Question

for a prism kept in air of apex angle 45 , it is found that the angle of emergence is 45 for grazing incidence. calculate the refractive index of the prism.

Answer 1

Given in the question :-

Refer to the attachment

$r_1 + r_2 + A = 45^0$

Also r₁ = θc

therefore

r₂ = 45° - θc

Then changing on the terms.

sinr₂ = sin(45°- θc)

Now , the refractive index μ

μsinr₂ = sini₂ = 1/√2 ------(i)

$\therefore sinr_2 = \frac{1}{\sqrt{2\mu}}$  &  $\theta_c = 1/\mu$----(ii)

from eq (i) & (ii)

$1/\sqrt{2\mu} = sin45^0 (cos\theta_c) - cos45^0 (sin\theta_c)$

Now, on solving

$1/\mu = \sqrt{1-1/\mu^2} -1/\mu$

4/μ² = 1- 1/μ²

μ = (5)¹/²

Hope it Helps :-)

Answer 2

Answer:5^1/2

Explanation:

see the photo/attachment