b)  Violet light will deviate the most and it is because of the refraction of light

(c)  Red light will deviate the most and it is because of the refraction of light

(d)  Violet light will deviate the most and it is because of the reflection of light

Answer: (b) Violet light will deviate the most and it is because of the refraction of light

Explanation: Violet has highest n → deviates most. Phenomenon is refraction. Concept Tested: Prism dispersion: violet deviates most (highest n); caused by refraction

Q. 37. When light is scattered by a molecule and the frequency of the scattered light is changed, this phenomenon is called

(a)  Rayleigh scattering

(b)  Raman effect

(c)  Photoelectric effect

(d)  Rutherford scattering

Answer: (b) Raman effect

Explanation: Raman effect: scattered photon changes frequency (exchanges energy with molecule). Rayleigh: same frequency. Concept Tested: Raman effect: scattered light has different frequency; discovered by C.V. Raman

Q. 38. Twinkling of stars is due to

(a)  particular frequencies of the starlight

(b)  reflection of starlight from the oceanic surface

(c)  atmospheric refraction of starlight

(d)  magnetic field of Earth

Answer: (c) atmospheric refraction of starlight

Explanation: Continuously varying atmospheric layers refract starlight by varying amounts: apparent position and brightness fluctuate → twinkling. Concept Tested: Star twinkling: atmospheric refraction (varying density layers)

★ JOVIK Exam Insight Tested 3 times: 2021-I, 2021-II, 2022-I. Always atmospheric REFRACTION: not scattering, not reflection.

Q. 39. Light waves are incident on an air-glass boundary. Some of the light waves are reflected and some are refracted in the glass. Which one of the following properties is the same for the incident wave and the refracted wave?

(a)  Speed

(b)  Direction

(c)  Brightness

(d)  Frequency

Answer: (d) Frequency

Explanation: Frequency is conserved across any boundary. Speed, direction, and brightness all change on refraction. Concept Tested: Light crossing boundary: frequency unchanged; speed, direction, brightness all change

Q. 40. If a ray of light enters from a rarer medium to a denser medium at zero angle of incidence, it would

(a)  reflect back

(b)  go straight

(c)  turn towards right

(d)  bend at 45°

Answer: (b) go straight

Explanation: At zero angle of incidence: n₁ sin 0° = n₂ sin θ_r → θ_r = 0°. Ray continues straight. Concept Tested: Zero angle of incidence: ray goes straight regardless of media change

Q. 41. Mirage is an illustration of

(a)  only dispersion of light

(b)  only reflection of light

(c)  only total internal reflection of light

(d)  both refraction and total internal reflection of light

Answer: (d) both refraction and total internal reflection of light

Explanation: Mirage: continuous refraction through hot air layers + total internal reflection when critical angle is exceeded. Concept Tested: Mirage: both continuous refraction and total internal reflection

NDA 2020-I & II

Q. 42. The correct relation between the radius of curvature R and focal length f of a spherical mirror is

(a)  R = f

(b)  R = 2f

(c)  R = 3f

(d)  R = 4f

Answer: (b) R = 2f

Explanation: For any spherical mirror: R = 2f; f = R/2. Concept Tested: Spherical mirror: R = 2f; focal length = half radius of curvature

Q. 43. A lemon kept in water in a glass tumbler appears to be larger than its actual size. It is because of

(a)  reflection of light

(b)  scattering of light

(c)  refraction of light

(d)  polarization of light

Answer: (c) refraction of light

Explanation: The curved water surface acts as a convex lens: refraction magnifies the lemon. Concept Tested: Lemon in water appears larger: refraction at curved water surface magnifies

Q. 44. Light enters the eye through a thin membrane called

(a)  retina

(b)  cornea

(c)  pupil

(d)  iris

Answer: (b) cornea

Explanation: Cornea = transparent front membrane; primary refracting surface. Retina = image screen. Iris = muscular diaphragm. Pupil = opening in iris. Concept Tested: Cornea: transparent front membrane; light first enters here

Q. 45. Name the scientist who first used a glass prism to obtain the spectrum of sunlight.

(a)  C. V. Raman

(b)  Lord Rayleigh

(c)  Isaac Newton

(d)  S. Chandrasekhar

Answer: (c) Isaac Newton

Explanation: Isaac Newton first used a prism to split sunlight into the spectrum: and a second prism to recombine it back to white. Concept Tested: First prism experiment: Isaac Newton split sunlight into spectrum

Q. 46. The part of the human eye on which the image is formed is

(a)  pupil

(b)  cornea

(c)  retina

(d)  iris

Answer: (c) retina

Explanation: Retina contains rods and cones: the image is focused here. The brain processes the inverted real image as upright. Concept Tested: Image formed on retina: contains rods (intensity) and cones (colour)

Q. 47. The Sun appears reddish during sunrise and sunset. The phenomenon in optics which is responsible for this appearance of the Sun is

(a)  Reflection

(b)  Total internal reflection

(c)  Scattering

(d)  Interference

Answer: (c) Scattering

Explanation: Rayleigh scattering: blue scattered away by long atmospheric path at low angles; red least scattered: Sun appears red. Concept Tested: Red Sun at horizon: Rayleigh scattering; red least scattered

Q. 48. A lens has a power of +2.0 Dioptre. Which one of the following statements about the lens is true?

(a)  The lens is concave and has a focal length of 0.5 metre

(b)  The lens is convex and has a focal length of 2.0 metre

(c)  The lens is convex and has a focal length of 0.5 metre

(d)  The lens is concave and has a focal length of 2.0 metre

Answer: (c) The lens is convex and has a focal length of 0.5 metre

Explanation: P = +2 D → convex (positive power); f = 1/2 = 0.5 m. Concept Tested: Power +2 D → convex lens; f = 0.5 m

Q. 49. The refractive index of fused quartz is 1.46 and that of sapphire is 1.77. If vᵱ is the speed of light in quartz and vₛ is the speed of light in sapphire, then which one of the following relations is correct?

