Nonreflective Film: Solving the Ref. Index Problem

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SUMMARY

The discussion focuses on solving the reference index problem in nonreflective film coatings applied between lens surfaces. The author proposes a method involving sandwiching the coating and calculating its thickness as lambda/2 multiplied by the reference index. The conditions for destructive interference are examined at both the front and back surfaces of the lens, highlighting the importance of phase differences in reflection. The analysis emphasizes the need for precise equations to describe these conditions due to the complexity of multiple rays emerging from the lens.

PREREQUISITES
  • Understanding of optical coatings and their applications
  • Knowledge of interference patterns in optics
  • Familiarity with the concept of phase difference in wave optics
  • Basic principles of lens design and light propagation
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  • Research the principles of destructive interference in thin films
  • Explore the mathematical derivation of optical path differences
  • Study the impact of refractive index on light transmission
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Optical engineers, physicists, and lens designers interested in enhancing lens performance through nonreflective coatings and understanding the underlying principles of light interference.

Andy1011
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Homework Statement
A glass lens of index 1.5630 is to be nonreflecting on both surfaces. What should be the refractive index and thickness of the coating for a light of 5500 A to produce 0 reflactance?
Relevant Equations
2nd = m lambda
2nd = (2m+1)lambda/2
I thought of sandwiching the coating between lens sufaces and then applied the condition of minimum which gave a thickness of lambda/2*ref. Index and I got totally stuck at the ref. Index.
 
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There are two conditions of destructive interference, one at the front surface and one at the back surface. The equaitons describing the conditions are not necessarily the same because of the phase difference that may or may not be there upon reflection. I would rederive them for myself instead of looking them up. There are four rays emerging from the lens that have to interfere destructively

Front surface
Path 1 air⇒coating; Path 2: coating⇒glass
Back surface
Path 1 coating⇒glass; Path 2: glass⇒air
 

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