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:

Options

A. `theta gt cos^(-1) [mu"sin"(A + sin^(-1)((1)/(mu)))]`
B. `theta lt cos^(-1) [mu"sin"(A + sin^(-1)((1)/(mu)))]`
C. `theta gt sin^(-1) [mu"sin"(A - sin^(-1)((1)/(mu)))]`
D. `theta lt sin^(-1) [mu"sin"(A - sin^(-1)((1)/(mu)))]`

Answer

C

Explanation

For all light to come out from face AC angle of emergence e = 90
Apply Snell's law at face AC
`mu "sin" r_(2) = 1 "sin"e`
`r_(2) = sin^(-1)((1)/(mu)) " " ` (if e = 90)
`r_(1) = A - sin^(-1)((1)/(mu)) " " (therefore r_(1) + r_(2) = A)`
Apply Snell's law at face AB
`1 "sin" theta = mu"sin"(r_(1))`
`theta = sin^(-1) (mu "sin"(A - sin^(-1)((1)/(mu)))`
for all light transmitted through AC , `e lt 90^(@)`
`implies theta gt sin^(-1) (mu "sin"(A - sin^(-1)((1)/(mu)))`