A horizontal soap film of uniform thickness t floats on a tray of water. The indices of refraction are
• air: na=1.00
• soap solution: ns=1.34
• water below the film: nw=1.33
Monochromatic light of wavelength λ0=600nm in air is incident nearly normal to the film from above. An observer looks straight down at the film and sees a bright or dark reflection depending on the film thickness.
(1) Part 1: (a) For the ray reflected from the air–soap interface and the ray reflected from the soap–water interface, state whether each ray undergoes a half-wavelength (π-rad) phase change upon reflection. Justify your answers using the relative indices of refraction at each interface.
(2) Part 2: (b) In terms of λ0 and ns, write an expression for the film thickness t that produces constructive interference in the reflected light for normal incidence.
(3) Part 3: (c) The instantaneous film thickness is measured to be t=110nm. For λ0=600nm, determine whether the reflected intensity is nearer a maximum or a minimum. Show your reasoning explicitly.
(4) Part 4: (d) As the film continues to drain, t decreases slowly. Describe qualitatively the sequence of color changes the observer will see and explain the physical reason for this sequence.