Chapter 35: The Wave Nature of Light; Interference Puzzles

Light is incident on a pair of interfaces as shown in the figure. We have learned that the reflected light is brighter when there is constructive interference between ray 1 (reflected at a) and ray 2 (reflected at b). If n₁ < n₂ < n₃, this occurs when the extra path length for ray 2 is an integral multiple of the wavelength. That is, when 2t = n.

Now, consider the light that is transmitted. This will be composed of ray 3 (never reflected) and ray 4 (reflected at b and c). This light will be brighter if there is constructive interference between rays 3 and 4.

Clearly, the extra path length for ray 4 compared to ray 3 is also 2t. Is there constructive interference for both the reflected and transmitted light? If so, does this violate conservation of energy? if there is no constructive interference, explain why not.

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