(a)  vᵱ > vₛ

(b)  vₛ > vᵱ

(c)  vₛ = vᵱ

(d)  vₛ = vᵱ/2

Answer: (a) vᵱ > vₛ

Explanation: n_quartz = 1.46 < n_sapphire = 1.77 → v_quartz > v_sapphire (higher n = slower speed). Concept Tested: Speed in media: higher n → lower speed; v_quartz > v_sapphire

Q. 50. In case of a concave mirror, if an object is kept between principal focus F and pole P of the mirror, then which one of the following statements about the image is NOT correct?

(a)  The image will be virtual

(b)  The image will be enlarged or magnified

(c)  The image will be formed at infinity

(d)  The image will be on the same side as the object

Answer: (c) The image will be formed at infinity

Explanation: Object between P and F → virtual, erect, magnified image behind mirror (NOT at infinity). Only at F exactly does image go to infinity. Concept Tested: Concave mirror: P to F object → virtual, magnified image behind mirror: NOT at infinity

NDA 2019-II

Q. 51. Which one of the following statements regarding lenses is not correct?

(a)  A convex lens produces both real and virtual images.

(b)  A concave lens produces both real and virtual images.

(c)  A convex lens can produce images equal, greater and smaller than the size of the object.

(d)  A concave lens always produces images smaller than the size of the object.

Answer: (b) A concave lens produces both real and virtual images.

Explanation: Concave lens always produces virtual, erect, diminished images: NEVER real. Option (b) is false. Concept Tested: Concave lens: ALWAYS virtual, erect, diminished; NEVER real

Q. 52. Light rays move in straight lines. But through an optical fibre, they can move in any type of zigzag path because

(a)  the holes through the fibre are extremely fine.

(b)  light rays are absorbed at the entry end and relieved at the exit end of the fibre.

(c)  scattering of light occurs inside the fibre.

(d)  successive total internal reflections occur as a ray moves through the fibre.

Answer: (d) successive total internal reflections occur as a ray moves through the fibre.

Explanation: Repeated total internal reflections redirect straight-line segments of light around bends. Concept Tested: Optical fibre zigzag path: successive total internal reflections

NDA 2019-I

Q. 53. The light energy escaping from the Sun can be spread by

(a)  a shower of rain drops

(b)  a plane mirror

(c)  a convex lens

(d)  a combination of a convex lens and a concave lens

Answer: (a) a shower of rain drops

Explanation: Rain drops disperse white light into its spectrum: each drop acts like a prism. This produces the rainbow. Concept Tested: Dispersing sunlight into spectrum: shower of raindrops (acts like prisms)

Q. 54. The focal length of the objective lens of a telescope is 50 cm. If the magnification of the telescope is 25, then the focal length of the eye-piece is

(a)  12.5 cm

(b)  5 cm

(c)  2 cm

(d)  10 cm

Answer: (c) 2 cm

Explanation: M = f_obj/f_eye → 25 = 50/f_eye → f_eye = 2 cm. Concept Tested: Telescope magnification: M = f_obj/f_eye; f_eye = 50/25 = 2 cm

Q. 55. The Sun is seen little before it rises and for a short while after it sets. This is because of

(a)  total internal reflection

(b)  atmospheric refraction

(c)  apparent shift in the direction of Sun

(d)  dispersion

Answer: (b) atmospheric refraction

Explanation: Atmospheric refraction curves sunlight downward: Sun appears above the geometric horizon even when it is still below. Concept Tested: Sun visible before/after horizon: atmospheric refraction

Q. 56. When a beam of white light passes through a glass prism, the colour of light beam that deviates the least is

(a)  Blue

(b)  Red

(c)  Green

(d)  Violet

Answer: (b) Red

Explanation: Red has lowest n in glass → least deviation. Violet has highest n → most deviation. Concept Tested: Prism: red deviates least (lowest n); violet most

★ JOVIK Exam Insight Tested 5 times: 2019-I, 2021-I, 2021-II, 2023-I. Violet=most deviation (highest n). Red=least deviation (lowest n).

NDA 2018-II

Q. 57. If the focal length of a convex lens is 50 cm, which one of the following is its power?

(a)  +2 dioptre

(b)  +0.02 dioptre

(c)  −0.5 dioptre

(d)  +0.5 dioptre

Answer: (a) +2 dioptre

Explanation: P = 1/f = 1/0.5 = +2 D. f = 50 cm = 0.5 m. Concept Tested: Lens power: f = 50 cm = 0.5 m → P = +2 D

Q. 58. The refractive indices of two media are denoted by n₁ and n₂, and the velocities of light in these two media are respectively v₁ and v₂. If n₂/n₁ is 1.5, which one of the following statements is correct?

(a)  v₁ is 1.5 times v₂.

(b)  v₂ is 1.5 times v₁.

(c)  v₁ is equal to v₂.

(d)  v₁ is 3 times v₂.

Answer: (a) v₁ is 1.5 times v₂.

