Question

A swimming pool is 1.4 m deep and 12 m long. Is it possible for you to dive to the very bottom of the pool so people standing on the deck at the end of the pool do not see you?

A) Assume you dive to the very bottom of the pool so people standing on the deck at the end of the pool can see you. Find the minimum height of the person's eyes at the far side of the pool, so you would be observable by this person. Take an angle 48.5∘ for a ray that is incident at the water-air interface (nwater = 1.33).

B) Therefore, is it possible for you to dive to the very bottom of the pool so people standing on the deck at the end of the pool do not see you?

Answer 1

length of the swimming pool, L = 12 m

width of the swimmimng pool, w = 1.4 m

(A) The minimum height of the person's eyes at the far side of the pool which is given as :

using snell's law, we have

n_a sin ₁ = n_w sin ₂                         

where, n_a = refractive index of air = 1

n_w = refractive index of water 1.33

₂ = refractive angle = 48.5 degree

inserting the values in above relations,

(1) sin ₁ = (1.33) sin 48.5⁰

sin ₁ = (1.33) (0.7489)

₁ = sin^-1 (0.996)

₁ = 84.8 degree

which is "incidence angle".

Now, using trigonometric identity,                     tan = h / L

tan 84.8⁰ = h / (12 m)

h = (10.9) (12 m)

h = 130.8 m

(B) Therefore, yes it is possible for you to dive to the very bottom of the pool so that people standing on the deck at the end of the pool do not see you.