In vacum, to travel distance d, light takes time t and in medium to travel distance 5d, it takes time T. The critical angle of the medium is

Options

A. `sin^(-1)""((5T)/(t)) `
B. `sin^(-1)""((5t)/(3T)) `
C. `sin^(-1)""((5t)/(T)) `
D. `sin^(-1)""((3t)/(5T)) `

Answer

C

Explanation

In vacuum , ` v_a=(d)/t` and in the medium, `v_m=(5d)/T`
`:.` R.I. of the medium `""_a n_m=(v_a)/(v_m)=(t)/((5d)/(T))=(T)/(5t)`
If C is the critical angle , then the R.I. of the medium , `""_(a)n_(m)=(1)/( sin C )`
`:. (T)/(5t)=(1)/(sin C) :. sin C =(5t)/(T)`
`:. C =sin^(-1)""((5t)/(T))`