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So here's the question:-

A thin film of transparent material of refractive index $1.52$ and thickness $0.42\ \rm \mu m$ forms a thin coating on glass of refractive index $1.60$. It is viewed by reflection with white light at normal incidence. What visible wavelength in vacuum is most strongly reflected?

Please could someone explain the meaning (I am not asking for an answer) as this question seems quite ambiguous.

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    $\begingroup$ The question is testing your understanding of the interference of light reflected at the two interfaces. $\endgroup$
    – my2cts
    Sep 30, 2018 at 8:30

2 Answers 2

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This question is about thin film reflection - which wavelengths would reflect better at certain incidences for certain film thickness, which is normally in the same range as the wavelengths.

https://en.wikipedia.org/wiki/Thin-film_interference

Is the wikipedia article for this one and related things.

It requires you to calculate the new wavelength in the film, realize that light reflects both on top of the film and after a reflection under the film, and then figure out at which wavelengths you have a harmonic. You'll see far stronger reflection for the harmonics.

This effect is often used in highly reflector mirrors - for example, lasers classically have an optical resonator, which is then created by two mirrors that use multiple thin layers to create a harmonic for the wavelength of the laser.

More specifically, taking this image from the above-mentioned wikipedia page: Thin film interference

Your angle is $0$, your $d$ is $4.2\times 10^{-7}$, your $n_1 = 1$ and your $n_2 = 1.52$.

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    $\begingroup$ I think the OP wasn't asking for an answer, but just a hint to understand the problem... $\endgroup$
    – Miyase
    May 17, 2022 at 8:28
  • $\begingroup$ Thank you for being very early with that comment on a clearly active post. If you read again, you'll notice I explain the general type of problem, and don't give the numerical answer or anything. $\endgroup$
    – Gloweye
    May 17, 2022 at 19:02
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    $\begingroup$ It isn't a big deal, but if one of my students came asking for a hint to get into this exercise, I'd consider your post to be almost equivalent to giving the answer. But as long as the original poster finds your answer useful, everything's fine. $\endgroup$
    – Miyase
    May 17, 2022 at 19:34
  • $\begingroup$ No, it very much isn't. A good answer to the embedded question would contain the realization that a wave travels through the film twice, a formula to spit out all harmonics, and then a list of those harmonics that are part of the visible spectrum. This answer, in contrast, explains the physics on a conceptual level, as well as a real-life example where it is used. If the lesson itself hasn't mentioned all of this, the lesson was bad. This WOULD have been most of the actual answer to "explain thin-film interference", but that wasn't the question. $\endgroup$
    – Gloweye
    May 18, 2022 at 11:36
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The trouble is that when you run the numbers you get two visible wavelengths. So then you have to decide which one to pick?

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  • $\begingroup$ As it’s currently written, your answer is unclear. Please edit to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers in the help center. $\endgroup$
    – Community Bot
    Feb 1 at 1:35

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