PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Wave propagation and light in media · Wave propagation and light in media
Optics and Photonics, Ch Reflection and transmission at interfaces
Problem
The chapter's soap film, index 1.33 in air and far thinner than a wavelength, reflects nothing because its front and back reflections are equal and opposite. Now put a film of oil (n=1.45), again far thinner than a wavelength, on two different surfaces, at normal incidence throughout. As in the chapter, carry the back reflection by the factor t12t21=1−r122 for the trip into and out of the film, and ignore anything reflected more than once inside it.
((a)) For the oil film floating on water (n=1.33), find the coefficient r12 of the front reflection and r23 of the back reflection, each with its sign under CV5, saying for each whether the reflection is external or internal. Add the front arrow to the back arrow carried by t12t21, and compare the sum with the coefficient of bare water in air.
((b)) Repeat for the same oil film lying on crown glass (n=1.50), comparing with bare glass in air.
((c)) Neither film looks black. Say in one sentence what a film far thinner than a wavelength does to the reflection from a surface, and why the soap film in air is the one case that cancels.