A right angled prism of refractive index n has a plate of refractive index n1 so that n1 i. Calculate the angle of incidence at AB for which the ray strikes the diagonal face at the critical angle.ii. Assuming n = 1.352, calculate the angle of incidence at AB for which the refracted ray passes through the diagonal face undeviated.

sin c = n1 / n (90°– r1) + 45 + (90° – c) = 180°r1 = 45°– c sin i / sin r1 = n sin i = n sin r1 = n sin (45°–c) = n (sin 45 cos c – cos 45 sin c) = n/2√ (cos c – sin c) = n/2√ ([ 1 – sin2C] −−−−−−−−−−−√– sin c) = [1/2√ (n2 – n12−−−−−−−√ ) – n1] ⇒i = sin−1 [1/2√ (n2 – n12−−−−−−−√ ) – n1] r2= 0 & r1 + r2 = 45°r1 = 45° sin i / sin r1 = n sin i = n sin r1= 1⋅352 sin 45 = 0⋅956 ⇒ i = sin−1 (0⋅956) = 72⋅58