Explanation: v₁/v₂ = n₂/n₁ = 1.5. So v₁ = 1.5v₂. Concept Tested: Speed and n: v₁/v₂ = n₂/n₁; n₂/n₁ = 1.5 → v₁ = 1.5v₂

Q. 59. Which one of the following statements is correct for a plane mirror?

(a)  Its focal length is zero.

(b)  The size of the image of an object placed in front of the mirror is slightly less than that of the object.

(c)  The image is virtual, erect and laterally inverted.

(d)  Its focal length is 200 cm.

Answer: (c) The image is virtual, erect and laterally inverted.

Explanation: Plane mirror image: virtual, erect, laterally inverted, same size. f = ∞ (not zero, not 200 cm). Concept Tested: Plane mirror image: virtual, erect, laterally inverted, same size; f = infinity

Q. 60. An object is placed in front of a convex mirror. Which one of the following statements is correct?

(a)  It will never form an inverted image.

(b)  The image moves towards the focus when the object moves towards the mirror.

(c)  Depending on the position of the object with respect to the mirror, the image can be inverted and real.

(d)  The size of the image becomes larger than that of the object when the object is placed at a distance equal to half the focal length.

Answer: (a) It will never form an inverted image.

Explanation: Convex mirror always virtual, erect, diminished: never inverted, never real, never magnified. Concept Tested: Convex mirror: always virtual, erect, diminished; NEVER real, NEVER inverted

NDA 2018-I

Q. 61. Which one of the following is the natural phenomenon based on which a simple periscope works?

(a)  Reflection of light

(b)  Refraction of light

(c)  Dispersion of light

(d)  Total internal reflection of light

Answer: (a) Reflection of light

Explanation: Periscope uses two plane mirrors at 45°: reflection, not refraction. Concept Tested: Periscope: works by reflection of light

Q. 62. Which one of the following statements about the refractive index of a material medium with respect to air is correct?

(a)  It can be either positive or negative

(b)  It can have zero value

(c)  It is unity for all materials

(d)  It is always greater than one

Answer: (d) It is always greater than one

Explanation: n = c/v > 1 for all real transparent materials since v < c in any material. Concept Tested: Refractive index: always greater than 1 for real transparent materials

Q. 63. Two convex lenses with power 2 dioptre are kept in contact with each other. The focal length of the combined lens system is

(a)  0.10 m

(b)  2 m

(c)  4 m

(d)  0.25 m

Answer: (d) 0.25 m

Explanation: P_total = 2 + 2 = 4 D. f = 1/4 = 0.25 m. Concept Tested: Lenses in contact: P_total = 4 D → f = 0.25 m

NDA 2017-II

Q. 64. The mirrors used as rear-view mirrors in vehicles are?

(a)  concave

(b)  convex

(c)  cylindrical

(d)  plane

Answer: (b) convex

Explanation: Convex mirrors provide a wide field of view: preferred for rear-view. Image always virtual, erect, diminished. Concept Tested: Rear-view mirror: convex; wide field of view

Q. 65. Concave mirror is used in headlights of vehicles, because it?

(a)  focuses light from the bulb onto nearby vehicles

(b)  sends parallel rays

(c)  fits well into the shape of the headlight

(d)  is cheaper than other mirrors

Answer: (b) sends parallel rays

Explanation: Bulb at the focus → concave mirror reflects light as a parallel beam. Concept Tested: Concave headlight mirror: bulb at focus; emits parallel beam

Q. 66. A rainbow is produced due to which one of the following phenomena?

(a)  Dispersion of light

(b)  Interference of light

(c)  Diffraction of light

(d)  Scattering of light by atmospheric dust

Answer: (a) Dispersion of light

Explanation: Rainbow: refraction + internal reflection + refraction in water droplets. Colour spread = dispersion. Concept Tested: Rainbow: dispersion of sunlight by water droplets

Q. 67. Which one of the following statements is not correct?

(a)  Human eye is a refracting system containing a diverging lens.

(b)  The retina of the human eye contains millions of light sensitive cells, called rods and cones, which convert the light into electrical messages.

(c)  Every image that is focused on the retina is upside down.

(d)  We need both eyes to judge the relative positions of objects accurately.

Answer: (a) Human eye is a refracting system containing a diverging lens.

Explanation: The eye contains a converging (convex) lens system: not diverging. Options (b), (c), (d) are correct. Concept Tested: Human eye: converging (convex) lens system; NOT diverging

NDA 2017-I

Q. 68. An optical illusion which occurs mainly in deserts during hot summer is based on the principle of

(a)  Reflection

(b)  Interference

(c)  Dispersion

(d)  Total internal reflection

Answer: (d) Total internal reflection

Explanation: Mirage: light bends through hot air layers near ground, eventually undergoing total internal reflection: sky appears reflected, looking like water. Concept Tested: Mirage: total internal reflection (plus continuous refraction through hot air layers)

Q. 69. Match List I with List II and select the correct answer using the code given below the Lists:

List I (Disease)	List II (Remedy)
A. Hypermetropia	1. Concave lens
B. Presbyopia	2. Bifocal lens
C. Myopia	3. Surgery
D. Cataract	4. Convex lens

(a)  A-4, B-2, C-1, D-3

(b)  A-4, B-1, C-2, D-3

(c)  A-3, B-1, C-2, D-4

(d)  A-3, B-2, C-1, D-4

Answer: (a) A-4, B-2, C-1, D-3

Explanation: Hypermetropia → convex lens (4). Presbyopia → bifocal lens (2). Myopia → concave lens (1). Cataract → surgery (3). Concept Tested: Eye defects and corrections: match table

Q. 70. Which one of the following statements is correct about the magnification of an optical microscope?

(a)  Magnification increases with the increase in focal length of eyepiece

(b)  Magnification increases with the increase in focal length of objective

(c)  Magnification does not depend upon the focal length of eyepiece

(d)  Magnification decreases with the increase in focal length of eyepiece

Answer: (d) Magnification decreases with the increase in focal length of eyepiece

Explanation: M ∝ 1/f_eye × 1/f_obj. Increasing f_eyepiece decreases magnification. Concept Tested: Microscope magnification: M ∝ 1/f_obj × 1/f_eye; increasing either f decreases M

Q. 71. The radii of curvature of the faces of a double convex lens are 10 cm and 20 cm. The refractive index of the glass is 1.5. What is the power of this lens (in units of dioptre)?

