Nonreflective Coating and Emission Relation?

[taco01]

Hi all, I've been able to find the answers to most of my questions in these forums, but this time I was not able to. So here goes my first post:

I've been learning about thin film interference, and it all makes sense to me except for the correlation between destructive interference caused by non-reflective coating on a lens and the amount of light getting through to the lens. Here's the general setup shown in my textbook: (also attached)

From my understanding, the thickness of the film being 1/4 of the wavelength of some color of light causes the reflected light waves to interfere destructively. When the thickness of the film is 1/2 of the wavelength it results in constructive interference. In both cases, the light waves interact with the film and glass the same way aside from the phase changes they experience.

In the book it says "[non-reflective coating] also increases the net amount of light that is transmitted through the lens, since the light that is not reflected will be transmitted."
Doesn't the light only appear to be not reflected to us because it gets canceled out by another light that is out of phase by 1/2 wavelength relative to it? However, the statement above implies that this thin film material simply transmits more light and reflects less light than the glass or lens.

Please point out any mistakes in my logic or in the post (newbie here). Thank you in advance.

 

[Ibix]

Welcome to PF.

Doesn't the light only appear to be not reflected to us because it gets canceled out by another light that is out of phase by 1/2 wavelength relative to it?

What would "appear to be not reflected" mean, apart from "not reflected"? The light is there but you can't see it? I'm afraid the diagram is just rather poor, and is misleading you.

First of all, bear in mind the scale - the film is a $\lambda/4$ film, so around 100nm thick. So light is not even approximately striking in a single thin line like that. It's a wavefront many times wider than the whole picture, and even "incoherent light" will have some degree of coherence on the scale of the diagram. So a diagram based on rays isn't really the best for understanding this.

So - remember that the ray drawn there is just the direction of travel of a wide wavefront. Then the reflection from the lower surface of the film overlaps with the incoming wavefront at the top of the film and interferes destructively with its reflection. It also interferes constructively with its transmission.

So the diagram should not show anything coming up from the top surface. There's nothing in that direction - because the waves interfere with another part of the same wave. (Arguably it show something coming back down from the top surface, although that's not really fully consistent either - limitations of ray optics.) The rest is just conservation of energy - if the energy isn't being reflected it must be being transmitted.

 

[taco01]

Welcome to PF.
So - remember that the ray drawn there is just the direction of travel of a wide wavefront. Then the reflection from the lower surface of the film overlaps with the incoming wavefront at the top of the film and interferes destructively with its reflection. It also interferes constructively with its transmission.

So the diagram should not show anything coming up from the top surface. There's nothing in that direction - because the waves interfere with another part of the same wave. (Arguably it show something coming back down from the top surface, although that's not really fully consistent either - limitations of ray optics.) The rest is just conservation of energy - if the energy isn't being reflected it must be being transmitted.

Thank you for the response, but I'm still having trouble understanding how this situation is different than one with a reflective coating. Would the overall flow of the waves still not be the same? If we're talking about a single wave front and nonreflective coating- the first part of the wave (the right side from the perspective of the wave) makes contact with the film, part of it is reflected, part of it is transmitted. The transmitted portion continues on and is partially reflected and partially transmitted from the bottom surface of the film, and at this point the reflected part is in phase with the incoming waves (that have been transmitted through the top of the film) and out of phase with the outgoing waves (that have been reflected from the top of the film).

The situation with a reflective coating would simply be reversed - it would be out of phase with the incoming waves (that have been transmitted through the top of the film) and in phase with the outgoing waves (that have been reflected from the top of the film).

So the only difference I can see that could effect the amount of light transmitted is that the waves reflected from the bottom of a nonreflective film constructively interfere with the incoming waves that have been transmitted through the top of the film, while the waves reflected from the bottom of a reflective film destructively interfere with the incoming waves that have been transmitted through the top of the film. This would explain nonreflective film effectively transmitting more light than reflective film, so is this the right way of thinking about it?

(Arguably it show something coming back down from the top surface, although that's not really fully consistent either - limitations of ray optics.)

By "something coming back down" do you mean the rest of the wave front that's coming down as the first part of it is being transmitted and reflected? Thanks again.