Question

It's nighttime, and you've dropped your goggles into a 3m deep swimming pool. If you hold a laser pointer 1.0m abovve the edge of the pool, you can illuminate the goggles if the laser beam enters the water 2.0m from the edge. How far are the goggles from the edge of the pool?

Answer 1

x_total = 3.07 m

Step-by-step explanation:

Let's analyze the situation presented, in this case we have the data to find the angle of incidence and with the law of refraction we can find the angle of refraction.

Let's start looking for the angle with which the laser pointer reaches the water, let's use trigonometry

tan θ₁ = 1.0 /2.0

θ₁ = tan⁻¹ 0.50

θ₁ = 26.57º

now let's use the law of refraction to find the angle of refraction (in water)

n₁ sin θ₁ = n₂ sin θ₂

the refractive index of air is n₁ = 1 and that of water n₂ = 1.33

sin θ₂ =
`(n_1)/(n_2) \ sin \theta_1`

sin θ₂ =
`(1)/(1.33) \ sin \ 26.57`

θ₂ = sin⁻¹ 0.3363

θ₂ = 19.65º

now we can find the distance from the entry point to the water to the lenses

tan θ₂ = x₂ / 3

x₂ = 3 tan θ₂

x₂ = 3 tan 19.65

x₂ = 1.07 m

the total distance from the edge of the pool is

x_total = 2 + x₂

x_total = 2 + 1.07

x_total = 3.07 m