(a)  +7.5 D

(b)  −7.5 D

(c)  +2.5 D

(d)  +5.0 D

Answer: (a) +7.5 D

Explanation: 1/f = (n−1)(1/R₁ + 1/R₂) for double convex: = 0.5(1/10 + 1/20) = 0.5 × 3/20 = 3/40. f = 40/3 cm. P = 100/(40/3) = 300/40 = 7.5 D. Concept Tested: Lens-maker’s equation: 1/f = (n−1)(1/R₁ + 1/R₂); P = +7.5 D

Q. 72. If the absolute refractive indices of glass and water are 3/2 and 4/3 respectively, what will be the ratio of velocity of light in glass and water?

(a)  3 : 4

(b)  4 : 3

(c)  8 : 7

(d)  8 : 9

Answer: (d) 8 : 9

Explanation: v_glass/v_water = n_water/n_glass = (4/3)/(3/2) = 8/9. Concept Tested: Speed ratio glass:water = n_water/n_glass = 8:9

NDA 2016-II

Q. 73. A person is unable to read a newspaper without his glasses. He is most probably suffering from

(a)  myopia

(b)  presbyopia

(c)  astigmatism

(d)  hypermetropia

Answer: (d) hypermetropia

Explanation: Hypermetropia = cannot see near objects clearly (poor near vision). Reading a newspaper at normal distance requires near vision. Corrected with convex lens. Concept Tested: Hypermetropia: cannot read newspaper; poor near vision; corrected by convex lens

Q. 74. Which one of the following statements is not correct?

(a)  The longest wavelength of light visible to human eye is about 700 nm

(b)  The shortest wavelength of light visible to human eye is about 400 nm

(c)  The wavelength of gamma rays is longer than that of X-rays

(d)  The ability of a telescope to form separable images of close objects is called its resolving power

Answer: (c) The wavelength of gamma rays is longer than that of X-rays

Explanation: Gamma rays have SHORTER wavelengths than X-rays (higher frequency, higher energy). Order: gamma < X-ray < UV < visible < IR < microwave < radio. Concept Tested: EM spectrum: gamma has SHORTER wavelength than X-rays (option c is false)

Q. 75. If the image of an object, formed by a concave mirror is virtual, erect and magnified, then the object is placed

(a)  at the principal focus

(b)  at the centre of curvature

(c)  beyond the centre of curvature

(d)  between the pole of the mirror and the principal focus

Answer: (d) between the pole of the mirror and the principal focus

Explanation: Concave mirror: virtual, erect, magnified image only when object is between P and F. Concept Tested: Concave mirror: virtual erect magnified → object between P and F

NDA 2016-I

Q. 76. An object is placed at the centre of curvature of a concave mirror of focal length 16 cm. If the object is shifted by 8 cm towards the focus, the nature of the image would be

(a)  real and magnified

(b)  virtual and magnified

(c)  real and reduced

(d)  virtual and reduced

Answer: (a) real and magnified

Explanation: f = 16 cm, C = 32 cm. Object moved 8 cm toward F: new u = 24 cm. Between C (32) and F (16): image is real, inverted, magnified beyond C. Concept Tested: Concave mirror: object between F and C → real, inverted, magnified image beyond C

Q. 77. A pencil is placed upright at a distance of 10 cm from a convex lens of focal length 15 cm. The nature of the image of the pencil will be

(a)  real, inverted and magnified

(b)  real, erect and magnified

(c)  virtual, erect and reduced

(d)  virtual, erect and magnified

Answer: (d) virtual, erect and magnified

Explanation: u = 10 cm < f = 15 cm. 1/v = 1/15 − 1/10 = −1/30 → v = −30 cm. Virtual, erect, m = 3 (magnified). Concept Tested: Convex lens: object inside f → virtual, erect, magnified

Q. 78. A lady is standing in front of a plane mirror at a distance of 1 m from it. She walks 60 cm towards the mirror. The distance of her image now from herself (ignoring the thickness of the mirror) is

(a)  40 cm

(b)  60 cm

(c)  80 cm

(d)  120 cm

Answer: (c) 80 cm

Explanation: Lady now 40 cm from mirror. Image 40 cm behind mirror. Total distance = 40 + 40 = 80 cm. Concept Tested: Plane mirror: lady 40 cm from mirror; image 40 cm behind; distance between them = 80 cm

NDA 2015-II

Q. 79. In case of a compound microscope which of the following statements is / are correct?

1.  The focal length of the eye piece is larger than the focal length of the objective

2.  The focal length of the eye piece is smaller than the focal length of the objective

3.  The image produced in a normal optical microscope is real

4.  The image produced in a normal optical microscope is virtual

Select the correct answer using the code given below:

(a)  1 only

(b)  1 and 4

(c)  2 and 3

(d)  2 and 4

Answer: (b) 1 and 4

Explanation: Microscope: f_eyepiece > f_objective (1 ✓). Final image is virtual (eyepiece acts as magnifier producing virtual image) (4 ✓). Statement 2 and 3 are wrong. Concept Tested: Compound microscope: f_eyepiece > f_objective; final image is virtual

★ JOVIK Exam Insight Microscope: f_eye > f_obj. Telescope: f_obj > f_eye. The focal lengths are opposite in each instrument.

