Question

A point source of light is 1.24 m below the surface of a pool. What is the diameter of the circle of light that a person above the water will see? Assume the water has an index of refraction of ????=1.33.

Answer 1

D = 2.828 m

Step-by-step explanation:

given,

distance of source of light = 1.24 m below surface of pool

refractive index of the water = n₁ = 1.33

refractive index of air = n₂ = 1

refraction angle be = 90°

let C be the critical angle

Radius = d tan C

d is the depth of the source

Using Snell's law

n₁ sin C = n₂ sin R

1.33 x sin C = 1 x sin 90°

`sin C = (1)/(1.33)`

`C = sin^(-1)(0.752)`

C = 48.75°

hence,

R = 1.24 x tan 48.75°

R = 1.414 m

Diameter = 2 x R

D = 2 x 1.414

D = 2.828 m