A Question About Thin Film Interference

Question

I learn in high school Physics class that when light travels from a medium to a more optically dense thin film, then the reflected rays will destructively interfere with each other. My questions are:

1. Will the interference of the rays being reflected off the top surface with the rays being reflected off the bottom of the film ever be constructive? Can you explain why it will be constructive?

2. Then in what situations will the rays destructively interfere with each other?

3. And if the reflected ray (the one reflected off the bottom of the thin-film) can be made so that it constructively interferes, how can it then be said that the bottom wave is always 180 degrees out of phase? Because to constructively interfere, you cannot be 180 degrees out of phase? So how can it be said that all reflected rays of the bottom of a more optically dense material will be 180 degrees out of phase with the reflected ray on top?

Thank you so much! This would immensely help my understanding of the topic! Please, though, try to answer the question at the level of a high school student.

Answer 1

Since the light is an EM wave, the type of interference between the light waves reflected from the top and bottom surfaces of a thin film (constructive, destructive or anything in between) depends on their relative phase, which, in turn, depends on the difference in the length of their paths at the point where they interfere and their wavelength inside the film.

The difference in the path lengths, in turn, depends on the thickness of the film, the angle of incidence (and reflection) and refractive indexes involved.

In addition, if the refractive index of a medium the light is coming from is smaller that the refractive index of a medium the light is going to, the phase of the reflected light will be flipped by $180^{\circ}$.

As an example, if, for a given thin film and angle of incidence, the difference in path lengths is equal to one wavelength and the reflections from both top and bottom surfaces undergoes $180^{\circ}$ phase shift, the interference will be constructive. If only one of the reflections underwent $180^{\circ}$ phase shift, the interference would be destructive.

Answer 2

For thin film "interference" to work the film thickness has to a certain thickness that depends on the wavelength of the light you are using, the index of the material and the angle of the light coming in. In sun glasses and especially in science and military, optical filters are composed of ~100 (often more) precisely vapour deposited layers to block or transmit many wavelengths at many angles.

The term interference is a classical explanation, good for high school, but a more advanced understanding is to know the photon has a wave function. (2 photons never cancel each other out, this is a violation of conservation of energy.) The wave function of light basically says that light likes to travel n multiples of its wavelength (where n is an integer) when it travels through any medium, a half wavelength is the worst case, hence light (of certain wavelength) cannot traverse the thin layer (of a certain thickness). When the layer is a similar thickness to the light wavelength it helps transmit the light, this is called an antireflection coating. Quantum mechanics tells us the interaction is probabilistic so once in a blue moon the photon may get thru. Yes there is both constructive and destructive happening in a classical way, but it really has to do with the intensity of the signal reflected at each boundary.