Three sheets of plastic have unknown indices of refraction. Sheet 1 is placed on

Question

Three sheets of plastic have unknown indices of refraction. Sheet 1 is placed on top of sheet 2, and a laser beam is directed onto the sheets from above so that it strikes the interface at an angle of 26.5 with the normal. The refracted beam in sheet 2 makes an angle of 30.6 with the normal. The experiment is repeated with sheet 3 on top of sheet 2, and with the same angle of incidence, the refracted beam makes an angle of 36.0 with the normal. If the experiment is repeated again with sheet 1 on top of sheet 3, what is the expected angle of refraction in sheet 3? Assume the same angle of incidence.

Explanation / Answer

From experiment 1 (sheet 1/sheet 2) we know that:
n1 * sin(26.5) = n2 * sin (30.6)

From experiment 2 (sheet 3/sheet 2) we know that
n3 * sin(26.5) = n2 * sin(36)

The equation for the experiment in question is
n1 * sin(26.5) = n3 * sin ?
and we want to solve for ?.

From the first two equations we have that
n1/n3 = sin(30.6)/sin(36)

Plugging this into the equation we are trying to solve we get
sin(30.6)/sin(36)*sin(26.5) = sin ?
? = arcsin (sin(30.6)/sin(36)*sin(26.5))

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