Question

it's nighttime, and you've dropped your goggles into a swimming pool that is 3.2 m deep. If you hold a laser pointer 1.0 m above the edge of the pool, you can illuminate the goggles if the laser beam enters the water 2.5 m from the edge. How far are the goggles from the edge of the pool?

Answer 1

5.2 m

Step-by-step explanation:

from the question we are given the following

depth of pool (d) = 3.2 m

height of laser above the pool (h) = 1 m

point of entry of laser beam from edge of water (l) = 2.5 m

we first have to calculate the angle at which the laser beam enters the water (∝),

tan ∝ = \frac{1}{2.2}

∝ = 24.44 degrees

from the attached diagram, the angle with the normal (i) = 90 - 24.4 = 65.56 degrees

lets assume it is a red laser which has a refractive index of 1.331 in water, and with this we can find the angle of refraction (r) using the formula below

refractive index = \frac{sin i}{sin r}

1.331 = \frac{sin 65.56}{sin r}

r = 43.16 degrees

we can get the distance (x) from tan r = \frac{x}{3.2}

tan 43.16 = \frac{x}{3.2}

x = 3 m

To get the total distance we need to add the value of x to 2.2 m

total distance = 3 + 2.2 = 5.2 m