A ray of light PQ is incident at an angle of 60 degree on the face of AB of prism - Physics - Ray Optics And Optical Instruments

Question

A ray of light PQ is incident at an angle of 60 degree on the
face of AB of prism of angle 30 degree The ray emerging out of the
prism makes an angle of 30 degree with the incident ray Show that
the emergent ray is perpendicular to the face BC through which it
emerges Also calculate the refrractive index of the prism material
?plz reply soon

Jyoti Pant · Accepted Answer

Given that: Angle of prism ,A= 30o Angle of incidence, $i_{1}$ = 60o Angle of deviation $δ$ = 30o

$i_{1} + i_{2} = A + δ O r t h e a n g l e o f i m e r g e n c e i_{2} = A + δ - i_{1} = 30 + 30 - 60 = 0 T h e r e f o r e t h e e m e r g e n t r a y i s n o r m a l t o t h e o t h e r f a c e a n d a l s o r_{1} + r_{2} = A I f i_{2} = 0, r_{2} = 0 S o r_{1} = A = 30^{0} U \sin g S n e l l' s l a w n = \frac{\sin i_{1}}{\sin r_{1}} = \frac{\sin 60}{\sin 30} = 1 732 N o w, \sin c e e m e r g e n t r a y i s n o r m a l t o o t h e r f a c e, S o δ = δ_{m} = 30^{0} T h e r e f o r e, n = \frac{\sin (A + δ_{m}) / 2}{\sin A / 2} = \frac{\sin (30 + 30) / 2}{\sin (30 / 2)} = 1 732$