Question

A) State what is meant by the refraction of light. State Snell's law for refraction of light and also express it mathematically.

B) The refractive index of water with respect to air is $\frac{4}{3}$. If the speed of light in air is $3\times {10}^8$ m/s, find the speed of light in water.

Answer 1

A) $\text{Definition}$: Refraction is the bending of light when it travels from one medium to another.

$\text{Snell's Law}$: Snell's law states that the ratio of the sine of the angle of incidence ($sini$) to the sine of the angle of refraction ($sinr$) is constant. This constant is known as the refractive index of the second medium with respect to the first medium ($n_{21}$).

Mathematically, $n_{21}=\frac{n_2}{n_1}=\frac{sini}{sinr}$, where $n_1$ and $n_2$ are the absolute refractive index (refractive index with respect to the air medium) of medium- 1 and medium- 2 respectively.

B) Given:

The speed of light in air is $c=3\times {10}^{8}m/s$

The refractive index of water with respect to air is $n_{wa}=\frac{4}{3}$

The speed of light in water $v=?$

From the definition of refractive index, $n_{wa}=\frac{c}{v}$

$\therefore \frac{4}{3}=\frac{3\times {10}^8}{v}$

$\Rightarrow v=\frac{9\times {10}^8}{4}=2.25\times {10}^{8}m/s$

Thus, the speed of light in water is $2.25\times {10}^{8}m/s$