Consider a thin film of soap illuminated by visible light with \(\lambda = 0.6 \,\mu m\) in vacuum. If the film is treated as a planar dielectric slab with \(\epsilon_r = 1.65\), surrounded on both sides by air,
(a) What is the minimum film thickness, \(d_{min}\) that produces zero reflection in the incident medium (air)?
(b) What film thickness, \(d_{max}\) produces maximal reflection?
(c) What is the reflection coefficient, \(\Gamma\) for the case of part b?
Answers:
(a) \(d_{min} = n \,\frac{\lambda}{4} \,\mu m\), \(n = 0, 1, 2,...\)
(b) \(d_{max} = \frac{\lambda}{4} + n \,\frac{\lambda}{2} \,\mu m\), \(n = 0, 1, 2,...\)
(c) \(\Gamma = 0\)