# Thin Films with consideration to Amplitude

1. May 27, 2008

### cblack

1. The problem statement, all variables and given/known data
Consider the case of a film of thickness $$\lambda$$/4 with an index nf where nf<ng=1.5 that is applied to a glass surface. For minimum reflection the reflected rays r1 and r2 must cancel each other out. Since r1 and r2 both reflect fast to slow, they are in phase on reflection, but with r2 travelling $$\lambda$$/2 farther than r1 they will be 180 degrees out of phase when r2 exits the film and superpositions with r1. For maximum cancellation, the intensities (ie. amplitude) must be as close to equal as possible.

calculate nf for minimum reflection.

2. Relevant equations

nf=$$\lambda$$air/$$\lambda$$coating

3. The attempt at a solution

I don't understand how the amplitude would change after passing through the film or how you would even work that into an equation. I don't have any equations that involve amplitude and it was never discussed in the text. I have no idea how to approach this problem or what equations should be used.

I assumed that $$\lambda$$air= 550nm since it's a midrange wavelength of visible light, but that's as far as I can go.