## Thin Film Interference

Here is a simple thin film intereference system. You can adjust the thickness of the film layer, and choose among several scenerios of layers.

 Set the thickness and choose the layers :            Thickness (t) (nm) =                        (range limited to = 200-1600 nm)            ---------------------------------------------------           Surface layers :                 Air/Water/Glass  n(film) = 1.33                 Air/Water/Air  n(film) = 1.33                 Air/Glass/Air  n(film) = 1.5            ---------------------------------------------------   * If you manually change values ... The boxes below show the "m" values, and the wavelengths for the Bright wavelengths (constructive) and Dark wavelengths (destructive).           DARK wavelengths                   BRIGHT wavelengths Intensity of Reflected Light           Spectrum of Visible Light The graph on top shows the Intensity as a function of the angle (1 = maximum intensity .. thus IN PHASE or BRIGHT ... zero = no intensity .. thus OUT OF PHASE or DARK). The "rainbow" on the bottom illustrates the wavelength colors of the top graph, and also indicates the BRIGHTS (white) and the DARKS (black) from the information in the boxes to the left.

### How to "Solve" this problem :

This is the "given a thickness of a film in a particular layer system ... what visible wavelengths will constructively or destructively interfere upon reflection from the top and bottom surface of the film" type problem.

1. Knowing film index and thickness will pin the 2tn value … so    give either bright or dark (at the moment, we don't care).
2. Visible range is 400 nm to 700 nm (in air) … plugging in 400 and 700 would give "endpoints" for M
3. Remember that we could have bright or dark .. m or (m+½) … thus, lets call it m* … m* could be integer or half-integer
4. Calculate ends of the range :
5. Figure out which whole numbers are between those two, and which half-integers are between them.
6. Plug back in to find the wavelengths (in two groups, whole integers, half-integers) :
7. If you get an answer outside of 400-700, you made a mistake in step 5!
8. Decide which group of wavelengths are brights, which are darks (based on surfaces).