392 Interference of Light WavesP37.31(a)The light reflected from the top of the oil film undergoes phasereversal. Since 145 133..>, the light reflected from the bottomundergoes no reversal. For constructive interference of reflectedlight, we then have212ntm=+FHGIKJλormntmm=+=+2122 1 45 280bgafaf. nm.FIG. P37.31Substituting for m gives:m=0 ,01620=nm (infrared)m=1 ,1541=nm (green)m=2 ,2325=nm (ultraviolet).Both infrared and ultraviolet light are invisible to the human eye, so the dominant color inreflected light is green.(b)The dominant wavelengths in the transmitted light are those that produce destructiveinterference in the reflected light. The condition for destructive interference upon reflectionis2ntm=ormnt==2812nm.Substituting for mgives:m=1 ,1812=nm (near infrared)
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