Answer to Question #137226 in Mechanics | Relativity for Jessica

Question

A ray of sunlight is passing from diamond into crown glass; the angle of incidence is 25.70°. The indices of refraction for the blue and red components of the ray are: blue (ndiamond = 2.444, ncrown glass = 1.531), and red (ndiamond = 2.410, ncrown glass = 1.520). Determine the angle between the refracted blue and red rays in the crown glass.

Answer 1

First, calculate the angle of refraction for blue in glass:

$$\theta_{gb}=\text{arcsin}\bigg(\frac{n_{db}}{n_{gb}}\cdot\text{sin}\theta_d\bigg)=43.8°.$$

Calculate the angle of refraction for red in glass:

$$\theta_{gr}=\text{arcsin}\bigg(\frac{n_{dr}}{n_{gr}}\cdot\text{sin}\theta_d\bigg)=43.4°.$$

The angle between the refracted blue and red rays in the crown glass is

$$\delta=\theta_{gb}-\theta_{gr}=0.40°$$