The speed of light in media `M_1` and `M_2` are `1.5 xx 10^8 m//s and 2.0 xx 10^8 m//s` respectively. A ray of light enters from medium `M_1` to `M_2` at an incidence angle `i`. If the ray suffers total internal reflection, the value of `i` is.

Options

A. Equal to `sin^(-1)((2)/(3))`
B. Equal to or less than `sin^(-1) ((3)/(5))`
C. Equal to or greater than `sin^(-1)((3)/(4))`
D. Less than `sin^(-1) ((2)/(3))`

Answer

C

Explanation

Given , `v_(1) = 1.5 xx 10^(8) m//s , v_(2) = 2.0 xx 10^(8) m//s`
Refractive index for medium `M_(1)` is
`mu_(1) = ( c)/(v_(1)) = (3 xx 10^(8))/(1.5 xx 10^(8)) = 2`
Refractive index for medium `M_(2)` is
`mu_(2) = ( c)/(v_(2)) = (3 xx 10^(8))/(2.0 xx 10^(8)) = (3)/(2)`
If `i` is the angle of incidence and `C` is the critical angle then for total internal reflection
`sin i ge sin C`
But `sin C = mu_(2)//mu_(1)`
`:. sin i ge (mu_(2))/(mu_(1)) ge (3//2)/(2) or i ge sin^(-1)((3)/(4))`