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I knew for destructive interference for reflected light in thin films: 2t = mλ

Where t is the thickness of the thin film, m is an integer (0,1,2...) and λ is the wavelength of light in the thin film.

However, on some websites and books t = $\frac{λ}{4}$

My questions are:

  1. Why does t = $\frac{λ}{4}$?
  2. Does it have something to do with a phase change on reflection of π?
  3. Does a phase change on reflection happen when light reflects off from less dense → more dense or vice versa?
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There are two things to consider:

  1. As you guessed there is a phase inversion for the reflected light when it is reflected off of a medium that is more optically dense (slower speed of light).
  2. You need to be clear on whether you are considering the reflected light or the transmitted light. Whatever film thickness produced destructive interference for transmitted light will simultaneously produce constructive interference for reflected light and vice versa.

Destructive interference for reflection would occur for $t=\frac{\lambda}{4}$ when the film has an index of refraction between that of the two other media. For example an anti reflective coating on a lens would have a value less than that of the glass (and more than that of air). In that way there is a phase inversion at both interfaces for light starting in the air, or neither for light originating in the glass, either case resulting in an effective path difference for reflection of half a wavelength.

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  • $\begingroup$ I meant destructive interference for the reflected light $\endgroup$
    – Yitian Chen
    Commented Aug 10, 2022 at 7:58
  • $\begingroup$ @quantumYitian see my edit $\endgroup$
    – M. Enns
    Commented Aug 10, 2022 at 15:00
  • $\begingroup$ @m-enns Yes thank you, I've seen it. This is my last doubt to verify my understanding. So do you mean 𝑡=𝜆/4 would only occur "when the film has an index of refraction between that of the two other media" (e.g Na<Nb<Nc)? I want to check if I understand this correctly: If Na<Nb>Nc, then does 2t = mλ? Since there is no phase change on reflection for light entering Nc from Nb as Nb>Nc. $\endgroup$
    – Yitian Chen
    Commented Aug 10, 2022 at 18:48
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    $\begingroup$ @QuantumYitian that's right, if Na<Nb>Nc then light reflected at one interface experiences a phase inversion but not at the other interface. This introduces an extra half wavelength in the effective path difference so to get destructive interference you want twice the thickness to be a whole number of wavelengths which brings you back to the first equation in your question. $\endgroup$
    – M. Enns
    Commented Aug 11, 2022 at 1:19

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