It is found that all the light rays sent from X towards Y reach point Z inside the glass sphere, as shown in figure. The speed of rays in glass cannot be

Options

A. `1.0xx10^(8) ms^(-1)`
B. `2.4 xx 10^(8) m s^(-1)`
C. `1.7 xx 10^(7) m s^(-1)`
D. `4xx10^(7) m s^(-1)`

Answer

B

Explanation

This is a case of total internal reflection.

Here `theta = 45^(@) and theta gt theta_(c)`
`rArr 45^(@) gt theta_(c) rArr sin 45^(@) gt sin theta_(c)`
`rArr (1)/(sqrt(2)) gt (1)/(mu) rArr mu gt sqrt(2) (" As "sin theta_(c) = (1)/(mu))`
`rArr (C )/(V) gt sqrt(2)`
`V lt (C )/(sqrt(2)) = (3xx10^(8))/(sqrt(2)) rArr V lt 2.1 xx 10^(8)`
Only (B) is not possible.