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 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)/(u)))]`.

Answer

A

Explanation

From Snell.s law,
`(sin theta)/(sinr)=mu" …(i)"`
`(sinr.)/(sini)=(1)/(mu)`
`rArr" "(sinr.)/(sin90^(@))=(1)/(mu)`
`rArr" "sinr.=(1)/(mu)`
`rArr" "r.=sin^(-1)((1)/(mu))`
From equation (i)
The ray will be transmitted from the prism under the following conditions :
`(sin theta)/(sin r) gt mu`
`because" "A=r+r.`
`r=A-sin^(-1)((1)/(mu))`
`sin theta gt mu sin [A-sin^(-1)((1)/(mu))]`
`theta gt sin^(-1)[mu sin (A-sin^(-1)((1)/(mu)))]`