Question

Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is `mu`, a ray, incident at an angle `theta`, on the face AB would get transmitted through the face AC of the prism provided:

A. `theta gtsin^(-1)[musin(A-sin^(-1)((1)/(mu)))]`
B. `theta ltsin^(-1)[musin(A-sin^(-1)((1)/(mu)))]`
C. `theta gtcos^(-1)[musin(A-sin^(-1)((1)/(mu)))]`
D. `theta ltcos^(-1)[musin(A-sin^(-1)((1)/(mu)))]`

Answer 1

For transmission `r_(2)lt i_(c)`
`A-r_(1)lti_(c)`
`sin (A-r_(1))lt sin i_(c)`
`sin(A-r_(1))lt(1)/(mu)`
`A-r_(1)lt sin^(-1)((1)/(mu))`
`r_(1)gtA-sin^(-1)((1)/(mu))`
`sin r_(1)gt sin [A-sin^(-1)((1)/(mu))]`
`therefore sin r_(1)=(sin theta)/(mu)`
`(sintheta)/(mu)gt sin[A-sin^(-1)((1)/(mu))]`
`theta gt sin^(-1) [mu sin {A-sin^(-1)((1)/(mu))}]`