Question

It’s nighttime, and you’ve dropped your goggles into a swimming pool that is 4.0 m deep. If you hold a laser pointer 1.5 m directly above the edge of the pool, you can illuminate the goggles if the laser beam enters the water 2.1 m from the edge.

How far are the goggles from the edge of the pool?

I don't understand this problem, can someone help break it down for me to understand it step by step?

Thanks

Answer 1

Let the laser angle with water surface be A,

A = arctan(1.5/2.1) = 35.54 degree

Laser angle with Normal = (90 - 35.54) = 54.46 degree

Let red laser, refractive index in water is 1.331

Angle of refraction in water,

1.331 = sin i /sin r

r = arcsin(sin 54.46 degree /1.331)

= 37.68 degree

For the path in water,

tan 37.68 degree = x/4

where, x is the lateral displacement of the laser since it hits the water

x = tan 37.68 degree * 4

So, the googles from the edge of pool = 2.1 + 3.1 = 5.2 m