Question

a right angled prism of refractive index n has a plate of refractive index n1 so that n1 less than n ,cemented to its diagonal face .the assembly is in air.a ray is incident on AB

1) calculate the angle of incidence at AB for which the ray strikes the diagonal face at the critical angle
2)assuming n=1.352 calculate the angle of incidence at AB for which the refracted ray passes through the diagonal face undeviated.
PLS ANS FAST

Answer 1

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