Question

A narrow beam of white light is incident on a sheet of quartz. The beam disperses in the quartz, with red light $(l\approx 400nm)$traveling at an angle of $26.3°$with respect to the normal and violet light $(l\approx 400nm)$ traveling at $25.7°$ . The index of refraction of quartz for red light is $1.45$. What is the index of refraction of quartz for violet light?

Short answer

The index of refraction of quartz for violet light is$1.48$.

Step-by-step solution

Given Information.

We have given that:

Red light = $(l\approx 700nm)$,

An angel = $26.3°$,

Normal violet light $(l\approx 400nm)$,

Traveling $25.7°$,

Index of refraction $1.45$.

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

Simply.

As we know:

${\lambda }_1\approx 700nm$

${\theta }_1=26.3°$

$n_2=1.45$

${\lambda }_2\approx 400nm$

${\theta }_2=25.7°$

Calculation

We need to find $n_2$by using formula:

$n_1\sin {\theta }_1=n_2\sin {\theta }_2$

$1.00\sin {\theta }_1=1.45\sin 26.3°$

$39.97°={\theta }_1$

$\Rightarrow 1.00\sin 39.97°=n_2\sin 25.7°$
$0.6423=n_{2}0.4336$
$n_2=\frac{0.6423}{0.4336}$

$n_2=1.48$