A small coin is resting on the bottom of a beaker filled with a liquid. A ray of light from the coin travels upto the surface of the liquid and moves along its surface How fast is the light travelling the liquid ?

Options

A. `1.8 xx 10^8 ms^(-1)`
B. `2.4 xx 10^8 ms^(-1)`
C. `3.0 xx 10^8 ms^(-1)`
D. `1.2 xx 10^8 ms^(-1)`

Answer

A

Explanation

As shown in figure , a light ray from the coin will not emerge out of liquid if, `i gt c`
therefore , minimum radius R corresponds to `i = c`

In `Delta DAB R/h = tan c implies R = h tan c implies R = h/(sqrt(mu^2 - 1))`
Given `R = 3 cm ` and `h = 4 cm`
`therefore 3/4 = 1/(sqrt(mu^2 - 1)) implies mu^2 = 25/9 implies mu = 5/3`
But
`mu = c/v implies v = c/mu = (3 xx 10^5)/(5//3)`
`= 1.8 xx 10^8 ms^(-1)`