A visible light camera is placed with the objective pointing straight up while b

Question

A visible light camera is placed with the objective pointing straight up while below the surface of a still pond on which a 1.90 times 10-3 mm thickness of oil (n = 1.23) is floating. What is in nm the lowest wavelength visible light that will be enhanced when sun shines straight overhead? Use the range given by Wikipedia for the visible light spectrum (390 to 700 nm) How many visible light wavelengths are enhanced in this case? What is in nm the highest wavelength visible light that will be enhanced when sun shines straight overhead?

Explanation / Answer

Part A)

Apply 2nt = (m + .5)wavelength

We have to try m values from 0, 1, 2, 3, ... to find them all. Here is what we get...

2(1.23)(1.9 X 10-6) = (7.5)(wavelength)

wavelength = 623 nm

At m = 8, wavelength = 550 nm

At m = 9 wavelemgth = 492 nm

At m = 10 wavelength = 445 nm

At m = 11 wavelength = 406 nm

Beyond that we are outside the visible range

Thus the smallest wavelength = 406 nm

Part B)

The number of wavelengths = 5

Part C)

The highest one is the 623 nm

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