Question

A ray of light consisting of blue light of wavelength 480 nm
and red light of wavelength 670 nm is incident on a 4.00-cmthick plate of quartz glass. The indices of refraction for these
wavelengths are 1.4636 and 1.4561, respectively. If the angle of
incidence is 70°, what is the separation between the two beams
when they emerge from the opposite face of the plate?

Answer 1

We need to find the angular separation between the refracted red and refracted blue beams while they are in the glass. Using Snell's law for red light as

$$\theta_2=\arcsin{\frac{n_2}{n_1}\sin{70}}\\\theta_2=\arcsin{\frac{1}{1.4561}\sin{70}}=40.19\degree$$

$$\theta_2'=\arcsin{\frac{n_2}{n_1'}\sin{70}}\\\theta_2'=\arcsin{\frac{1}{1.4636}\sin{70}}=39.94\degree$$

The angular separation between the refracted red and refracted blue beams while they are in the glass is

$$\theta_2-\theta_2'=40.19-39.94=0.25\degree$$