Finding the refractive index for nonreflective film coating

[Andy1011]

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.

 

[kuruman]

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