A drop of sulfuric acid (n=1.83) in the shape of a hemisphere with radius2.0 mmsits on the smooth horizontal surface of a sapphire (n=1.77). A thin laser beam enters the droplet from the air, and reaches the water-sapphire boundary at the exact center of their circle of contact. At that point, the laser beam is completely reflected off the surface of the sapphire.

(a) (20 points) What is the maximum height above the sapphire that the laser beam could enter the droplet to be internally reflected at the center of the droplet as described above?

(b) (5 points) What is the angle of incidence as the beam enters the droplet?