MCAT Physics Question 110: Answer and Explanation

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Question: 110

5. A ray of light (f = 5 × 1014 Hz) travels from air into crystal into chromium. If the indices of refraction of air, crystal, and chromium are 1, 2, and 3, respectively, and the incident angle is 30°, then which of the following describes the frequency and the angle of refraction in the chromium?

  • A. 5 × 1014 Hz; 9.6°
  • B. 5 × 1014 Hz; 57°
  • C. 1.0 × 1010 Hz; 9.6°
  • D. 1.0 × 1010 Hz; 57°

Correct Answer: A

Explanation:

This question contains two parts—we have to determine the frequency and the angle of refraction of the light ray. The first part, however, is straightforward because the frequency of a light ray traveling from one medium to another does not change. Because the frequency must be 5 × 1014 Hz, we can eliminate choices (C) and (D). For the angle of refraction, we can either calculate it or determine it using logic. First, the light ray goes from air into crystal; that is, from a low index of refraction to a higher one. According to Snell's law, the angle of refraction will be smaller than the incident angle (closer to the normal). When the light ray moves from crystal to chromium, it again goes from a lower index of refraction into a higher one, thus making the angle of refraction even smaller, eliminating choice (B). This question could also be answered by calculation using Snell's law, but the calculations are time consuming and unnecessary.

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