SAT Subject Physics Practice Question 221: Answer and Explanation

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Question: 221

67. Consider two adjacent transparent media. The speed of light in Medium 1 is v1, and the speed of light in Medium 2 is v2. If v1 < v2, then total internal reflection will occur at the interface between these media if a beam of light is

A. incident in Medium 1 and strikes the interface at an angle of incidence greater than sin–1(v1/v2).
B. incident in Medium 1 and strikes the interface at an angle of incidence greater than sin–1(v2/v1).
C. incident in Medium 2 and strikes the interface at an angle of incidence greater than sin–1(v1/v2).
D. incident in Medium 2 and strikes the interface at an angle of incidence greater than sin–1(v2/v1).
E. Total internal reflection is impossible in the situation described.

Correct Answer: A

Explanation:

In order for total internal reflection to occur, the beam must be incident in the medium with the higher index of refraction and strike the interface at an angle of incidence greater than the critical angle. Since v1 < v2, the refractive index of Medium 1, n1 = c/v1, must be greater than the index of Medium 2 (n2 = c/v2), and the critical angle is θcrit = sin−1 (n2/n1) = sin−1 (v1/v2).

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