Question

A researcher is studying the properties of spherical bubbles of a fluid with index of refraction ?? = 1.47. She has determined that, due to the action of gravity, the thickness ? of the thin bubble film varies with respect to the polar angle ? (measured from the vertical axis, as seen in the figure below), and follows the form:

?(?)=?0 +?1sin^4((?/2))

where ?0 and ?1 are constants, both > 0.

Using a laser that has a variable wavelength, the researcher has obtained the following data: Shining the laser beam into the bubble at normal incidence (i.e., along the radial line toward the bubble’s center) at the angle ?1 = 0°, the intensity of the reflected light is at a maximum at wavelength ?1 = 450 nm. Additionally, when she shines the laser at normal incidence to the bubble film at the angle ?2 = 110°, the reflected light has a minimum reflected intensity at wavelength ?2 = 640 nm.

Assuming that ?(?) is the minimum film thickness possible for all ?, determine the constants ?0and ?1.

Answer 1