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 pf the prism provided.

Options

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

Answer

A

Explanation

For transmission, `r_2 lt i_c` (Critical angle)
`thereforeA-r_1 lt i_c` `(because r_1+r_2=A)`
`thereforesin(A-r_1) lt sini_c`
`therefore sin(A-r_1) lt (1)/(mu)` `(because sini_c=1/mu)`
`therefore A-r_1 lt sin^(-1)(1/mu)`
`thereforer_1 gt A-sin^(-1)(1/mu)`
`thereforesinr_1 gt sin[A-sin^(-1)(1/mu)](because sin theta=mu sin r_1)`
`therefore(sin theta)/(mu) gt sin[A-sin^(-1)((1)/(mu))]`
`therefore sin theta gt mu sin(A-sin^(-1)""(1)/(mu))`
`therefore theta gt sin^(-1)(musin(A-sin^(-1)""(1)/(mu)))`