Nonreflective Film: Solving the Ref. Index Problem

AI Thread Summary
The discussion focuses on addressing the refractive index problem in nonreflective films by sandwiching the coating between lens surfaces. It highlights the conditions for destructive interference occurring at both the front and back surfaces of the lens, emphasizing that the equations governing these conditions may differ due to potential phase differences upon reflection. The speaker expresses a desire to rederive the necessary equations independently rather than relying on existing resources. Additionally, the conversation notes that four rays must emerge from the lens to achieve the desired destructive interference. Understanding these principles is crucial for effectively designing nonreflective coatings.
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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