JEE Physics Ray Optics And Optical Instruments MCQs Set 29

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Chapter-wise Objective Questions: Ray Optics and Optical Instruments

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Multiple Choice Questions

Question 1: A prism has a refracting angle of 60°. When placed in the position of minimum deviation, it produces a deviation of 30°. The angle of incidence is
(a) 30°
(b) 45°
(c) 15°
(d) 60°
Show Answer & Explanation

Answer: (b) 45°

Explanation:
1. i = (A + D)/2 = (60° + 30°)/2 = 45°.

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

Question 2: In the case of reflection over a spherical surface, which of these are correct? I. The normal is taken as perpendicular to the tangent at the point of incidence. II. The perpendicular to the incident ray is perpendicular to the plane of incidence. III. The line joining the centre of curvature of the mirror with the point of incidence is the normal. IV. The line joining the centre of curvature and the pole of the curved surface is the normal.
(a) I and II
(b) I and III
(c) II and III
(d) II and IV
Show Answer & Explanation

Answer: (b) I and III

Explanation:
1. The normal is perpendicular to the tangent, which is the line from the centre of curvature to the point of incidence.
2. The line joining the centre of curvature to the pole is the principal axis, not the normal at a general point.

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

Question 3: A convex mirror is used to form the image of an object. Then which of the following statements is/are true? I. The image lies between the pole and the focus. II. The image is diminished in size. III. The image is real.
(a) I only
(b) II only
(c) I and III
(d) I and II
Show Answer & Explanation

Answer: (d) I and II

Explanation:
1. A convex mirror gives a virtual, erect, diminished image between the pole and the focus.

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

Question 4: A ray of light travelling inside a rectangular glass block of refractive index √2 is incident on the glass-air surface at an angle of incidence of 45°. The refractive index of air is one. Under these conditions the ray will
(a) emerge into the air without any deviation
(b) be reflected back into the glass
(c) be absorbed
(d) emerge into the air with an angle of refraction equal to 90°
Show Answer & Explanation

Answer: (d) emerge into the air with an angle of refraction equal to 90°

Explanation:
1. sin c = 1/√2, so the critical angle is 45°.
2. At exactly the critical angle the refracted ray grazes the surface (refraction angle 90°).

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

Question 5: Yellow light is refracted through a prism producing minimum deviation. If i1 and i2 denote the angle of incidence and emergence for this prism, then
(a) i1 = i2
(b) i1 > i2
(c) i1 < i2
(d) i1 + i2 = 90°
Show Answer & Explanation

Answer: (a) i1 = i2

Explanation:
1. At minimum deviation the ray passes symmetrically, so i = e.

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

Question 6: Two identical thin plano-convex glass lenses (refractive index 1.5), each having radius of curvature of 20 cm, are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index 1.7. The focal length of the combination is
(a) -25 cm
(b) -50 cm
(c) 50 cm
(d) -20 cm
Show Answer & Explanation

Answer: (b) -50 cm

Explanation:
1. The power of the system is the sum of surface powers (n2 - n1)/R.
2. Plane faces give 0.
3. Glass-to-oil at the first curved surface (R = -20): (1.7 - 1.5)/(-20) = -0.01.
4. Oil-to-glass at the second (R = +20): (1.5 - 1.7)/20 = -0.01.
5. P = -0.02 cm⁻¹, so f = -50 cm.

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

Question 7: Match the columns (f is the focal length of the mirror).
Column IColumn II
(A) An object placed at the focus before a convex mirror(1) Magnification is +0.5
(B) An object placed at the centre of curvature before a concave mirror(2) Magnification is +1
(C) An object placed at the focus before a concave mirror(3) Magnification is -infinity
(D) An object placed at the centre of curvature before a convex mirror(4) Magnification is -1
(5) Magnification is +0.33

(a) A-1, B-3, C-4, D-5
(b) A-4, B-1, C-3, D-5
(c) A-1, B-4, C-3, D-5
(d) A-1, B-5, C-3, D-4
Show Answer & Explanation

Answer: (c) A-1, B-4, C-3, D-5

Explanation:
1. Convex mirror, object at f: v = f/2 and m = +0.5 (A-1).
2. Concave mirror, object at C: m = -1 (B-4).
3. Concave mirror, object at f: image at infinity (C-3).
4. Convex mirror, object at 2f: v = 2f/3 and m = +0.33 (D-5).