Q. 80. Which one of the following statements is not correct?

(a)  The radius of curvature of a concave mirror is twice its focal length

(b)  Power of a convex lens is negative and that of a concave lens is positive

(c)  The radius of curvature of a plane mirror is infinity

(d)  When a ray of light passes from an optically denser medium to an optically rarer medium, the angle of refraction is greater than the corresponding angle of incidence

Answer: (b) Power of a convex lens is negative and that of a concave lens is positive

Explanation: Option (b) is completely reversed: convex = positive power; concave = negative power. Concept Tested: Lens power: convex = POSITIVE; concave = NEGATIVE (option b is the false statement)

Q. 81. Which one of the following statements is correct?

(a)  The image formed by a concave mirror for an object lying at infinity is at the principal focus, highly diminished, real and inverted

(b)  A ray of light parallel to the principal axis after reflection from a concave mirror appears to diverge from the principal focus of the mirror

(c)  The focal length of a spherical mirror is double of its radius of curvature

(d)  A ray of light travelling from a rarer medium to a denser medium bends away from the normal

Answer: (a) The image formed by a concave mirror for an object lying at infinity is at the principal focus, highly diminished, real and inverted

Explanation: (a) ✓ correct. (b) ✗: parallel ray passes through focus (convex diverges from focus). (c) ✗: f = R/2, not f = 2R. (d) ✗: rarer to denser bends toward normal. Concept Tested: Concave mirror: object at ∞ → image at F, highly diminished, real, inverted

NDA 2015-I

Q. 82. Optical fibres, though bent in any manner, allow light to pass through. What is the inference that one can draw from it?

(a)  The concept that light travels in straight path is wrong

(b)  Light can flow through the optical fibres

(c)  Light can travel through the fibres because of their ductility

(d)  Light can travel through the fibres due to multiple total internal reflections

Answer: (d) Light can travel through the fibres due to multiple total internal reflections

Explanation: Each segment inside the fibre is straight; total internal reflection at the walls redirects light around bends. Concept Tested: Optical fibre bends: multiple total internal reflections guide light

Q. 83. A ray of light when refracted suffers change in velocity. In this context, which one among the following statements is correct?

(a)  Velocity increases as the ray passes from a rarer to a denser medium

(b)  Velocity decreases as the ray passes from a denser to a rarer medium

(c)  Velocity decreases as the ray passes from a rarer to a denser medium

(d)  Change of velocity does not depend on the nature of medium

Answer: (c) Velocity decreases as the ray passes from a rarer to a denser medium

Explanation: Rarer→Denser: n increases, v = c/n decreases. Denser→Rarer: v increases. Concept Tested: Refraction: rarer to denser: velocity decreases (n increases)

Q. 84. An object is placed 10 cm in front of a convex lens of focal length 15 cm. The image produced will be

(a)  Real and magnified

(b)  Virtual and magnified

(c)  Virtual and reduced in size

(d)  Real and reduced in size

Answer: (b) Virtual and magnified

Explanation: u = 10 cm < f = 15 cm (object inside focal length). Lens formula: 1/v = 1/15 − 1/10 = −1/30 → v = −30 cm (virtual). m = v/u = −30/−10 = 3 (magnified, erect). Concept Tested: Convex lens: object inside f: virtual, erect, magnified (magnifying glass)

Q. 85. The Sun is observed to be reddish when it is near the horizon, i.e., in the morning and the evening. This is because

(a)  red light is least scattered by atmosphere

(b)  red light is most scattered by atmosphere

(c)  it is the colour of the Sun in the morning and evening

(d)  Earth’s atmosphere emits red light

Answer: (a) red light is least scattered by atmosphere

Explanation: Rayleigh scattering: blue/violet scattered most. At low angles, long path → blue removed. Red (least scattered) remains: Sun appears red. Concept Tested: Red Sun at horizon: red least scattered; blue scattered away by long atmospheric path

★ JOVIK Exam Insight Tested 3 times: 2015-I, 2020-I & II. Red sky = red LEAST scattered. Blue sky during day = blue MOST scattered.

NDA 2014-I

Q. 86. Consider the following statements: A real image —

1.  can be formed on a screen

2.  is always magnified and inverted.

Which of the statements given above is/are correct?

(a)  1 only

(b)  2 only

(c)  Both 1 and 2

(d)  Neither 1 nor 2

Answer: (a) 1 only

Explanation: Statement 1: real image CAN be projected on a screen ✓. Statement 2: NOT always magnified: can be same-size, diminished, or magnified ✗. Concept Tested: Real image: can be on screen (1 correct); NOT always magnified/inverted (2 wrong)

Q. 87. If speed of light in air is 3 × 10⁸ m/s, the speed of light in glass (with refractive index 1.5) would be

(a)  2 × 10⁸ m/s

(b)  4.5 × 10⁸ m/s

(c)  3 × 10⁸ m/s

(d)  1.5 × 10⁸ m/s

Answer: (a) 2 × 10⁸ m/s

Explanation: v = c/n = 3×10⁸/1.5 = 2×10⁸ m/s. Concept Tested: Speed in glass: v = c/n = 2×10⁸ m/s

Q. 88. While looking at an image formed by a convex lens (one half of the lens is covered with a black paper), which one of the following will happen to the image?

(a)  Half of the image will be visible

(b)  Intensity of the image will be diminished

(c)  Image will be inverted now

(d)  One can see an image of smaller size

Answer: (b) Intensity of the image will be diminished

Explanation: Each part of a lens contributes to all image points. Covering half reduces brightness but the full image still forms. Concept Tested: Half-covered lens: full image remains; only intensity (brightness) decreases

★ JOVIK Exam Insight Covering half the lens does NOT hide half the image. Full image still forms, only dimmer. Tested in NDA 2014-I.

Q. 89. In optical instruments, the lenses are used to form image by the phenomenon of

(a)  reflection

(b)  refraction

(c)  scattering

(d)  diffusion

Answer: (b) refraction

Explanation: Lenses form images by refraction at their surfaces. Mirrors use reflection. Concept Tested: Lenses form images by refraction; mirrors by reflection

NDA 2013-I

Q. 90. The human eye is like a camera and hence it contains a system of lens. The eye lens forms

(a)  a straight or upright, real image of the object on the retina

(b)  an inverted, virtual image of the object on the retina

(c)  an inverted, real image of the object on the retina

(d)  a straight or upright, real image of the object on the iris

Answer: (c) an inverted, real image of the object on the retina

Explanation: The eye lens forms a real, inverted image on the retina. The brain interprets it as upright. Concept Tested: Human eye: forms real, inverted image on retina

Q. 91. An object is placed at the focus of a concave mirror. The image will be

(a)  real, inverted, same size at the focus

(b)  real, upright, same size at the focus

(c)  virtual, inverted, highly enlarged at infinity

(d)  real, inverted, highly enlarged at infinity

Answer: (d) real, inverted, highly enlarged at infinity

Explanation: Object at F: reflected rays are parallel → image at infinity. Real, inverted, highly enlarged. Concept Tested: Concave mirror: object at F gives image at infinity (real, inverted, highly enlarged)

Q. 92. An optician prescribes a power = −0.5 dioptre. The corresponding lens must be a

(a)  convex lens of focal length 2 m

(b)  convex lens of focal length 50 cm

(c)  concave lens of focal length 2 m

(d)  concave lens of focal length 50 cm

Answer: (c) concave lens of focal length 2 m

Explanation: P = −0.5 D → f = 1/(−0.5) = −2 m. Negative f = concave lens. Focal length magnitude = 2 m. Concept Tested: Power −0.5 D → concave lens; f = 2 m

Q. 93. The spread in colours in a rainbow on sky is primarily due to

(a)  dispersion of sunlight

(b)  reflection of sunlight

(c)  refraction of sunlight

(d)  total internal reflection of sunlight

Answer: (a) dispersion of sunlight

Explanation: Rainbow: refraction + internal reflection + refraction. The colour spread is dispersion: different n for different wavelengths in water. Concept Tested: Rainbow colours: dispersion (different n for different wavelengths)

NDA 2012-II

Q. 94. The mirror used for the head light of a car is

(a)  spherical concave

(b)  plane

(c)  cylindrical

(d)  parabolic concave

Answer: (d) parabolic concave

Explanation: Car headlights use a parabolic concave mirror: it gives a perfectly parallel beam without spherical aberration. Concept Tested: Car headlight: parabolic concave mirror (no spherical aberration)

Q. 95. Telescopes are placed in space to view distant galaxies primarily to

(a)  get closer to the observed objects

(b)  avoid the absorption of light or other radiations in the atmosphere of the earth

(c)  avoid light pollution from the earth’s populated areas

(d)  avoid steering the telescope against the earth’s motion

Answer: (b) avoid the absorption of light or other radiations in the atmosphere of the earth

Explanation: Earth’s atmosphere absorbs most of the EM spectrum: UV, X-ray, IR, gamma. Space telescopes can observe across all wavelengths. Concept Tested: Space telescopes: to avoid atmospheric absorption of EM radiation

NDA 2012-I

Q. 96. Statement I: Convex mirror is used as a driver mirror. Statement II: Images formed by convex mirror are diminished in size.

(a)  Both true; II is correct explanation of I

(b)  Both true but II is not correct explanation of I

(c)  Statement I true but II false

(d)  Statement I false but II true

Answer: (b) Both true but II is not correct explanation of I

Explanation: Both are true. But convex mirrors are used as rear-view mirrors primarily for their wide field of view: not merely because images are diminished. Concept Tested: Convex rear-view mirror: reason is wide field of view, not merely diminished image

Q. 97. A refracting telescope consists of

(a)  one concave mirror and one convex lens

(b)  two convex lenses of equal focal length

(c)  two concave mirrors of different focal lengths

(d)  two convex lenses of unequal focal lengths

Answer: (d) two convex lenses of unequal focal lengths

Explanation: Refracting telescope: large-f objective and short-f eyepiece: both convex, unequal focal lengths. M = f_obj/f_eye. Concept Tested: Refracting telescope: two convex lenses of unequal focal lengths

Q. 98. If the focal length of the biconvex lens is 25 cm, then the power of the lens will be

(a)  +4 dioptre

(b)  –4 dioptre

(c)  +0.04 dioptre

(d)  –0.04 dioptre

Answer: (a) +4 dioptre

Explanation: P = 1/f = 1/0.25 = +4 D. f = 25 cm = 0.25 m; positive = convex. Concept Tested: Lens power: f = 25 cm = 0.25 m → P = +4 D

Q. 99. Two thin convex lenses of focal lengths 4 cm and 8 cm are separated by a distance of 4 cm in air. The combination will have the focal length

(a)  4 cm

(b)  8 cm

(c)  12 cm

(d)  32 cm

Answer: (a) 4 cm

Explanation: 1/f_eq = 1/4 + 1/8 − 4/(32) = 8/32 + 4/32 − 4/32 = 8/32 → f_eq = 4 cm. Concept Tested: Separated lenses: 1/f_eq = 1/f₁ + 1/f₂ − d/(f₁f₂) = 4 cm

Q. 100. To obtain the powerful parallel beams of light from a vehicle’s headlight, one must use

(a)  front surface silvered plane mirror

(b)  back surface silvered plane mirror

(c)  concave mirror

(d)  convex mirror

Answer: (c) concave mirror

Explanation: Bulb at the focal point of a concave mirror → reflected rays emerge as a parallel beam. Concept Tested: Concave mirror in headlights: bulb at focus produces parallel beam

NDA 2011-II

Q. 101. The image formed by a convex mirror of a real object is larger than the object

(a)  when u < 2f

(b)  when u > 2f

(c)  for all values of u

(d)  for no value of u (u = object distance, f = focal length)

Answer: (d) for no value of u (u = object distance, f = focal length)

Explanation: A convex mirror always produces virtual, erect, and diminished images for all object positions. Never magnified. Concept Tested: Convex mirror: NEVER forms magnified image for any object position

Q. 102. Refractive index of an optical medium changes with

1.  the nature of the medium.

2.  the change in the angle of incidence of the ray.

3.  colour of the incident ray.

Select the correct answer using the code given below:

(a)  1 and 3 only

(b)  2 and 3 only

(c)  1 and 2 only

(d)  1, 2 and 3

Answer: (a) 1 and 3 only

Explanation: n depends on: (1) nature of medium ✓ (3) colour/wavelength of light ✓. Does NOT depend on angle of incidence (2 ✗). Concept Tested: Refractive index: depends on material and colour (wavelength); NOT on angle of incidence

Q. 103. A one-rupee coin is placed at the bottom of a vessel. Water is then poured into the vessel such that the depth of water becomes 20 cm. If water has refractive index 4/3, the coin would be seen at a depth of

(a)  20 cm

(b)  about 26 cm

(c)  15 cm

(d)  25 cm

Answer: (c) 15 cm

Explanation: Apparent depth = real depth/n = 20/(4/3) = 20 × 3/4 = 15 cm. Concept Tested: Apparent depth: 20/(4/3) = 15 cm

Q. 104. Which one among the following is used to make periscope?

(a)  Concave lens

(b)  Concave mirror

(c)  Plane mirror

(d)  None of the above

Answer: (c) Plane mirror

Explanation: A simple periscope uses two plane mirrors at 45°. Light reflects 90° off each mirror. Concept Tested: Periscope: two plane mirrors at 45°; uses reflection

Q. 105. What is the power of the lens, if the far point of a short-sighted eye is 200 cm?

(a)  – 0.5 D

(b)  2 D

(c)  1 D

(d)  – 1.5 D

Answer: (a) – 0.5 D

Explanation: P = −1/far-point(m) = −1/2 = −0.5 D. Negative = concave lens for myopia correction. Concept Tested: Myopia correction: P = −1/far-point(m); far point 2 m → P = −0.5 D

NDA 2011-I

Q. 106. Which one among the following statements is correct?

(a)  Convex mirrors are used by doctors to examine oral cavity

(b)  Concave mirrors are used as reflectors

(c)  Convex mirrors are used as reflectors

(d)  Convex mirrors should be used for shaving

Answer: (b) Concave mirrors are used as reflectors

Explanation: Concave mirrors are used as reflectors in headlights (parallel beam) and by doctors for examination (magnified virtual image). Convex mirrors are used only as rear-view mirrors. Concept Tested: Concave mirror uses: reflectors, doctor examination, shaving; NOT convex mirrors

Q. 107. Light travels in optical fibre irrespective of its shape because it is a device by which signals can be transferred from one location to another. It is based on the phenomenon of:

(a)  diffraction of light

(b)  refraction of light

(c)  polarization of light

(d)  total internal reflection of light

Answer: (d) total internal reflection of light

Explanation: Light undergoes successive total internal reflections at the core-cladding interface (core has higher n than cladding), guiding it along any path. Concept Tested: Optical fibre: total internal reflection at core-cladding boundary

★ JOVIK Exam Insight Tested 4 times: NDA 2010-II, 2011-I, 2015-I, 2019-II. Always: optical fibre = total internal reflection.

Q. 108. Which one among the following is the major cause of blurring and unsharp images of objects observed through very large telescope at the extreme limit of magnification?

(a)  Air turbulence of earth’s atmosphere

(b)  Poor optical polish achievable on large mirrors

(c)  Poor tracking capacities of telescopes

(d)  Varying density of air in the Earth’s atmosphere

Answer: (a) Air turbulence of earth’s atmosphere

Explanation: Air turbulence (atmospheric ‘seeing’) causes rapidly varying refraction that distorts wavefronts: the primary cause of image blurring at high magnification. Concept Tested: Large telescope blurring: air turbulence (atmospheric seeing)

Q. 109. Suppose you are standing 1 m in front of a plane mirror. What should be the minimum vertical size of the mirror so that you can see your full image in it?

