Question

1. A thin film of soap with n = 1.33 hanging in the air reflects dominantly red light with λ = 670 nm. What is the minimum thickness of the film? 2. Now this film is on a sheet of glass, with n = 1.53. What is the wavelength of the light in air that will now be predominantly reflected?

Answer 1

for the hanging film
the light reflected from the front surface is phase inverted because it is going from low n to higher n
and
the ray from the back is not inverted (nigh n to lower n)
so
the path difference needs to be 1/2 wavelength to put them back in phase (constructive interference)
that means the minimum thickness must be 1/4 wavelength
1/4 * 693 = 173.25 nm

when backed by glass the ray from the rear surface phase shifted (lower n to higher n)
so the total path length must be 1 wavelength to put the two rays back in phase
so the thickness must be 1/2 wavelength
1/2 * 693 = 346.5 nm