Air-Water (n=1.3)-Air film (soap film) Normal incidence Can we make a device with greater contrast in transmission? T Dd/l

Air-Diamond (n=2.4)-Air film T F = 0.88 Dd/l

Air- Kryptonite? (n=10) -Air F = 18 Dd/l Interference ideas for why increasing r makes these peaks so sharp?

Multiple reflection view of T at low angle As long as |x| < 1, this will converge But for |x| 1, the dependence on phase is very fast!

If |r|,|r’| approach 1, many reflections contribute to the interference for R and T. Many phasors of nearly equal size give much more contrast in magnitude and much sharper features than just a few of very different size. Very important concept in many contexts of interference

Multiple reflection view of T Suppose R = rr = 0.1. The relative strength of the first three transmitted fields are 1, 0.1, 0.01… etc . If added in phase (0 shift) you get ____ If added out of phase (p shift) , you get ____ Max/min fields______ Max/min T’s _______

Multiple reflection view of T Suppose R = rr = 0.75 The relative strengths of the transmitted fields are 1, 0.75, 0.752 …. etc . Now we must add many more fields to get the transmission.

Multiple reflection view of T Sketch with phasors the addition of the fields 1, 0.75, 0.752 …. etc in phase This adds up to something close to 2 4 6 8 10

Multiple reflection view of T Sketch with phasors the addition of the fields 1, 0.75, 0.752 …. Out of phase (p shift) This adds up to something close to 0.1 0.2 0.4 0.6 1 Max/min fields______ Max/min T’s _______

Multiple reflection view of T Sketch with phasors the addition of the fields 1, 0.75, 0.752 …. at p/4 shift This adds up to something close to 0.2 0.4 0.6 1 2 Do the same for 1, 0.1, 0.01 In a relative sense, which is most sensitive to phase?

General feature of wave interference: if you want sharp features you have to add lots of waves with varying phase. (e.g. Fourier)

If I want to make an instrument that distinguishes wavelengths, I can get sharp transmission by increasing n to increasing R. But it’s hard to obtain and work with kryptonite.

Fabry-Perot Etalon/Interferometer High R due to large k in in metal coating.

Fabry-Perot Etalon/interferometer for low R: Fabry-Perot Etalon/interferometer for high R, same d Red: l = 1.00 Blue: l = 1.01 Is the device most sensitive to l changes for small or large d?

Free spectral range: At a given d, how much can l change before it confuses us by “lapping” its original peak near d?

Given a choice, is it better to increase d or increase R to make as small as possible? a) increase d b) increase R

Multiple reflection view of T

Solar corona taken with the LASCO C1 coronagraph which employed a tunable Fabry-Pérot interferometer near an iron atom emission line at 530.8 nm. Color coded image of the doppler shift of the line, after subtracting solar rotation.

What you see on a screen for any interferometer There is always some angular divergence

Two close sodium emission lines are visible Experiment on video