Anti-reflective coating confusion

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SUMMARY

The discussion centers on the relationship between the thickness of an anti-reflective coating and the angle of incidence, as described by the equation 2ndcos(Θ) = mλ. For a given wavelength (λ), the thickness (d) of the film increases with a slight increase in the angle of incidence (Θ). This conclusion is supported by considering both the path length of the first and second reflected waves, which collectively influence the interference conditions in thin films.

PREREQUISITES
  • Understanding of thin film interference
  • Familiarity with the equation 2ndcos(Θ) = mλ
  • Basic knowledge of wave optics
  • Concept of angle of incidence in optics
NEXT STEPS
  • Study the derivation of the interference condition for thin films
  • Explore the impact of varying angles on optical path length
  • Research practical applications of anti-reflective coatings in optics
  • Learn about the design and fabrication of thin film coatings
USEFUL FOR

Students in optics, physicists, and engineers involved in the design of optical coatings and those seeking to understand the principles of thin film interference.

Solarmew
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My professor confused me today :(
I'm trying to figure out the thickness of an anti reflection coating and it looks like from the equation
2ndcos(Θ) = mλ
that for a given λ the thickness of the film should increase for incidence slightly away from normal.
But he said that intuitively it should decrease because the waves now have to travel a longer distance through the material... which kinda makes sense, but contradicts the equation.
Could someone please explain to me exactly what it happening and whether the thickness should be expected to increase or decrease if we increase the angle and why?
@.@
 
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Solarmew said:
My professor confused me today :(
I'm trying to figure out the thickness of an anti reflection coating and it looks like from the equation
2ndcos(Θ) = mλ
that for a given λ the thickness of the film should increase for incidence slightly away from normal.
But he said that intuitively it should decrease because the waves now have to travel a longer distance through the material... which kinda makes sense, but contradicts the equation.
Could someone please explain to me exactly what it happening and whether the thickness should be expected to increase or decrease if we increase the angle and why?
@.@
The distance that the 2nd reflected wave travels through the film will increase, but that's not the full story. You also need to consider the extra distance the first reflected wave must travel (due to things being at an angle).

Follow the derivation, given here: Interference Condition for Thin Films
 

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