A light ray is incident on a layer of oil floating on water. The index of refraction of oil is greater than that of water, which is greater than that of air. Call the angle of incidence in air \(\theta_{a}\), the angle of refraction in oil \(\theta_{o}\), and the angle of refraction in water \(\theta_{w}\).

(a) Draw a diagram showing all three layers and all angles.

(b) Show that \(n_{\mathrm{a}} \sin \theta_{a}=n_{\mathrm{w}} \sin \theta_{\mathrm{w}}\).

(c) The result in part \(b\) implies that in calculating the final direction \(\left(\theta_{w}\right)\) of a light ray passing from medium 1 into medium 2 and then into medium 3 , all having different \(n\) values, we can ignore the presence of medium 2. Can you also ignore medium 2 if what you are calculating is the location where the ray strikes the bottom of the container of water?