Answer to Question #140402 in Physics for victory

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-cm-thick plate of quartz glass. The indices of refraction for these wavelengths are 1.4636 and 1.4561, respectively. If the angle of incidence is 70degree, 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

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