Chapter 22, Problem 23P

A person looking into an empty container is able to see the far edge of the container’s bottom, as shown in Figure P22.23a. The height of the container is h, and its width is d. When the container is completely filled with a fluid of index of refraction n and viewed from the same angle, the person can see the center of a coin at the middle of the container’s bottom, as shown in Figure P22.23b. (a) Show that the ratio h/d is given by

$\frac{h}{d}=\sqrt{\frac{n^{\text{2}}-\text{1}}{\text{4}-n^{\text{2}}}}$

(b) Assuming the container has a width of 8.00 cm and is filled with water, use the expression above to find the height of the container.