soap bubble (n = 1.40) having a wall thickness of 130 nm is floating in air. (a)

Question

soap bubble (n = 1.40) having a wall thickness of 130 nm is floating in air.
(a) What is the wavelength of the visible light that is most strongly reflected?
=_______nm

(b) Explain how a bubble of different thickness could also strongly reflect light of this same wavelength.

=

(c) Find the two smallest film thicknesses larger than the one given that can produce strongly reflected light of this same wavelength.
=_________ nm
=______________nm

Explanation / Answer

In general, the condition for constructive interference in such situations is 2 n t = (m+0.5)*(landa) >>>> landa = (2 n t)/(m+0.5) (t = thickness) landa = (2 n t)/(m+0.5) = 2*1.40*130/(m+0.5) = 364/(m+0.5) m = 0 >>>> landa = 364/(0+0.5) = 728 nm (this is visible) m = 1 >>>> landa = 364/(1+0.5) = 242.67 nm (this is not visible) >>>>> answer is landa = 728 nm -------------------------------------------------------------------- b) According to the 2nt'=(m+0.5)*landa, if we change the thickness of the bubble, the path difference will change too. If we put m=1, then we can find another thickness for bubble with constructive interference. -------------------------------------------------------------------- c) t' = new thickness 2nt'=(m+0.5)*landa >>>> t' = (m+0.5)*landa/(2n) = (m+0.5)*728/(2*1.40) = (m+0.5)*260 for m=1 >>>>> thickness = (1+0.5)*260 = 390 nm for m=2 >>>>> thickness = (2+0.5)*260 = 650 nm

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