A horizontal cylindrical tank 2.28 m in diameter is half full of water. The spac

Question

A horizontal cylindrical tank 2.28m in diameter is half full of water. The space above the water is filled with a pressurized gas of unknown refractive index. A small laser can move along the curved bottom of the water and aims a light beam toward the center of the water surface (the figure (Figure 1) ). You observe that when the laser has moved a distance S = 1.07m or more (measured along the curved surface) from the lowest point in the water, no light enters the gas.

Part A)

What is the index of refraction of the gas?

Part B)

How long does it take the light beam to travel from the laser to the rim of the tank when S>1.07m ?

Part C)

How long does it take the light beam to travel from the laser to the rim of the tank when S<1.07m ?

Explanation / Answer

) Critical angle of the water/gas interface = 360 x 1.07/(pi x 2.28) = 53.78

Taking ref. index of water = 1.33, we have:

sin 53.78 = n/1.33 where n is the refractive index of the gas

n = 1.073

2) When total internal reflection occurs, distance travelled = 2.28m which is the diameter of the tank.

Time needed = 2.28/[(3 x 10^8)/1.33] = 10.108 ns

3) For the first 1.14 m, time needed = 1.14/[(3 x 10^8)/1.33] s

For the last 1.14 m, time needed = 1.14/[(3 x 10^8)/1.073] s

Hence total time = 9.1314 ns

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