JEE Physics Ray Optics And Optical Instruments MCQs Set 30

Physics Objective Questions and Answers: Ray Optics and Optical Instruments

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Multiple Choice Questions

Question 1: The focal lengths of the objective and eyepiece of an astronomical telescope are 2 m and 5 cm respectively. The final image is formed at (i) the least distance of distinct vision and (ii) infinity. The magnifying powers in the two cases will be
(a) -48, -40
(b) -40, -48
(c) -40, +48
(d) -48, +40
Show Answer & Explanation

Answer: (a) -48, -40

Explanation:
1. (i) m = -(f_o/f_e)(1 + f_e/D) = -40 × (1 + 5/25) = -48.
2. (ii) m = -f_o/f_e = -40.

Teacher's Note:
1. Recall the basic fact.

Question 2: A ray of light is incident on a thick slab of glass of thickness t. The emergent ray is parallel to the incident ray but displaced sideways by a distance d. If the angles of incidence i and refraction r are small, then d is
(a) \( t\left(1-\frac ir\right) \)
(b) \( rt\left(1-\frac ir\right) \)
(c) \( it\left(1-\frac ri\right) \)
(d) \( t\left(1-\frac ri\right) \)
Show Answer & Explanation

Answer: (c) \( it\left(1-\frac ri\right) \)

Explanation:
1. d = t sin(i - r)/cos r, which for small angles is t(i - r).
2. This equals i t (1 - r/i).

Teacher's Note:
1. Lateral shift.

Question 3: A ray of light travelling in the direction (1/2)(î + √3 ĵ) is incident on a plane mirror. After reflection it travels along the direction (1/2)(î - √3 ĵ). The angle of incidence is
(a) 30°
(b) 45°
(c) 60°
(d) 75°
Show Answer & Explanation

Answer: (a) 30°

Explanation:
1. The mirror surface is along x, so its normal is along y.
2. cos θ = √3/2 between the ray and the normal, so θ = 30°.

Teacher's Note:
1. Recall the basic fact.

Question 4:
Assertion (A): The resolving power of a telescope is more if the diameter of the objective lens is more.
Reason (R): An objective lens of large diameter collects more light.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. R = D/(1.22λ) increases with D.
2. Collecting more light is also true but the resolving power rises because of the reduced diffraction, not because of the light gathered.

Teacher's Note:
1. Compare the two statements.

Question 5: A ray of light passes through a stack of four transparent media with parallel plane faces and refractive indices μ1, μ2, μ3 and μ4 in that order. If the emergent ray is parallel to the incident ray, we must have
(a) \( \mu_1=\mu_2 \)
(b) \( \mu_2=\mu_3 \)
(c) \( \mu_3=\mu_4 \)
(d) \( \mu_4=\mu_1 \)
Show Answer & Explanation

Answer: (d) \( \mu_4=\mu_1 \)

Explanation:
1. μ1 sin i1 = μ2 sin i2 = ... = μ4 sin i4.
2. For the emergent ray to be parallel to the incident ray, i4 = i1, so μ4 = μ1.

Teacher's Note:
1. Snell's law across parallel faces.

Question 6: The image formed by the objective of a compound microscope is
(a) real and diminished
(b) real and enlarged
(c) virtual and enlarged
(d) virtual and diminished
Show Answer & Explanation

Answer: (b) real and enlarged

Explanation:
1. The objective forms a real, inverted, enlarged image.

Teacher's Note:
1. Recall the basic fact.

Question 7: A ray of light from a denser medium strikes a rarer medium at an angle of incidence i. The reflected and refracted rays make an angle of 90° with each other. The angles of reflection and refraction are r and r'. The critical angle is
(a) \( \sin^{-1}(\tan r) \)
(b) \( \sin^{-1}(\tan i) \)
(c) \( \sin^{-1}(\tan r') \)
(d) \( \tan^{-1}(\sin i) \)
Show Answer & Explanation

Answer: (b) \( \sin^{-1}(\tan i) \)

Explanation:
1. The 90° condition gives r' = 90° - i.
2. So n_rarer/n_denser = sin i/sin r' = sin i/cos i = tan i.
3. The critical angle satisfies sin c = n_rarer/n_denser = tan i.

Teacher's Note:
1. Recall the basic fact.

