Question

A ray PQ incident on the refracting surface BA is refracted in the prism BAC as shown in the figure and emerged from the other face of the prism AC (refracting) as RS such that AQ=AR. If angle of prism A = 60o and​μ of the material is​√3, then find​θ.

Answer 1

Given:
PQ--incident ray
RS- Emergent ray
∟A=60 degrees
μ=​√3
AQ= QR
∟AQR=∟ARQ
i1=i2
r1=r2
By the formula:
μ= Sin(A+Dm)/2/SinA/2

​√3=Sin(60+Dm)/2 / Sin60/2

​√3×Sin30= Sin(60+Dm)/2
​√3/2 = Sin ( 60 +Dm)/2
sin^-1(​√3/2)=(60+Dm)/2
60=(60+Dm)/2
120=60+Dm
Dm=60 degrees
As Dm is corresponding to ​θ
So angle ​θ= 60 degrees