A ray of light undergoes deviation of `30^@` when incident on an equilateral prism of refractive index `sqrt2.` what is the angle subtended by the ray inside the prism with the base of the prism?

Explanation

`delta=30^@`, `A=60^@`, `mu=sqrt2`
Let us first calculate `delta_m`
`mu=(sin((A+delta_m)/(2)))/(sin(A//2))`
`sqrt2=(sin((60^@+delta_m)/(2)))/(sin30^@=1//2)`
`sin((60^@+delta_m)/(2))=1/sqrt2=sin45^@`
`(60^@+delta_m)/(2)=45^@`
`delta_m=30^@=delta`
Since `delta=delta_m`, i.e. ray inside the prism is parallel to the base of the prism.