Referring to Figure 1. The longest wavelength that will produce a minimum of int

Question

Referring to Figure 1. The longest wavelength that will produce a minimum of intensity in the thin film of thickness t = 214nm is Lambda = 749nm when the thin film is in air: Find the index of refraction of the material the thin film is made from. Find the next two wavelengths that will also produce a minimum of intensity in this thin film. Find the two longest wavelengths that will produce a maximum of intensity in this thin film. Figure I: When light is incident on the thin film of thickness t = 214 nrn and unknown index of refraction n, it is found that the longest wavelength that will produce a minimum of intensity is Lambda = 749nm.

Explanation / Answer

Part A)

Apply 2nt = m(wavelength) for this scenario

2(n)(214 X 10-9) = 1(749 X 10-9)

n = 1.75

Part B)

The next two wavelengths will be when m is 2 and 3...

2(1.75)(214 X 10-9) = 2(wavelength)

wavelength = 374.5 nm

And...

2(1.75)(214 X 10-9) = 3(wavelength)

wavelength = 249.7 nm

Part C)

For the maximum, the formula changes to

2nt = (m + .5)(wavelength), so the two longest will be when m = 0 and m = 1...

2(1.75)(214 X 10-9) = .5(wavelength)

wavelength = 1498 nm

And...

2(1.75)(214 X 10-9) = 1.5(wavelength)

wavelength = 499.3 nm

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