.

A Christmas tree ornament is constructed by vapor-depositing a chemical film (with n = 1.7) on a ``thick'' ($\sim 2$ mm) spherical glass (n = 1.5) bubble as drawn schematically above. The thin chemical film is not uniform in thickness, and its variation in the range 0-2 microns (micrometers) produces brilliant streaks of color in the reflected light.

a) What is the smallest (nontrivial) mean thickness $t$ of the film such that reflected light to has a constructive interference maximum in the center of the visible spectrum ($\lambda =$ 400-700 nm in free space where $n = 1$).

b) When the film first starts to deposit on the glass (and has a thickness $t$ of only a few nanometers) does the film on the bulb turn shiny (constructively reflecting all wavelengths) or transparent (destructively reflecting all wavelengths)? Explain.