Question

The figure below shows the path of a beam of light through several layers with different indices of refraction. (Assume n₄ = 1.10.)

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,
• and n₄.

A ray of light starts from within the top medium and extends down and to the right at an angle θ₁ from 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 is θ₂.

(a) If θ₁ = 22.0°, what is the angle θ₂ of the emerging beam?
°

(b) What is the smallest incident angle θ₁ to have total internal reflection at the surface between the medium with n = 1.20 and the medium with n₄ = 1.10?
°

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Answer 1