Light takes `t_(1)` second to travel a distance x cm in vacuum and the same light takes `t_(2)` second to travel 10x cm in medium. The critical angle for the corresponding medium is

Options

A. `sin^(-1) ((10t_(1))/(t_(2)))`
B. `sin^(-1) ((t_(1))/(10 t_(2)))`
C. `sin^(-1) ((t_(1))/(10 t_(2)))`
D. `sin^(-1) ((10 t_(2))/(t_(1)))`

Answer

A

Explanation

Speed of light in vacuum `v_(a) = (x)/(t_(1))`
Speed of light in the medium `v_(m) = (10x )/(t_(2))`
`therefore` R.I. of the medium `(""_(a) n_(m))`
`= (v_(a))/(v_(m)) = (x)/(t_(1)) xx (t_(2))/(10 x) = (t_(2))/(10 t_(1))` and the R.I. of the medium `""_(a) n_(m) = (1)/(sin C)`
`therefore sin C = (1)/(""_(a) n_(m)) = (1)/((t_(2))/(10 t_(1))) = (10 t_(1))/(t_(2))`
`therefore C = sin ^(-1) ((10t_(1))/(t_(2)))`