Geometrical problem related to thin film interference

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Discussion Overview

The discussion revolves around a geometrical problem related to thin film interference, specifically focusing on proving the optical path length difference in a scenario involving non-perpendicular incidence. Participants are exploring the relationship between various segments of the geometry presented in an accompanying image.

Discussion Character

  • Exploratory, Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant seeks to prove the optical path length difference formula \(\Delta=n(BC+CD)-BE=2nd\cos(r)\) and expresses uncertainty about deriving the term \(2nd\cos(r)\).
  • The same participant mentions attempts to use trigonometry without success, indicating a struggle with the geometric relationships involved.
  • Another participant shares a link to a Wikipedia page on thin-film interference, suggesting it may provide relevant background information.
  • A later reply expresses gratitude, indicating some level of assistance or support was found in the discussion.

Areas of Agreement / Disagreement

The discussion remains unresolved, with no consensus reached on how to derive the optical path length difference or the specific geometric relationships involved.

Contextual Notes

Participants have not clarified certain assumptions regarding the geometry or the definitions of the segments involved, which may affect the derivation of the optical path length difference.

khaos89
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Look at the picture below, I have to prove that the optical path length difference is

\Delta=n(BC+CD)-BE=2nd\cos(r)

[PLAIN]http://img200.imageshack.us/img200/2271/schermata082455775alle1.th.png

The problem is just how to get 2nd\cos(r)

I actually don't have any idea :\

I have tried to work with trigonometry but no luck yet...

(I am posting it here because it's not related to course work, i am just trying to understand how it works when we don't have perpendicular incidence)
 
Last edited by a moderator:
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Sorry, here we go with the pic:

[PLAIN]http://img193.imageshack.us/img193/2271/schermata082455775alle1.png
 
Last edited by a moderator:
Thanks a lot :)
 

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