Teacher's Note:
1. Use 1/v + 1/u = 1/f.

Question 8: Identify the mismatch in the following.
(a) Myopia - concave lens
(b) For rear view - concave mirror
(c) Hypermetropia - convex lens
(d) Astigmatism - cylindrical lens
Show Answer & Explanation

Answer: (b) For rear view - concave mirror

Explanation:
1. A rear-view mirror is a convex mirror.

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

Question 9: The magnifying power of a telescope is 9. When it is adjusted for parallel rays, the distance between the objective and the eyepiece is found to be 20 cm. The focal lengths of the lenses are
(a) 18 cm, 2 cm
(b) 11 cm, 9 cm
(c) 10 cm, 10 cm
(d) 15 cm, 5 cm
Show Answer & Explanation

Answer: (a) 18 cm, 2 cm

Explanation:
1. f_o/f_e = 9 and f_o + f_e = 20, so f_e = 2 cm and f_o = 18 cm.

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

Question 10: A telescope has an objective lens of 10 cm diameter and is situated at a distance of one kilometre from two objects. The minimum distance between these two objects which can be resolved by the telescope, when the mean wavelength of light is 5000 Å, is of the order of
(a) 5 cm
(b) 0.5 m
(c) 5 m
(d) 5 mm
Show Answer & Explanation

Answer: (d) 5 mm

Explanation:
1. Δθ = 1.22 λ/D = 1.22 × 5 × 10⁻⁷/0.1 = 6.1 × 10⁻⁶ rad.
2. Separation = 1000 × 6.1 × 10⁻⁶ = 6.1 mm, of the order of 5 mm.

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

Question 11: The critical angle for light going from medium X into medium Y is θ. The speed of light in medium X is v. Then the speed of light in medium Y is
(a) \( v(1-\cos\theta) \)
(b) \( v/\sin\theta \)
(c) \( v/\cos\theta \)
(d) \( v\cos\theta \)
Show Answer & Explanation

Answer: (b) \( v/\sin\theta \)

Explanation:
1. sin θ = n_Y/n_X = v_X/v_Y, so v_Y = v/sin θ.

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

Question 12: Astigmatism is corrected using
(a) a cylindrical lens
(b) a plano-convex lens
(c) a plano-concave lens
(d) a convex lens
Show Answer & Explanation

Answer: (a) a cylindrical lens

Explanation:
1. A cylindrical lens corrects the different curvatures in different planes of the eye.

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

Question 13: The focal lengths of a converging lens are f_V and f_R for violet and red light respectively. Then
(a) f_V > f_R
(b) f_V = f_R
(c) f_V < f_R
(d) any of the three is possible depending on the average refractive index
Show Answer & Explanation

Answer: (c) f_V < f_R

Explanation:
1. Violet has the larger μ, so it is bent more and has the smaller focal length.

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

Question 14: A vessel of depth x is half filled with oil of refractive index μ1 and the other half is filled with water of refractive index μ2. The apparent depth of the vessel when viewed from above is
(a) \( \frac{x(\mu_1+\mu_2)}{2\mu_1\mu_2} \)
(b) \( \frac{x\mu_1\mu_2}{2(\mu_1+\mu_2)} \)
(c) \( \frac{x\mu_1\mu_2}{\mu_1+\mu_2} \)
(d) \( \frac{2x(\mu_1+\mu_2)}{\mu_1\mu_2} \)
Show Answer & Explanation

Answer: (a) \( \frac{x(\mu_1+\mu_2)}{2\mu_1\mu_2} \)

Explanation:
1. Apparent depth = (x/2)/μ1 + (x/2)/μ2 = x(μ1 + μ2)/(2μ1μ2).

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

Question 15: If i is the angle of incidence and r is the angle of refraction, then the ratio sin i/sin r is I. a constant for a pair of media, II. called the refractive index of medium 2 with respect to medium 1, III. called the absolute refractive index of medium 2, IV. varying with temperature.
(a) I, II and III
(b) II, III and IV
(c) I, II and IV
(d) I, III and IV
Show Answer & Explanation

Answer: (c) I, II and IV

Explanation:
1. The ratio is the relative index n21, constant for the pair (and temperature dependent).
2. It is the absolute index only if medium 1 is vacuum, so III is not generally true.

