# Refraction at a spherical surface

1. Apr 29, 2005

### sghaussi

hello again:

A Spherical Fish Bowl. A small tropical fish is at the center of a water-filled spherical fish bowl 28.0 cm in diameter.

Find the apparent position of the fish to an observer outside the bowl. The effect of the thin walls of the bowl may be ignored.

i'm dealing with the formula : (n_a/s) + (n_b/s_prime) = 0

n_a = index of refraction of air (1.00) ?
n_b = index of refraction of water (1.33)?
s = position of fish = 14 cm ?
s_prime = position of image?

I tried plugging into the above formula, however I keep getting the wrong answer. Also, I tried switching n_a with n_b but that also didn't work. I'm thinking that the position of my fish isn't 14 cm? What am I doing wrong?

2. Apr 29, 2005

### SpaceTiger

Staff Emeritus
That equation is only for a flat surface. More generally, it's:

$$\frac{n_1}{s}+\frac{n_2}{s'}=\frac{n_2-n_1}{R}$$

where R is the radius of curvature of the bowl.