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Snell’s law applies to all waves, not just light. The general form is sin(?1) /?1 =...

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Physics

Snell’s law applies to all waves, not just light. The generalform is sin(?1) /?1 = sin(?2) ⁄?2 where ??1 is the speed of thewave in medium 1, and ?2 is the speed of the wave in medium 2.

A. Starting with Snell’s law in its familiar form ??1 sin(?1) =?2 sin(?2) and the definition of the index of refraction ?≡ ? ⁄ ?for light, derive the general form above.

One of the applications of Snell’s law that is pretty importantto the Navy is the effect of thermoclines in the ocean on the soundwaves used by sonar systems to find submarines. The oceanstypically have thermoclines (sharp changes in temperature,salinity, etc.) at depths of ?~200 ?. The speed of sound above thethermocline is ? = 1510 ?/? and the speed below is ?= 1500 ?/?.

B. For which direction is total internal reflection possible?For sound coming from below the thermocline, or for sound comingfrom above? Explain your reasoning.

C. What is the critical angle ?? for total internal reflectionin this case?

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