for a prism kept in air of apex angle 45 , it is found that the angle

1.	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» *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 :-)*