A tank holds a layer of oil, 1.58 m thick, which floats on a layer of syrup that

Question

A tank holds a layer of oil, 1.58 m thick, which floats on a layer of syrup that is 0.66 m thick. Both liquids are

clear and do not intermix. A ray, which originates at the bottom of the tank on a vertical axis, crosses the

oil-syrup interface at a point 0.90 m from the axis. The ray continues and arrives at the oil-air interface, 2.00 m

from the axis and at the critical angle. In the figure, the index of refraction of the syrup is closest to:

The answer is 1.24. Please show all formulas and work. Thanks!

Explanation / Answer

We only need to deal with the syrup to find the horizontal displacement of the light as it travels through the oil:

Horizontal displacement = 2.0m - 0.9m = 1.1m

The Vertical displacement is the thickness of the oil, which is 1.83m.

The angle of this beam is:

Arctan( 1.1m / 1.83m )
= 31.01

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