Thin film constructive interference

[ikihi]

Homework Statement

Three experiments involving a thin film (in air) sandwiched between two layers of air are shown with n_air < n_film. If t denotes the film thickness and λ denotes the wavelength of the light in the film, which experiments will produce constrictive interference as seen by the observer? The incident light is nearly normal to the surface.

Homework Equations

2nt = (m+0.5)λ

The Attempt at a Solution

I think the solution is I and III will produce constructive interference. I'm not totally sure why, but I think in experiment 1 and experiment 3 light undergoes one phase reversal and t satisfys (2nt = m+0.5)λ. Experiment 2 has 2 phase reversals?

 

[Doc Al]

The only phase shift occurs upon reflection at the first boundary (air to film). For each case, compare the phase of the two reflected beams. What must be their phase difference for constructive interference?

 

[ikihi]

The only phase shift occurs upon reflection at the first boundary (air to film). For each case, compare the phase of the two reflected beams. What must be their phase difference for constructive interference?

If the crests of the waves line up (phase shift of 0, λ, 2λ, etc) the resulting wave is bigger, giving constructive interference. If a crest lines up with a trough (phase shift of λ/2, 3λ/2, etc), there is cancellation (destructive interference).

 

[Doc Al]

If the crests of the waves line up (phase shift of 0, λ, 2λ, etc) the resulting wave is bigger, giving constructive interference. If a crest lines up with a trough (phase shift of λ/2, 3λ/2, etc), there is cancellation (destructive interference).

Perfect.

Now compare the phase shift of the 2nd wave (the one that reflects off of the second surface) with that of the 1st wave (the one that reflects off the first surface).