Question

A narrow beam of white light is incident on a sheet of quartz. Thebeam disperses in the quartz, with red light (λË700nm)traveling at an angle of 26.3o with respect to thenormal and violet light (λË400nm) traveling at25.7o. The index of refraction of quartz for red lightis 1.45. What is the index of refraction of quartz for violetlight?

Answer 1

Answer:

The index of refraction of quartz for violet light is 1.47.

Explanation:

It is given that, a narrow beam of white light is incident on a sheet of quartz.

The beam disperses in the quartz, with red light at an angle, $\theta_r=26.3^{\circ}$ wrt to the normal and violet light traveling at an angle of $\theta_v=25.7^{\circ}$

The index of refraction of quartz for red light is 1.45.

We need to find the index of refraction of quartz for violet light.

Using Snell's law of red light as follows :

$\mu_a\sin\theta_i=\mu_r\sin\theta_r$

Here,

$\mu_a$ is the refractive index of air

$\theta_i$ is the angle of incidence

We can find the value of angle of incidence as follows :

$\sin\theta_i=\dfrac{\mu_r \sin\theta_r}{\mu_a}\\\\\sin\theta_i=\dfrac{1.45\times \sin(26.3)}{1}\\\\\theta_i=\sin^{-1}(0.642)\\\\\theta_i=39.79^{\circ}$

Now again using Snell's law for violet light as follows :

$\mu_a\sin\theta_i=\mu_v\sin\theta_v\\\\\mu_v=\dfrac{\mu_a\sin\theta_i}{\sin\theta_v}\\\\\mu_v=\dfrac{1\times \sin(39.79)}{\sin(25.7)}\\\\\mu_v=1.47$

So, the index of refraction of quartz for violet light is 1.47.