Answer
3.31 m.
Work Step by Step
For a plane refracting surface, $\frac{n_a}{s}+\frac{n_b}{s’}=0$.
We know that $n_a=1.00$ and we are looking for s. We see that $n_b = 1.33$ because the medium is water. The image is 5.20m - 0.80m = 4.40m above the surface of the water, so s’=-4.40 m.
$$\frac{n_a}{s}+\frac{n_b}{s’}=0$$
$$\frac{1.00}{s}+\frac{1.33}{-4.40m}=0$$
$$s=(4.40m)\frac{1.00}{1.33}=3.31m$$
In reality, the diving board is closer to the water than it looks to the swimmer.
