The diagram shows light incident from above on a film of thickness d. Each of th

Question

The diagram shows light incident from above on a film of thickness d. Each of the three materials in the figure can be chosen to be air, with index of refraction n=1.00, water, with index n=1.33, or glass, with index n=1.50. Under which of the following conditions will the reflected light be completely or nearly eliminated by interference?
(lambda2 refers to the wavelength of the light inside the thin film.)
(Note: In the case that d<<lambda2, you can assume the thickness is so small that the travel distance in material 2 has negligible affect on the phase of the wave. Treat this as if the two interfaces are almost right on top of each other.)

True False d=lambda2/4, material 1 is glass, 2 is water, 3 is glass.
True False  d=lambda2/4, material 1 is air, 2 is water, 3 is glass.
True False  d=lambda2/4, material 1 is water, 2 is glass, 3 is air.
True False  d=lambda2/2, material 1 is glass, 2 is water, 3 is glass.
True False  d=lambda2/2, material 1 is air, 2 is water, 3 is glass.

Explanation / Answer

relevant equation: 2*n*d*sin? = (m-(1/2))*? m=integer ?=wavelength n=index of refraction = speed of light in vacuum/speed of light in medium d= thickness

We are looking for places where the refracted light is eliminated by interference, so we are looking for destructive interference.

Destructive if Path-length Difference(PLD) 2nd= (m + (1/2))? when the sources are exactly in phase.

Destructive if Path-length Difference(PLD) 2nd = m? when the sources are exactly out of phase.

There are phase reversals when it is reflecting of a higher n.

1) d=lambda2/4, material 1 is air(n=1.00), 2 is water, 3 is glass. True because There would be 2 phase reversals [1 between air and water and the other between water and glass] So the wavelength would be exactly in phase which means it needs to have PLD of

(1/2)? d=2?/4 (2?/4) = (1/2)? (2/4)?= (1/2)? (1/2)?= (1/2)? ?

2) d=lambda2/2, material 1 is air(n=1.00), 2 is water(n=1.33), 3 is glass(n=1.50). False because There would be 2 phase reversals [1 between air and water and the other between water and glass] So the wavelength would be exactly in phase which means it needs to have PLD of

(1/2)? d=2?/2 2?/2 = (1/2)? (2/2)? = (1/2)??

similarly others can be done.

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