A soap bubble is essentially a very thin film of water (n=1.33)surrounded by air

Question

A soap bubble is essentially a very thin film of water (n=1.33)surrounded by air. The colors that you see in soap bubbles areproduced by interference. a) derive an expression for thewavelengths c for which constructiveinterference causes a strong reflection from a soap buubble ofthickness d (hint: think about the reflection phase shifts at bothboundaries) b) what visible wavelengths of light are strongly reflectedfrom a 390 nm thick soap bubble? What color would such a soapbubble appear to be?
a) derive an expression for thewavelengths c for which constructiveinterference causes a strong reflection from a soap buubble ofthickness d (hint: think about the reflection phase shifts at bothboundaries) b) what visible wavelengths of light are strongly reflectedfrom a 390 nm thick soap bubble? What color would such a soapbubble appear to be?

Explanation / Answer

The path difference between the two light waves that arereflected from the top and bottom surfaces of a sope film isresponcible for the interference of light                  x= 2dsin + /2 = wave length d = thickness of the film = angle of incidence /2 = phase shift that takes place at the light raytop suface of the silm after reflection. for constuctive interference                   2dsin + /2 = 0 or n.........................eq1       and for distructiveinterference                 2dsin + /2 = n/2..........................eq2 b) in the abve equation1 taking wavelength = 390nm       constructive interference willbe observed only when eq1 is satisfied for given values of d and .               

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