Walker, Halliday & Resnick — Electromagnetic Waves: Problem 20

20 In Fig. 33-38a, a beam of light in material 1 is incident on a boundary at an angle \(\theta_1 = 40^\circ\). Some of the light travels through material 2, and then some of it emerges into material 3. The two boundaries between the three materials are parallel. The final direction of the beam depends, in part, on the index of refraction \(n_3\) of the third material. Figure 33-38b gives the angle of refraction \(\theta_3\) in that material versus \(n_3\) for a range of possible \(n_3\) values. The vertical axis scale is set by \(\theta_{3a} = 30.0^\circ\) and \(\theta_{3b} = 50.0^\circ\). (a) What is the index of refraction of material 1, or is the index impossible to calculate without more information? (b) What is the index of refraction of material 2, or is the index impossible to calculate without more information? (c) If \(\theta_1\) is changed to \(75^\circ\) and the index of refraction of material 3 is 2.4, what is \(\theta_3\)?