Question 8: A narrow beam of white light goes through a slab having parallel faces. Then
(a) the light never splits into different colours
(b) the emergent beam is white
(c) the light inside the slab is split into different colours
(d) the light inside the slab is white
Show Answer & Explanation

Answer: (c) the light inside the slab is split into different colours

Explanation:
1. Light disperses inside the slab, but the parallel faces recombine the colours, so the emergent beam is white.

Teacher's Note:
1. Check inside the slab and after it.

Question 9: If D is the deviation of a normally falling light beam on a thin prism of angle A and δ is the dispersive power of the same prism, then
(a) D is independent of A
(b) D is independent of refractive index
(c) δ is independent of refractive index
(d) δ is independent of A
Show Answer & Explanation

Answer: (d) δ is independent of A

Explanation:
1. δ = (μ_v - μ_r)/(μ_y - 1) depends only on the material. D = (μ - 1)A depends on A and μ.

Teacher's Note:
1. Recall the basic fact.

Question 10: A thin convergent glass lens (μ_g = 1.5) has a power of +5.0 D. When this lens is immersed in a liquid of refractive index μ, it acts as a divergent lens of focal length 100 cm. The value of μ must be
(a) 4/3
(b) 5/3
(c) 5/4
(d) 6/5
Show Answer & Explanation

Answer: (b) 5/3

Explanation:
1. P = (μ_g/μ - 1)K, with K = 10 D from the air value.
2. In the liquid, P = -1 D, so 1.5/μ - 1 = -0.1, hence μ = 5/3.

Teacher's Note:
1. Recall the basic fact.

Question 11: Chromatic aberration in a lens is caused by
(a) reflection
(b) interference
(c) diffraction
(d) dispersion
Show Answer & Explanation

Answer: (d) dispersion

Explanation:
1. The variation of refractive index with wavelength (dispersion) is the cause.

Teacher's Note:
1. Recall the basic fact.

Question 12: Which of the following is/are correct relations? I. n21 = 1/n12. II. n32 = n31 x n12. III. n21 = n_1a/n_2a. IV. n21 = n_2a/n_1a. (a denotes air.)
(a) I, II and IV
(b) I, III and IV
(c) II, III and IV
(d) I, II, III and IV
Show Answer & Explanation

Answer: (a) I, II and IV

Explanation:
1. n21 = n2/n1 = n_2a/n_1a, so IV is correct and III is wrong.
2. I and II are standard relations.

Teacher's Note:
1. Recall the basic fact.

Question 13: When white light enters a prism, it gets split into its constituent colours. This is due to
(a) high density of prism material
(b) μ is different for different wavelengths
(c) diffraction of light
(d) velocity changes for different frequency
Show Answer & Explanation

Answer: (b) μ is different for different wavelengths

Explanation:
1. Dispersion arises because μ depends on the wavelength.

Teacher's Note:
1. Recall the basic fact.

Question 14: A ray of light travelling in a transparent medium of refractive index μ falls on a surface separating the medium from air at an angle of incidence of 45°. For which of the following values of μ can the ray undergo total internal reflection?
(a) μ = 1.33
(b) μ = 1.40
(c) μ = 1.50
(d) μ = 1.25
Show Answer & Explanation

Answer: (c) μ = 1.50

Explanation:
1. TIR needs sin 45° ≥ 1/μ, i.e. μ ≥ √2 = 1.414.
2. Only 1.50 satisfies this.

Teacher's Note:
1. Recall the basic fact.

Question 15: One face of a rectangular glass plate 6 cm thick is silvered. An object held 8 cm in front of the first face forms an image 12 cm behind the silvered face. The refractive index of the glass is
(a) 0.4
(b) 0.8
(c) 1.2
(d) 1.6
Show Answer & Explanation

Answer: (c) 1.2

Explanation:
1. The silvered face appears at 6/μ behind the first face, so the image lies 8 + 12/μ behind the first face.
2. This is 12 cm behind the silvered face, so 8 + 12/μ = 12 + 6 = 18, hence 12/μ = 10 and μ = 1.2.

Teacher's Note:
1. Use apparent depth and the mirror image.

Question 16:
Assertion (A): The image of an extended object placed perpendicular to the principal axis of a mirror will be erect if the object is real but the image is virtual.
Reason (R): The image of an extended object placed perpendicular to the principal axis of a mirror will be erect if the object is virtual but the image is real.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. Both statements are true: virtual images of real objects are erect, and real images of virtual objects are also erect.
2. The second does not explain the first.

