Question

A sheet of glass has $n_{red}=1.52$ and $n_{violet}=1.55$. A narrow beam of white light is incident on the glass at $30°$. What is the angular spread of the light inside the glass?

Short answer

The angular spread of the light inside the glass is$0.39°$.

Step-by-step solution

Given Information.

We have given the refractive index$n_{red}=1.52$and$n_{violet}=1.55$.

We need to find the angular spread of light inside the glass.

Diagram

Calculation.

$n_1\sin {\sigma }_1=n_R\sin {\sigma }_R$

${\sigma }_R={\sin }^{-1}\left(\frac{n_1\sin {\sigma }_1}{n_R}\right)=19.20$

$n_1=1.00$

${\sigma }_1=30$

$n_R=1.52$

${\sigma }_V={\sin }^{-1}\left(\frac{n_1\sin {\sigma }_1}{n_V}\right)=18.82cw$

$n_1=1.00$

${\sigma }_1=30$

$n_V=1.55$

$\sigma ={\sigma }_R+{\sigma }_V=19.20°-18.82°=0.385°$

Here $n$is the refractive index and $\sigma$is the refractive angle.