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

Snell’s law applies to all waves, not just light. The general form is sin(?1) /?1 = sin(?2) ⁄?2 where ??1 is the speed of the wave 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 important to the Navy is the effect of thermoclines in the ocean on the sound waves used by sonar systems to find submarines. The oceans typically have thermoclines (sharp changes in temperature, salinity, etc.) at depths of ?~200 ?. The speed of sound above the thermocline 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 coming from above? Explain your reasoning.

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

Expert Solution

genius_generous answered 9 months ago

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