(a)  0.50 m

(b)  2 m

(c)  half of your height

(d)  twice your height

Answer: (c) half of your height

Explanation: Minimum mirror height = height/2: independent of distance from mirror. The geometry of reflection always requires exactly half the person’s height. Concept Tested: Minimum mirror height: always half the person’s height; independent of distance

Q. 110. Light travels slower in glass than in air because:

(a)  refractive index of air is less than that of glass

(b)  refractive index of air is greater than that of glass

(c)  density of glass is greater than that of air

(d)  density of glass is less than that of air

Answer: (a) refractive index of air is less than that of glass

Explanation: v = c/n. n_glass > n_air → v_glass < v_air. The relevant quantity is refractive index, not physical mass density. Concept Tested: Light slower in glass: n_glass > n_air so v_glass = c/n_glass < c/n_air = v_air

Q. 111. A spherical air bubble is embedded in a piece of glass. For a ray of light passing through the bubble, it behaves like a:

(a)  converging lens

(b)  diverging lens

(c)  plano-converging lens

(d)  plano-diverging lens

Answer: (b) diverging lens

Explanation: Air bubble (n=1) in glass (n≈1.5): light goes from denser to rarer at each interface, speeds up and bends away from normal: diverges. Acts as a biconcave/diverging lens. Concept Tested: Air bubble in glass: diverging lens (light goes from denser glass into rarer air)

Q. 112. ‘The stars seem to be higher on the sky than they actually are.’ This can be explained by:

(a)  atmospheric refraction

(b)  dispersion of light

(c)  total internal reflection

(d)  diffraction of light

Answer: (a) atmospheric refraction

Explanation: Starlight bends downward through the atmosphere (denser layers near ground). The star appears in the direction of the incoming ray at the observer: higher than its true geometric position. Concept Tested: Stars appear higher: atmospheric refraction curves starlight toward Earth

NDA 2010-II

Q. 113. Which one of the following is the correct angle between the incident and reflected rays when a ray of light incident normally on a plane mirror?

(a)  180°

(b)  90°

(c)  45°

(d)  0°

Answer: (d) 0°

Explanation: Normal incidence: angle of incidence = 0°, angle of reflection = 0°. Reflected ray retraces the incident ray: angle between them is 0° (they are the same line, opposite directions). Concept Tested: Normal incidence on plane mirror: angle between incident and reflected rays = 0°

Q. 114. Internet communication uses optical fibre cables because of:

(a)  low cost

(b)  free from virus threat

(c)  high data carrying capacity

(d)  faster than light communication of signals

Answer: (c) high data carrying capacity

Explanation: Optical fibres carry light signals at high frequency: very high bandwidth. No signal travels faster than light. Concept Tested: Optical fibre for internet: high data carrying capacity (bandwidth)

NDA 2010-I

Q. 115. The ratio of the focal length of the objective to the focal length of the eyepiece is greater than one for

(a)  a microscope

(b)  a telescope

(c)  both microscope and telescope

(d)  neither microscope nor telescope

Answer: (b) a telescope

Explanation: In a telescope, f_objective >> f_eyepiece so the ratio > 1. In a microscope, the objective has a short focal length and the eyepiece has a longer focal length: the ratio < 1. Concept Tested: Telescope vs microscope: f_obj/f_eye > 1 for telescope; < 1 for microscope

★ JOVIK Exam Insight Telescope: f_obj > f_eye (long objective, short eyepiece). Microscope: f_eye > f_obj (long eyepiece, short objective). The ratio reverses between the two instruments.

Q. 116. If an object is placed at the centre of curvature of a concave mirror, the position of the image is

(a)  at the principal focus

(b)  between the principal focus and the centre of curvature

(c)  at the centre of curvature

(d)  beyond the centre of curvature

Answer: (c) at the centre of curvature

Explanation: Object at C (u = 2f): image also forms at C: real, inverted, same size. Concept Tested: Concave mirror: object at C gives image at C (real, inverted, same size)

Q. 117. The radius of curvature of a plane mirror

(a)  is zero

(b)  is infinity

(c)  can be anywhere between zero and infinity

(d)  None of the above

Answer: (b) is infinity

Explanation: A plane mirror is the limiting case of a spherical mirror with R → ∞. Focal length f = R/2 → ∞ also. Concept Tested: Plane mirror: R = ∞; f = ∞

Q. 118. A coin in a beaker filled with water appears raised. This phenomenon occurs because of the property of

(a)  reflection of light

(b)  refraction of light

(c)  total internal reflection of light

(d)  interference of light

Answer: (b) refraction of light

Explanation: Light from water to air bends away from the normal, making the coin appear shallower (raised). Apparent depth = real depth/n = 20 × 3/4 = 15 cm. Concept Tested: Apparent depth: coin raised due to refraction at water-air surface

Q. 119. A ray of light falls on a transparent glass plate. A part of it is reflected and a part is refracted. The reflected and refracted rays can be perpendicular to each other for

(a)  angle of incidence equal to 90°

(b)  angle of incidence equal to zero

(c)  only one angle of incidence

(d)  more than one angle of incidence

Answer: (c) only one angle of incidence

Explanation: This occurs at Brewster’s angle θ_B = arctan(n). For any given glass there is exactly one Brewster’s angle where reflected and refracted rays are perpendicular. Concept Tested: Brewster’s angle: reflected and refracted perpendicular at exactly one angle of incidence

---