A ray of light passing through a prism having mu=sqrt2 suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. What is the angle of prism.

A ray of light passing through a prism having mu=sqrt2 suffers minimum

1.	A ray of light passing through a prism having mu=sqrt2 suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. What is the angle of prism.
Answer» Solution :As the prism is in the position of minimum DEVIATION `delta_m=(2i-A)` with `r=A//2` According to given problem, `i=2r=A` [as `r=A//2`] `delta_m= 2A-A=A` and hence from `mu=(sin[(A+delta_m)//2])/(sin (A//2))i.e., SQRT2=(sin A)/(sin A//2) (or)` `sqrt2 sin""A/2=2 sin ""A/2 COS ""A/2 i.e., cos ""A/2=1/sqrt2 (or)` `A/2= cos^-1[1/sqrt2]=45^@ i.e., A=90^@`