Question

A ray of monochromatic light is incident on one refracting face of a prism of angle `75^(@)`. It passes through the prism and is incident on the other face at the critical angle. If the refractive index of the material of the prism is `sqrt(2)`, the angle of incidence on the first face of the prism is

Answer 1

`mu=(1)/(sin C)`and`sqrt(2)=(1)/(sin C)`
or`sinC=(1)/(sqrt(2))` or `C=45^(@)`
now`A=r_(1)+r_(2)=r_(1)+C ( because r_(2)=C)`
or`75^(@)=r_(1)+45^(@) :.r_(1)=30^(@)`
further`mu=(sin i_1)/(sin r_(1))` or `sin i_(1)=muxxsinr_(1)=sqrt(2)xxsin 30^(@)`
or`sin i_(1)=sqrt(2)xx(1)/(2)=(1)/(sqrt(2)) rArri_(1)=45^(@)`