Question

White light in air (n = 1.00) strikes crown glassat 40.00°. Find the difference in the refractedangles for red light (n = 1.520) and violet light (n= 1.538).

Answer 1

Given:

• White light:

n = 1.00

Angle, θ = 40.00°

• Red light:

n = 1.520

• Violet light:

n = 1.538

Let's find the difference in the refracted angles for red light an violet light.

To find the refracted angle for each light, apply the formula:

$n_1sin\theta_1=n_2sin\theta_2$

Thus, we have the following:

• Red light

$\begin{gathered} n_wsin\theta_w=n_rsin\theta_r \\ \\ \theta_r=sin^{-1}(\frac{n_wsin\theta_w}{n_r}) \\ \\ \theta_r=sin^{-1}(\frac{1.00sin40}{1.520}) \\ \\ \theta_r=sin^{-1}(0.4228866) \\ \\ \theta_r=25.02^o \end{gathered}$

The refracted angle for red light is 25.02°.

• Violet light.

We have:

$\begin{gathered} \theta_v=sin^{-1}(\frac{1.00sin40.00}{1.538}) \\ \\ \theta_v=sin^{-1}(0.4179373) \\ \\ \theta_v=24.70^o \end{gathered}$

The refracted angle for violet light is 24.70°.

The difference between the refracted angles will be:

$\begin{gathered} \theta=\theta_r-\theta_v \\ \\ \theta=25.02^0-24.70^o \\ \\ \theta=0.32^0 \end{gathered}$

Therefore, the difference in the refracted angles for red light and violet light is 0.32°.

• ANSWER:

0.32°