A ray of light is incident at 60^ on one face of a prism of angle 30^ and the emergent ray makes 30^ with the incident ray. The refractive index of the prism is ( 30^ =0 5, 60^ = 3 / 2 )

Step-by-step solution

Given A =30^ , i ₁=30^ and =30^ For a prism, array ll & = (i₁+i₂ )- (r₁+r₂ ) & = (i₁+i₂ )-A & 30=60+i₂-30^ & i₂=0 array This means the emergent ray is perpendicular to the face from which emerges out. As i ₂=0, r ₂=0 But r ₁+ r ₂= A r ₁+0=30^ r ₁=30^ Using Snell's law at the first face of the prism, aligned & ₁ i₁= ₂ r₁ & 1 60= ₂ 30 aligned aligned & 3 2 = ₂ 2 & ₂= 3 =1.732 aligned