JEE Physics Ray Optics and Optical Instruments MCQs Set 05

Practice MCQs for JEE Physics Ray Optics and Optical Instruments

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Multiple Choice Questions

Question 1: A ray of light passes through an equilateral prism (μ = 1.5) such that the angle of incidence equals the angle of emergence and the latter is equal to 3/4 of the prism angle. The angle of deviation is
(a) \( 60^\circ \)
(b) \( 30^\circ \)
(c) \( 45^\circ \)
(d) \( 120^\circ \)
Show Answer & Explanation

Answer: (b) \( 30^\circ \)

Explanation:
1. \( i=e=\tfrac34\times60^\circ=45^\circ \).
2. \( \delta=i+e-A=90^\circ-60^\circ=30^\circ \).

Teacher's Note:
1. Use delta = i + e - A.

Question 2: The prism angle of a glass prism is 10\( ^\circ \). Its refractive indices for red and violet colours are 1.51 and 1.52. Its dispersive power is
(a) 0.015
(b) 0.020
(c) 0.011
(d) 0.019
Show Answer & Explanation

Answer: (d) 0.019

Explanation:
1. \( \omega=\dfrac{\mu_v-\mu_r}{\mu-1} \) with \( \mu=\dfrac{1.51+1.52}{2}=1.515 \).
2. \( \omega=0.01/0.515=0.019 \).

Teacher's Note:
1. Use the mean index.

Question 3: The refractive indices of crown glass for red, yellow and violet are 1.5140, 1.5170 and 1.5318, and for flint glass 1.6434, 1.6499 and 1.6852. The dispersive powers of crown and flint glass are respectively
(a) 0.034 and 0.064
(b) 0.064 and 0.034
(c) 1.00 and 0.064
(d) 0.034 and 1.0
Show Answer & Explanation

Answer: (a) 0.034 and 0.064

Explanation:
1. Crown: \( (1.5318-1.5140)/0.5170=0.0344 \).
2. Flint: \( (1.6852-1.6434)/0.6499=0.0643 \).

Teacher's Note:
1. Flint glass is more dispersive.

Question 4: A thin prism P1 of angle 4\( ^\circ \) made of glass of refractive index 1.54 is combined with another thin prism P2 of glass of refractive index 1.72 to produce dispersion without deviation. The angle of prism P2 is
(a) 5.33°
(b) 4°
(c) 3°
(d) 2.6°
Show Answer & Explanation

Answer: (c) 3°

Explanation:
1. No deviation: \( (\mu_1-1)A_1=(\mu_2-1)A_2 \).
2. \( 0.54\times4=0.72A_2 \) gives \( A_2=3^\circ \).

Teacher's Note:
1. Equal and opposite mean deviations.

Question 5: The angle of minimum deviation measured with a prism is 30\( ^\circ \) and the angle of the prism is 60\( ^\circ \). The refractive index of the prism material is
(a) \( \sqrt2 \)
(b) 2
(c) \( 3/2 \)
(d) \( 4/3 \)
Show Answer & Explanation

Answer: (a) \( \sqrt2 \)

Explanation:
1. \( \mu=\dfrac{\sin\frac{A+\delta_m}{2}}{\sin\frac A2}=\dfrac{\sin45^\circ}{\sin30^\circ} \).
2. \( \mu=\sqrt2 \).

Teacher's Note:
1. Standard prism formula.

Question 6: The angle of a prism is A and one of its surfaces is silvered. Light rays falling at an angle of incidence 2A on the first surface return back through the same path after suffering reflection at the second silvered surface. The refractive index of the prism material is
(a) \( 2\sin A \)
(b) \( 2\cos A \)
(c) \( \tfrac12\cos A \)
(d) \( \tan A \)
Show Answer & Explanation

Answer: (b) \( 2\cos A \)

Explanation:
1. The ray retraces its path if it strikes the silvered face normally, so \( r_1=A \).
2. \( \mu=\sin2A/\sin A=2\cos A \).

Teacher's Note:
1. Normal incidence on the silvered face.

Question 7: Rainbow is formed due to
(a) Scattering and refraction
(b) Total internal reflection and dispersion
(c) Reflection only
(d) Diffraction and dispersion
Show Answer & Explanation

Answer: (b) Total internal reflection and dispersion

Explanation:
1. Sunlight is refracted and dispersed into colours in raindrops and undergoes internal reflection before emerging.
2. So reflection inside the drop with dispersion forms the bow.

