In searching the bottom of a pool at night, a watchman shinesa
narrow beam of light from his flashlight, 1.3 m above the
waterlevel, onto the surface of the water at a point 2.7 m from the
edgeof the pool (figure 23-50). where does the spot of light hit
thebottom of the pool, measured from the wall beneath his foot, if
thepool is 2.1 m deep?

The spot of light hits the bottom of the pool at 4.634 m from the wall beneath the watchman's feet.

Explanation:

Use the diagram attached below this answer to see the notation we will use.

For this case, we're trying to find x and we have:

h=1.3 m

b=2.1 m

a=2.7 m

We also know Snell's law for refraction:

n is the refractive index of each substance (in this case, air and water), which are:

Triangle theory says that and:

Using Snell's law:

Using triangle theory:

The distance of spot of light from his feet equals 3.425 meters.

Explanation:

The situation is represented in the attached figure below

The angle of incidence is computed as

Now by Snell's law we have

where

are the refractive indices of the incident and the refracting medium respectively

are the angle of incidence and the angle of refraction respectively

Thus using the Snell's relation we have

from the attached figure we can see

Thus distance of spot on the pool bed from his feet equals