Question 1:
What is the smallest thickness of a soap film (n=1.33) that would appear black if illuminated with 470nm light? Assume there is air on both sides of the soap film.

i used t = wavelength/2n to find t = 177nm

Part 2 asks : What are two other possible thicknesses for the film to appear black?

i used t = 3(wavelength)/2n and 5(wavelength)/2n but thats not the right answer so what am i doing wrong?

Part 3 asks: If the thickness was much less than , why would the film also appear black?


Question 2:

A lens appears greenish yellow (wavelength = 570nm is strongest) when white light reflects from it. What minimum thickness of coating (n=1.26) do you think is used on such a glass (n=1.53) lens?


once again i used t = wavelength/2n

i found n to be (1.26*1.53)^1/2

This got the wrong answer. What am i doing wrong?

Any help is greatly appreciated.
Thank You

Question 1.

I am not an expert, but to me it seems the film will appear black when waves interfere destructively. This will first occur when the path difference is half a wavelength . Thus twice the film thickness (the ray goes in and out) should be equal to half the wavelength (i.e. "crest" comes on top of a "trough") or

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where lambda is the wavelength in the film.

The wavelength in the film will be different. It should increase i think so

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Part 2

For the subsequent black occurences,2t will be 3 lambda/2 and
5 lambda/2 as the addition of one wavelength still makes "crest" comes on top of a "trough".


Part 3

For the film to look bright, constructive interference has to occur which means that the path difference 2t should be lambda at least, whereas the film thickness here is much less.

Question 2:

A lens appears greenish yellow (wavelength = 570nm is strongest) when white light reflects from it. What minimum thickness of coating (n=1.26) do you think is used on such a glass (n=1.53) lens?

This can be soved as before, finding the wavelength in the n = 1.26 coating.

2t must now be equal to the wavelength in the coating for constructive interference.

The n of glass is given to consider phase change on reflection.

When reflection occurs from a medium of higher refractive index, there is a phase change of 180. However both the rays

1) reflecting from the surface of the coating after coming thru air and

2) reflecting from the surface of the lens after travelling thru the coating

encounter a higher refractive index and both are phase shifted by 180 and hence this need not be considered.