Teacher's Note:
1. Compare the two statements.

Question 17: A simple telescope consisting of an objective of focal length 60 cm and a single eye lens of focal length 5 cm is focussed on a distant object in such a way that parallel rays emerge from the eye lens. If the object subtends an angle of 2° at the objective, the angular width of the image is
(a) 10°
(b) 24°
(c) 50°
(d) (1/6)°
Show Answer & Explanation

Answer: (b) 24°

Explanation:
1. m = f_o/f_e = 12.
2. Angular width of the image = 12 × 2° = 24°.

Teacher's Note:
1. Recall the basic fact.

Question 18: In the secondary rainbow, the order of colours observed from the earth is
(a) violet innermost, red outermost
(b) red innermost, violet outermost
(c) random
(d) white and dark alternately
Show Answer & Explanation

Answer: (b) red innermost, violet outermost

Explanation:
1. The extra reflection reverses the order: red is inside and violet outside.

Teacher's Note:
1. Recall the basic fact.

Question 19: When light is refracted into a medium,
(a) its wavelength and frequency both increase
(b) its wavelength increases but frequency remains unchanged
(c) its wavelength decreases but frequency remains unchanged
(d) its wavelength and frequency both decrease
Show Answer & Explanation

Answer: (c) its wavelength decreases but frequency remains unchanged

Explanation:
1. The frequency is fixed by the source.
2. The speed falls in a denser medium, so the wavelength decreases.

Teacher's Note:
1. Recall the basic fact.

Question 20: A rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10 cm in such a way that its end closer to the pole is 20 cm away from the mirror. The length of the image is
(a) 10 cm
(b) 15 cm
(c) 2.5 cm
(d) 5 cm
Show Answer & Explanation

Answer: (d) 5 cm

Explanation:
1. The near end is at u = -20 cm: v = -20 cm.
2. The far end is at u = -30 cm: 1/v = -1/10 + 1/30, so v = -15 cm.
3. Length of image = 20 - 15 = 5 cm.

Teacher's Note:
1. Recall the basic fact.

Question 21: Which of the following phenomena is used in optical fibres?
(a) total internal reflection
(b) scattering
(c) diffraction
(d) refraction
Show Answer & Explanation

Answer: (a) total internal reflection

Explanation:
1. Light is guided in a fibre by repeated total internal reflection.

Teacher's Note:
1. Recall the basic fact.

Question 22: A double convex lens of focal length 6 cm is made of glass of refractive index 1.5. The radius of curvature of one surface is double that of the other surface. The value of the smaller radius of curvature is
(a) 6 cm
(b) 4.5 cm
(c) 9 cm
(d) 4 cm
Show Answer & Explanation

Answer: (b) 4.5 cm

Explanation:
1. 1/6 = 0.5(1/R + 1/2R) = 0.75/R, so R = 4.5 cm.

Teacher's Note:
1. Recall the basic fact.

Question 23: The field of view is maximum for
(a) a plane mirror
(b) a concave mirror
(c) a convex mirror
(d) a cylindrical mirror
Show Answer & Explanation

Answer: (c) a convex mirror

Explanation:
1. A convex mirror gives a wide field of view, so it is used as a rear-view mirror.

Teacher's Note:
1. Recall the basic fact.

Question 24: A beam of monochromatic blue light of wavelength 420 nm in air travels in water (μ = 4/3). Its wavelength in water will be
(a) 280 nm
(b) 560 nm
(c) 315 nm
(d) 400 nm
Show Answer & Explanation

Answer: (c) 315 nm

Explanation:
1. λ_water = λ_air/μ = 420 × 3/4 = 315 nm.

Teacher's Note:
1. Recall the basic fact.

Question 25: A glass slab of thickness 4 cm contains the same number of waves as 5 cm of water when both are traversed by the same monochromatic light. If the refractive index of water is 4/3, what is that of glass?
(a) 5/3
(b) 5/4
(c) 16/15
(d) 1.5
Show Answer & Explanation

Answer: (a) 5/3

Explanation:
1. The number of waves is optical path/λ0, so 4 μ_g = 5 × 4/3.
2. μ_g = 5/3.

Teacher's Note:
1. Recall the basic fact.

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Multiple Choice Questions (MCQs) for JEE Physics Ray Optics and Optical Instruments

JEE Physics Ray Optics and Optical Instruments Objective Test Questions

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