Category: Ray Optics

Q: A rectangular glass slab ABCD of refractive index n₁ is immersed in water of refractive index n₂ (n₁ > n₂). A ray of light is incident at the surface AB of the slab as shown. The maximum value of the angle of incidence α_max, such that the ray comes out only from the other surface CD, is given by

(A) $\large sin^{-1}[\frac{n_1}{n_2}cos(sin^{-1}\frac{n_2}{n_1})]$

(B) $\large sin^{-1}[ n_1 cos(sin^{-1}\frac{1}{n_2})]$

(C) $sin^{-1}\frac{n_1}{n_2}$

(D)$ sin^{-1}\frac{n_2}{n_1}$

Ans: (A)

Sol: Let C = critical angle

n₁ sin⁡C= n₂ sin⁡90°  ⇒ sin⁡C = n₂/n₁

Applying Snell’s law at face AB

$\large \frac{n_1}{n_2} = \frac{sin\alpha_{max}}{sinr}$

$\large \frac{n_1}{n_2} = \frac{sin\alpha_{max}}{sin(90-C)}= \frac{sin\alpha_{max}}{cosC}$

$\large sin\alpha_{max} = \frac{n_1}{n_2}cosC$

$\large \alpha_{max} = sin^{-1}[\frac{n_1}{n_2}cosC]$

$\large \alpha_{max} = sin^{-1}[\frac{n_1}{n_2}cos(sin^{-1}\frac{n_2}{n_1})]$

 

Q: A point source of light S, placed at a distance L in front of the centre of a plane mirror of width d, hangs vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror at a distance 2L from it as shown. The greatest distance over which he can see the image of the light source in the mirror is

(A) d/2

(B) d

(C) 2 d

(D) 3 d

Ans: (d)

Sol:

As triangle ΔS’AB & ΔS’PQ are similar

$\large \frac{d}{PQ} = \frac{L}{3L} $

PQ = 3 d

Q: A diverging beam of light from a point source S having divergence angle α  falls symmetrically on a glass slab as equal. The angles of incidence of the two extreme rays are equal. If the thickness of the glass slab is t and its refractive index is n, then the divergence angle of the emergent beam is

(A) zero

(B) α

(C) sin^–1 (1/n)

(D) 2 sin^–1 (1/n)

Ans: (B)

Q: A hollow double concave lens is made of very thin transparent material. It can be filled with air or either of two liquids L₁ or L₂ having refracting indices n₁ and n₂ respectively (n₂ > n₁ > 1). The lens will diverge a parallel beam of light if it is filled with

(A) air and placed in air

(B) air and immersed in L1

(C) L1 and immersed in L2

(D) L2 and immersed in L1

Ans: (D)

Sol: According to lens maker’s formula

$\large \frac{1}{f} = (\frac{n_L}{n_m} – 1)(\frac{1}{R_1} – \frac{1}{R_2})$

In case of double concave

$ (\frac{1}{R_1} – \frac{1}{R_2})$ will be negative .

For lens to be diverging in nature $(\frac{n_L}{n_m} – 1)$ should be +ve or n_L > n_m

But here , n₂ > n₁ , therefore Lens should be filled with L₂ and immersed in L₁

Q: In a compound microscope, the intermediate image is

(A) virtual, erect and magnified

(B) real, erect and magnified

(C) real, inverted and magnified

(D) virtual, erect and reduced

Ans: (C)