How Is the Longest Wavelength of Light Determined for Anti-Reflective Coatings?

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SUMMARY

The longest wavelength of light strongly reflected from a coated glass surface is determined by the thickness of the anti-reflective coating and the refractive indices of the materials involved. In this case, a 95.6-nm-thick magnesium fluoride layer (ncoating = 1.38) on glass (nglass = 1.5) is designed to minimize reflection in the visible spectrum. The correct calculation for the longest wavelength involves using the formula for constructive interference, which requires understanding the phase change upon reflection and the optical path length. The condition for strong reflection occurs when the optical path difference is an integer multiple of the wavelength.

PREREQUISITES
  • Understanding of optical interference principles
  • Knowledge of refractive indices and their significance
  • Familiarity with the concept of phase change upon reflection
  • Basic proficiency in wavelength calculations in optics
NEXT STEPS
  • Study the principles of optical interference in thin films
  • Learn about the phase change of light upon reflection at different media
  • Explore the derivation of the wavelength condition for constructive interference
  • Investigate the applications of anti-reflective coatings in optics
USEFUL FOR

Students in optics, physicists, and engineers involved in designing optical coatings or studying light behavior in various media.

Barry Melby
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Homework Statement


A sheet of glass (nglass = 1.5) is coated with a 95.6-nm-thick layer of magnesium fluoride (ncoating = 1.38) to prevent reflection in the visible spectrum. Assume the incoming light is normal to the surface.
What is the longest wavelength of light strongly reflected from this coated surface?

Homework Equations

The Attempt at a Solution



95.6 = x/4(1.38) = 527 nm
This is incorrect however.
 
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Please show your reasoning.
Note: you have written 95.6 = 527 ... which is, indeed, false. I don't think that is what you meant.

Under what circumstances does a reflected wave invert?
What condition is needed for strong reflection off the top surface of the film?
 

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