Question

discuss refraction through prism of angle A and derive mu=sin (A+sigm m/2) sin A/2 ?

Answer 1

The passage of light incident from air into a glass prism is deviated due to refraction occurring twice, once at the boundary separating air-class and next at the boundary separating glass-air as shown in figure.

A: Refracting angle of prism

i: Angle of incidence

e: Angle of emergence

r1, r2: Refracting angles

: Angle of deviation

: Refractive index of glass wrt air

 

The geometry of prism imposes relations between i.e., A, S and r1, r2, A as follows :

Now, reversing the path of the ray of the light, i.e TSQP instead of PQST as the path, it is seen that the angle of deviation is same. Thus, in general there are two angles of incidence i & e, for which d is same; however when d is the minimum angle of deviation, dm then i = e as illustrated in graph of d Vsi.