Answer
The angular spread of the light in the glass is $~~0.38^{\circ}$
Work Step by Step
We can find the angle $\theta_r$ of the red light after it enters the glass:
$n_r~sin~\theta_r = n_1~sin~\theta_1$
$sin~\theta_r = \frac{n_1~sin~\theta_1}{n_r}$
$\theta_r = sin^{-1}~(\frac{n_1~sin~\theta_1}{n_r})$
$\theta_r = sin^{-1}~(\frac{1.00~sin~30^{\circ}}{1.52})$
$\theta_r = sin^{-1}~(0.328947)$
$\theta_r = 19.20^{\circ}$
We can find the angle $\theta_r$ of the violet light after it enters the glass:
$n_v~sin~\theta_v = n_1~sin~\theta_1$
$sin~\theta_v = \frac{n_1~sin~\theta_1}{n_v}$
$\theta_v = sin^{-1}~(\frac{n_1~sin~\theta_1}{n_v})$
$\theta_v = sin^{-1}~(\frac{1.00~sin~30^{\circ}}{1.55})$
$\theta_v = sin^{-1}~(0.32258)$
$\theta_v = 18.82^{\circ}$
The angular spread of the light in the glass is $~~0.38^{\circ}$