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

Question 16: Electromagnetic radiation belonging to ____ region of the spectrum is called light.
(a) 100 nm to 400 nm
(b) 400 nm to 750 nm
(c) 750 nm to 10 nm
(d) 1000 nm to 1400 nm
Show Answer & Explanation

Answer: (b) 400 nm to 750 nm

Explanation:
1. Visible light spans about 400 nm to 750 nm.

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

Question 17: What causes chromatic aberration?
(a) marginal rays
(b) central rays
(c) difference in radii of curvature of its surfaces
(d) variation of focal length of the lens with colour
Show Answer & Explanation

Answer: (d) variation of focal length of the lens with colour

Explanation:
1. μ varies with wavelength, so f varies with colour.

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

Question 18: The turning back of light into the same medium after incidence on a boundary separating two media is called
(a) reflection of light
(b) refraction of light
(c) dispersion of light
(d) interference of light
Show Answer & Explanation

Answer: (a) reflection of light

Explanation:
1. That is the definition of reflection.

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

Question 19: Total internal reflection can take place only if
(a) light goes from an optically rarer medium to an optically denser medium
(b) light goes from an optically denser medium to a rarer medium
(c) the refractive indices of the two media are close to each other
(d) the refractive indices of the two media are widely different
Show Answer & Explanation

Answer: (b) light goes from an optically denser medium to a rarer medium

Explanation:
1. TIR needs light going from a denser to a rarer medium with the angle of incidence above the critical angle.

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

Question 20:
Assertion (A): The focal length of a convex mirror will increase if the mirror is placed in water.
Reason (R): The focal length of a convex mirror of radius R is equal to f = R/2.
(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: (d) A is false, but R is true.

Explanation:
1. The focal length of a mirror depends only on its radius of curvature, not on the medium, so the assertion is false.
2. The reason is true.

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

Question 21: The resolving power of a telescope increases with
(a) increase in focal length of the eyepiece
(b) increase in focal length of the objective
(c) increase in aperture of the eyepiece
(d) increase in aperture of the objective
Show Answer & Explanation

Answer: (d) increase in aperture of the objective

Explanation:
1. R = D/(1.22λ), so it grows with the aperture of the objective.

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

Question 22: A ray of light is incident normally on one refracting surface of an equilateral prism. If the refractive index of the material of the prism is 1.5, then
(a) the emergent ray is deviated by 30°
(b) the emergent ray is deviated by 60°
(c) the emergent ray just grazes the second refracting surface
(d) the ray undergoes total internal reflection at the second refracting surface
Show Answer & Explanation

Answer: (d) the ray undergoes total internal reflection at the second refracting surface

Explanation:
1. The angle of incidence at the second face is A = 60°.
2. The critical angle is sin⁻¹(1/1.5) = 41.8°, which is less than 60°, so the ray is totally internally reflected.

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

Question 23:
Assertion (A): The image formed by a concave mirror is certainly real if the object is virtual.
Reason (R): The image formed by a concave mirror is certainly virtual if the object 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: (c) A is true, but R is false.

Explanation:
1. A virtual object (converging rays) always gives a real image with a concave mirror, so the assertion is true.
2. A real object can give a real or a virtual image, so the reason is false.

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

Question 24: Wavelengths of light used in an optical instrument are λ1 = 4000 Å and λ2 = 5000 Å. The ratio of the respective resolving powers (corresponding to λ1 and λ2) is
(a) 16 : 25
(b) 9 : 1
(c) 4 : 5
(d) 5 : 4
Show Answer & Explanation

Answer: (d) 5 : 4

Explanation:
1. Resolving power is proportional to 1/λ, so the ratio is 5000/4000 = 5 : 4.

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

Question 25: If a glass prism is dipped in water, its dispersive power
(a) increases
(b) decreases
(c) does not change
(d) may increase or decrease depending on whether the angle of the prism is less than or greater than 60°
Show Answer & Explanation

Answer: (b) decreases

Explanation:
1. ω = (μ_v - μ_r)/(μ_y - 1) with relative indices decreasing in water, so the dispersive power is lower.

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

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