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. `2.4 xx 10^(8) m//s`
B. `3.0 xx 10^(8) m//s`
C. `1.2 xx 10^(8) m//s`
D. `1.8 xx 10^(8) m//s`

Answer

D

Explanation

From figure, `sin C = (3/sqrt((4)^(2) + (3)^(2)) = 3/5`
where C is the critical angle. Also, `sin C = ""^(l)mu_(g)`
`sin C = 1/(""^(a)mu_(l)) ["since" ""^(l)mu_(a) = 1/(""_(a)mu_(l))]`
Also, `""^(a)mu_(l) = ("velocity of light in air (c)")/("velocity of light in liquid (v)")`
`therefore sin C = v/c = v/(3 xx 10^(8))`
or `v = 3 xx 10^(8) xx 3/5 = 1.8 xx 10^(8) ms^(-1)`