Teacher's Note:
1. Rainbow needs sunlight and raindrops.

Question 8: The refractive index of the material of a prism is \( \sqrt2 \) and its refracting angle is 30\( ^\circ \). One of the refracting surfaces is silvered. A beam of monochromatic light entering the prism from the other face will retrace its path after reflection from the silvered surface if its angle of incidence on the prism is
(a) \( 60^\circ \)
(b) \( 0^\circ \)
(c) \( 30^\circ \)
(d) \( 45^\circ \)
Show Answer & Explanation

Answer: (d) \( 45^\circ \)

Explanation:
1. Retracing needs \( r_1=A=30^\circ \).
2. \( \sin i=\sqrt2\sin30^\circ=0.707 \), so \( i=45^\circ \).

Teacher's Note:
1. Same idea as the 2A condition.

Question 9: A spherical surface of radius of curvature R separates air (refractive index 1.0) from glass (refractive index 1.5). The centre of curvature is in the glass. A point object P in air has a real image Q in the glass. The line PQ cuts the surface at a point O and PO = OQ. The distance PO is equal to
(a) R
(b) 3R
(c) 2R
(d) 5R
Show Answer & Explanation

Answer: (d) 5R

Explanation:
1. \( \dfrac{1.5}{v}-\dfrac1u=\dfrac{1.5-1}{R} \) with \( v=d \) and \( u=-d \).
2. \( \dfrac{2.5}{d}=\dfrac{0.5}{R} \), so \( d=5R \).

Teacher's Note:
1. Use the single-surface refraction formula.

Question 10: Two convex lenses of focal lengths 20 cm and 25 cm are placed in contact. The power of the combination is
(a) +1 D
(b) +9 D
(c) -1 D
(d) -9 D
Show Answer & Explanation

Answer: (b) +9 D

Explanation:
1. \( P=100/20+100/25=5+4=9 \) D.
2. Powers add for lenses in contact.

Teacher's Note:
1. Power in dioptre = 100/f(cm).

Question 11: Two lenses of powers +2.50 D and -3.75 D are combined to form a compound lens. Its focal length in cm is
(a) 40
(b) -40
(c) -80
(d) 160
Show Answer & Explanation

Answer: (c) -80

Explanation:
1. \( P=2.5-3.75=-1.25 \) D.
2. \( f=100/(-1.25)=-80 \) cm.

Teacher's Note:
1. Net power is negative so the lens diverges.

Question 12: Lenses of powers 3 D and -5 D are combined to form a compound lens. An object is placed at a distance of 50 cm from this lens. The position of its image is
(a) -10 cm
(b) +10 cm
(c) -25 cm
(d) +25 cm
Show Answer & Explanation

Answer: (c) -25 cm

Explanation:
1. \( P=-2 \) D, so \( f=-50 \) cm.
2. \( 1/v=1/f+1/u=-1/50-1/50 \) gives \( v=-25 \) cm.

Teacher's Note:
1. Diverging lens gives a virtual image on the object side.

Question 13: A convex lens of focal length 40 cm is in contact with a concave lens of focal length 25 cm. The power of the combination is
(a) -1.5 D
(b) -6.5 D
(c) +6.5 D
(d) +6.67 D
Show Answer & Explanation

Answer: (a) -1.5 D

Explanation:
1. \( P=100/40-100/25=2.5-4=-1.5 \) D.
2. The combination is diverging.

Teacher's Note:
1. Concave lens has negative power.

Question 14: An object is put at a distance of 5 cm from the first focus of a convex lens of focal length 10 cm. If a real image is formed, its distance from the lens will be
(a) 15 cm
(b) 20 cm
(c) 25 cm
(d) 30 cm
Show Answer & Explanation

Answer: (d) 30 cm

Explanation:
1. The object is 15 cm from the lens (outside the focus), so \( u=-15 \).
2. \( 1/v=1/10-1/15=1/30 \), so \( v=30 \) cm.

Teacher's Note:
1. Object distance from the lens is f + 5.

Question 15: An equiconvex lens has a power of 5 dioptre. If it is made of glass of refractive index 1.5, the radius of curvature of each surface will be
(a) 20 cm
(b) 10 cm
(c) 40 cm
(d) Infinity
Show Answer & Explanation

Answer: (a) 20 cm

Explanation:
1. \( P=(\mu-1)(2/R) \) gives \( 5=0.5\times2/R \).
2. \( R=0.2 \) m = 20 cm.

