A student discovers that light takes specific time duration t to travel 5.0 m in the air. Calculate the distance that light would need to cover in i) diamond and ii) benzene liquid within the same time duration, t. Note that the refractive indices for both mediums are: η_diamond = 2.42 and η_benzene = 1.49. 

A child drills a hole in one side of a cardboard box and mounts a screen behind the hole. The distance between the hole and the screen is 20 cm. Calculate the distance between the hole and a 2.4 m tall shrub in front of the hole when the image is 6.0 cm tall.

Bulletproof glass has layers of materials such as glass laminate, polycarbonate, and acrylic that have a nearly equal refractive index to keep the glass transparent. Bulletproof glass has a 31.75 mm thick polycarbonate layer (η = 1.581). Calculate the time taken by a light that is incident normally to the surface of the polycarbonate layer to go through the 31.75 mm thick layer.

Using Huygens Principle, derive the law of reflection which states that the angle of incidence is equal to the angle of reflection on a smooth surface.