The figure below shows four situations in which light reflects perpendicularly from a thin film of
thickness L, with indexes of refraction as given.
a) For which situation(s) does reflection at the film interfaces cause a zero phase difference for the
two reflected rays?
b) For which situation(s) will the film be dark if the path length difference 2L causes a phase
difference of 0.5λ?
SOLUTION
Reflected rays undergo a 180⁰ phase shift when 𝑛2 < 𝑛1 and no phase shift when reflecting from a
medium of lower index of refraction. Thus, the first and last examples above do not experience phase
shifts due to the interface, while the situations (2) and (3) have a ray that is shifted 180⁰ compared to
the incident ray.
The films will be dark if the reflected rays are out of phase, or off by 180⁰. Traveling through the 2L
distance of the center layer results in a 0.5λ phase shift (which is in addition to the phase shifts caused
by the interfaces themselves). Adding these two results gives the following: