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) m//s`
B. `2.4 xx10^(8)m//s`
C. `3.0 xx10^(8)m//s`
D. `1.2xx10^(8)m//s`

Answer

A

Explanation

Critical angle is the angle of incidence is denser medium for which the angle of refraction in rarer medium is `90^(@)`.
As shown in the figure, a light ray from the coin will not emerge out of liquid, if `igtC`.
Therefore, minimum radius `R` corresponds to `i=C`. In `DeltaSAB,`
`(R)/(h)=tan C`
or`R=htanC`
or `R=(h)/(sqrt(mu^(2)-1))`
Given, `R=3cm, h=4cm`
Hence `(3)/(4)=(1)/(sqrt(mu^(2)-1))`
or `mu^(2)=(25)/(9)`or `mu=(5)/(3)`
But `mu=(c)/(v)` or `v=(c)/(mu)=(3xx10^(8))/(5//3)`
`=1.8xx10^(8)m//s`