A soap bubble is formed in still air. Because gravity causes the liquid to drain slowly, the film thickness increases steadily from the very top of the bubble toward its equator.
White light is incident nearly normal to the bubble surface, and an observer looks at the reflection from the side where the outside medium is air. Assume the refractive index of the soap solution is approximately 1.33 and the interior of the bubble is air.
Answer the following about the colors that appear on the bubble as its thickness varies.
(a) Describe qualitatively why, for a thin film viewed by reflection, some wavelengths in the visible spectrum are reinforced while others are suppressed.
(b) Explain, without detailed numerical calculation, why the very top of an old bubble often appears black (or very dark) even though it is illuminated by white light.
(c) As the thickness increases from nearly zero at the top to a few hundred nanometres farther down, predict the approximate sequence of dominant colors an observer is likely to see. Justify your sequence by referring to the order number m and the relationship between wavelength and the constructive-interference condition for this situation.
(d) Discuss how the 180∘ phase change that occurs upon reflection from the outside surface of the bubble affects whether the first non-zero thickness gives constructive or destructive interference for the shortest visible wavelengths.