Question

A beam of white light enters a transparent material. Wavelengths for which the index of refraction is n are refracted at angle u2. Wavelengths for which the index of refraction is n + dn, where dn V n, are refracted at angle u2 + du.

a. Show that the angular separation of the two wavelengths, in radians, is du = -1dn/n2 tan u2.

b. A beam of white light is incident on a piece of glass at 30.0°. Deep violet light is refracted 0.28° more than deep red light. The index of refraction for deep red light is known to be 1.552. What is the index of refraction for deep violet light?

Short answer

The angular separation of the two wavelengths, in radians, is du = -1dn/n2 tan u2.

Step-by-step solution

Part (a) step 1 : Given Information

The angular separation of the two wavelengths, in radians, is du = -1dn/n2 tan u2.

part (a) step 2 : Calculation

Part (b)  step 1 : Given information

The index of refraction for deep violet light.

Part (b) step 2 : Simplify