The figure below shows the path of a beam of light through several layers with different indices of refraction. (Assumen₄=1.04.)An illustration shows four media, represented as long, horizontal rectangles, arranged one on top of the other such that each medium has a higher index of refraction than the medium below it. The indexes of the four media from top to bottom are as follows:

• 1.60,
• 1.40,
• 1.20,
• andn₄.

A ray of light starts from within the top medium and extends down and to the right at an angle₁from the vertical. The ray refracts through all subsequent materials below it, with each transition to a lower material bending the ray farther and farther from the vertical. Its angle of refraction as the ray emerges into the fourth medium is₂.(a) If₁=32.0,what is the angle₂of the emerging beam? (b) What is the smallest incident angle₁to have total internal reflection at the surface between the medium withn= 1.20and the medium withn₄=1.04?