Hello, I have some practice problems and I would appreciate somehelp. Will rate

Question

Hello, I have some practice problems and I would appreciate somehelp. Will rate lifesaver. Thanks! Also, can youplease solve this with appropriate algebra instead ofcalculus. Thanks!

1) A loop of wire is dipped in soapy water and held so thatthe soap film is vertical. The top of the film appearsblack. Why? Below the black region there are coloredbands. Is the first band red or violet?

Explanation / Answer

refractive index of the soap water = n, thickness of the film =t path difference = 2nt + /2 at the top, t --> 0, = /2, so the destructiveinterference happens there for any wavelength, so black there. from top to bottom, t is increasing, when = 2nt + /2 =, or = 4nt, constructive interference happens andappears bright, the shortest wavelength appears bright first, orviolet is the first band.

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