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 les 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

Refractive index for medium `M_(1)` si
`mu_(1)=(c)/(V_(1))=(3 xx10^(8))/(1.5 xx10^(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)`
For total internal reflection
`sin I ge sin C`
where `i=` angle of incidence
`C=` critical angle
But `sin C=(mu_(2))/(mu_(1))`
`sin ge (mu_(2))/(mu_(1)) ge (3//2)/(2) rArr i gt sin^(-1)((3)/(4))`.