Question

Light having a speed in vacuum of3.0�108m/s enters a liquid of refractive index 2.0. In this liquid, its speed will be A)0.75�108m/sB)6.0�108m/sC)1.5�108m/sD)3.0�108m/sE)None of the above choices are correct.

Answer 1

Right answer: $1.5({10}^{8})m/s$

The Absolute Refractive index $n$ is the quotient of the speed of light in vacuum $c$ and the speed of light in the medium whose index is calculated $v$, as shown in the expression below:

$n=\frac{c}{v}$     (1)

This is a dimensionless value.

If we know that:

$c=3({10}^{8})m/s$

$n_{1}=1$ is the refractive index in vacuum

$n_{2}=2$ is the refractive index in the liquid

We can use equation (1), with the values of $n_{2}$ and $c$ to calculate $v_{liquid}$, which is the velocity of light in this medium:

$n_{2}=\frac{c}{v_{liquid}}$     (2)

$v_{liquid}=\frac{c}{n_{2}}$     (3)

$v_{liquid}=\frac{3({10}^{8})m/s}{2}$    (4)

Finally:

$v_{liquid}=1.5({10}^{8})m/s$>>>>This is the speed of light in the liquid.

Therefore the correct option is c.