Teacher's Note:
1. Lens maker's formula.

Question 16: An object is placed 9 cm from the first principal focus of a convex lens and produces a real image 25 cm from its second principal focus. The focal length of the lens is
(a) 9 cm
(b) 25 cm
(c) 15 cm
(d) 17 cm
Show Answer & Explanation

Answer: (c) 15 cm

Explanation:
1. Newton's formula \( x_1x_2=f^2 \).
2. \( f^2=9\times25=225 \), so \( f=15 \) cm.

Teacher's Note:
1. Distances are measured from the foci.

Question 17: A glass convex lens (μ = 1.5) has a focal length of 8 cm in air. When immersed in water (μ = 1.33) its focal length will be about
(a) 2 m
(b) 4 cm
(c) 16 cm
(d) 32 cm
Show Answer & Explanation

Answer: (d) 32 cm

Explanation:
1. \( f_w=f_a\dfrac{\mu_g-1}{\mu_g/\mu_w-1}=8\times\dfrac{0.5}{1.128-1} \).
2. \( f_w\approx31 \) cm, nearest to 32 cm.

Teacher's Note:
1. Focal length increases in water.

Question 18: Two thin convex lenses of focal lengths 10 cm and 15 cm are separated by a distance of 10 cm. The focal length of the combination is
(a) 4.2 cm
(b) 6 cm
(c) 10 cm
(d) 15 cm
Show Answer & Explanation

Answer: (c) 10 cm

Explanation:
1. \( 1/F=1/f_1+1/f_2-d/(f_1f_2)=0.1+0.0667-10/150 \).
2. \( 1/F=0.1 \), so \( F=10 \) cm.

Teacher's Note:
1. Use the separated-lens formula.

Question 19: A convex lens of power P is immersed in water. Its power will
(a) Increase
(b) Decrease
(c) Remain unchanged
(d) Increase for red colour and decrease for blue colour
Show Answer & Explanation

Answer: (b) Decrease

Explanation:
1. Power \( =(\mu_g/\mu_w-1)(1/R_1-1/R_2) \).
2. Since \( \mu_w>1 \), the factor decreases, so the power decreases.

Teacher's Note:
1. Lenses are weaker in water.

Question 20: The focal length of a convex lens is 10 cm and its refractive index is 1.5. If the radius of curvature of one surface is 7.5 cm, the radius of curvature of the second surface will be
(a) 7.5 cm
(b) 15.0 cm
(c) 75 cm
(d) 5.0 cm
Show Answer & Explanation

Answer: (b) 15.0 cm

Explanation:
1. \( 1/10=0.5(1/7.5+1/R_2) \).
2. \( 1/R_2=0.2-0.1333=0.0667 \), so \( R_2=15 \) cm.

Teacher's Note:
1. Both surfaces are convex.

Question 21: A plano-convex lens (μ = 1.5) has a radius of curvature of 10 cm. It is silvered on its plane surface. The focal length after silvering is
(a) 10 cm
(b) 20 cm
(c) 15 cm
(d) 25 cm
Show Answer & Explanation

Answer: (a) 10 cm

Explanation:
1. Lens focal length \( f=R/(\mu-1)=20 \) cm.
2. Light passes twice through the lens and reflects from a plane mirror, so \( F=f/2=10 \) cm.

Teacher's Note:
1. The system behaves like a concave mirror.

Question 22: A plano-convex lens is made of refractive index 1.6. The radius of curvature of the curved surface is 60 cm. The focal length of the lens is
(a) 50 cm
(b) 100 cm
(c) 200 cm
(d) 400 cm
Show Answer & Explanation

Answer: (b) 100 cm

Explanation:
1. \( f=R/(\mu-1)=60/0.6=100 \) cm.
2. One surface is plane.

Teacher's Note:
1. Plano-convex: f = R/(mu - 1).

Question 23: In a plano-convex lens the radius of curvature of the convex surface is 10 cm and the focal length of the lens is 30 cm. The refractive index of the lens material is
(a) 1.5
(b) 1.66
(c) 1.33
(d) 3
Show Answer & Explanation

Answer: (c) 1.33

Explanation:
1. \( \mu-1=R/f=10/30=1/3 \).
2. \( \mu=1.33 \).

Teacher's Note:
1. Rearrange the lens maker's formula.

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