(a) You have a large triangular prism made of silica (ns = 1.45) resting on a table. The internal angles of the triangle are 90 degree and 45 degree. You also have a laser beam (wavelength = 633 nm) set up parallel to the tabletop.

How would you point the laser beam onto the prism to make the light travel through the prism then leave in a direction

i. at 90 degree
ii. at 180 degree

to the direction the light was traveling when it hit the prism?

For each case, draw a neat schematic diagram of the prism and laser beam showing all the relevant information.

(b) To maximise the light leaving the prism, someone suggests a coating of glass (ng = 1.6), but they only have enough material to coat up to two sides of the prism with thin films. For each of the configurations above, choose which side(s) of the prism, if any, you would get coated. Justify your choice.

Hint: Make use of total internal reflection if you can.

(c) If you wanted to create a right-angled triangular prism that split sunlight into its different colours, what property would it need to have?

(d) A rainbow effect can also be seen if sunlight shines on:

1. a film of oil on water
2. a prism coating with variation in its thickness

Explain this phenomenon using your understanding of physics. Make it clear how this is different from the phenomenon described in (c).