Refraction At Spherical Surfaces Practice Problems

A turtle lives in a spherical glass tank filled with water that has a radius of 25 cm. The turtle notices a dog sniffing around their tank. The dog's nose is located 10 cm from the tank's outside edge. From the turtle's perspective inside the tank, how far is the dog's nose located from the outside edge of the tank? (Assume that the glass tank's thickness can be ignored.)

Imagine that a laser beam is directed parallel to an optical axis which then passes through the center of a perfectly transparent spherical crystal. Convergence will occur at a point located on the crystal's rear surface. Determine what the crystal's refractive index will be.

A jewelry appraiser uses a large, solid glass sphere with a radius of 9.0 cm. He places a small, intricate diamond 8.0 cm from the sphere's surface. The diamond's image is formed on the opposite side of the glass sphere. Determine the distance between the diamond image and the sphere's center.

A rubber duck is submerged in a round bottom flask containing water (n = 1.33) and is 15 cm from the wall of the flask. The spherical section of the flask has a 44 cm diameter. What should the apparent distance and magnification of the duck be if the person is standing right next to the flask? (The walls of the flask are very thin, so ignore refraction caused by them)

A lapidary cuts and polishes one side of a cylinder-shaped diamond (n = 2.41) into a spherical surface of radius 6 cm. A Rubik's cube 10cm tall is placed on its axis 30 cm left of the vertex. Determine how far away the image is as well as its height. Should the image be real or virtual?