Refractive index of a prism is `sqrt(7//3)` and the angle of prism is `60^(@)`. The minimum angle of incidence of a ray that will be transmitted through the prism is

Options

A. `30^(@)`
B. `45^(@)`
C. `15^(@)`
D. `50^(@)`

Answer

a.

Explanation

`r_(2) lt theta_(c),A-r_(1) lt theta_(c)`
`r_(1) gt A-theta_(c)`
`sinr_(1) gt sin(A-theta_(c))`
`(sini)/(mu)gtsin(A-theta_(c))`
`sinigtmu(sinAcostheta_(c)-cosAsintheta_(c))`
`sqrt((7)/(3))(sqrt(3)/(2)sqrt(1-(3)/(7))-sqrt((3)/(7)))=1-(1)/(2)=(1)/(2)`
`sinigt(1)/(2)` or `igt30^(@)`