Question

A film of soapy water (n = 1.33) on top of a sheet of crystalline quartz has a thickness of 168 nm. What wavelength is most strongly reflected if it is illuminated perpendicular to its surface? (This is the apparent color of the soapy film.)

Answer 1

Thinking unilaterally:

Because the soapy film is on a quartz surface, the loss is on the second surface, which is in contact with the quartz crystal.

In this case the difference in the optical path is given by the formula:

n₂ = index of refraction for the soap medium

d = thickness of the soap film

r = refraction angle when light passes from medium n₁ (air) to medium n₂ (soap).

At the normal incidence the formula becomes:

Maximum deviation involves minim. Which is for violet: (around 350-400 nm in the visible spectrum).

The same logic applies for the case when consider the loss of half-wavelength taking place at the first surface, from air to soap medium.

The only difference is that the corresponding term in the formula has :

OBS: If considering that the loss of half-wavelength takes place in this case both at the first and the second surfaces (since the relationship between the refractive indices is: ), we'll get at the normal incidence:

()

Thus, does not depend on the wavelength!

Interesting problem...