A small coin is resting on the bottom of a beaker filled with a liquid. A ray of light from the coin travels up to the surface of the liquid and moves along its surface (see figure ).
How fast is the light travelling in the liquid ?

Options

A. `1.8xx10^(8)ms^(-1)`
B. `2.4xx10^(8)ms^(-1)`
C. `3.0xx10^(8)ms^(-1)`
D. `1.2xx10^(8)ms^(-1)`

Explanation

(a) As shown in figure, a light ray from the the coin will not emerge out of liquied if `i gt C`.
Therefore, minimum radius `R` corresponds to `i=C`. In `DeltaSAB`,
`R/h=tan C` or `R=htanC`
or `R=h/(sqrt(n^(2)-1))`

`[ :' sin C=1/n` and `tan C =(sin C)/(sqrt(1-sin^(2)C))]`

Given `R=3cm, h=4cm`
Hence `3/4=1/(sqrt(n^(2)-1))`
or `n^(2)=25/9` or `n=5/3`
But `n=c/v` or `v=c/n=(3xx10^(8))/(5//3)=1.8xx10^(8)ms^(-1)`