Question

A rectangular cavity ABCD is carved inside an equilateral prism PQR of refractive index v2 as shown in the
figure. If 8 is the deviation in a ray entering at face PQ and emerging at face PR, without passing through
AB or CD then
B.
53°
D
R
(A)
there is no effect of cavity on the value of
(B) there is some effect of cavity on the value of 8
(C) if the cavity is filled with water (refractive index 4/3), 8 min = 30°
(D) if the cavity is filled with some liquid (refractive index 2), Smin = 15°​

Answer 1

Answer:

The rectangular cavity inside the prism works as a rectangular prism and hence produces no deviation to the path of a light ray that passes from its parallel faces.

So, the total deviation produced by a prism is remained the same with or without a cavity. Hence option (A) is correct.

(A) There will not be any effect of a cavity on δ (angle of deviation)

Furthermore, if the minimum angle of deviation of any prism is δm and the angle of the prism is A, then the refractive index of the prism is given by:

$\mu = \frac{sin(\frac{A+\delta_m}{2} )}{sin(\frac{\delta_m}{2} ) }$

where, μ = √2 , ∠A = 60° (equilateral prism)

$\sqrt{2} = \frac{sin(\frac{60+\delta_m}{2} )}{sin(\frac{\delta_m}{2} )}$

The above equation does not hold good for δm = 30°. So, options (C) and (D) are not true.

The only correct option is (A).