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.)

TrueFalse d=lambda₂/4, material 1 is water, 2 is glass, 3 is air.
TrueFalse d=lambda₂/2, material 1 is glass, 2 is air, 3 is water.
TrueFalse d<<lambda₂, material 1 is air, 2 is glass, 3 is air.
TrueFalse d=lambda₂/4, material 1 is glass, 2 is water, 3 is glass.
TrueFalse d=lambda₂/4, material 1 is air, 2 is water, 3 is glass.

Answer 1

Solution False dMaterial 1 is water, 2 is glass, and 3 is air The ray undergoes 180° phase change upon reflection, ray 1 from the upper surface and ray 2 has not any phase change. The net change in phase due to reflection therefore 180° and the condition for a reflection minimum requires a path difference of λ hence 4 True dMaterial 1 is glass, 2 is air, and 3 is water Ray 2 undergoes a 180° phase change upon reflection. Ray 1 has not any phase change False d <<λ2 Material 1 is air. 2 is glass, and 3 is air

False dMaterial 1 is glass, 2 is water, and 3 is glass. 4 True Material s air, 2 is water, and 3 is glass. 4 Both the rays undergo a 180° phase change upon reflection, ray 1 from the upper surface, ray 2 from lower surface. Therefore net change in phase due to reflection is zero. And the condition for a reflection minimum requires a path difference of λ hence 2d 2. 4