Question

It's nighttime, and you ve dropped your goggles into a 3.2-m-deep swimming pool. If you hold a laser pointer 0.90 m above the edge of the pool, you can illuminate the goggles if the laser beam enters the water 2.2 m from the edge. How far are the goggles tfrom the edge of the pool? Express your answer to two significant figures and include the appropriate units

Answer 1

Answer:

The distance of the goggle from the edge is 5.30 m

Explanation:

Given:

The depth of pool (d) = 3.2 m

let 'i' be the angle of incidence

thus,

i = $tan^{-1}(\frac{2.2}{0.90})$

i = 67.75°

Now, Using snell's law, we have,

n₁ × sin(i) = n₂ × 2 × sin(r)

where,

r is the angle of refraction

n₁ is the refractive index of medium 1 = 1 for air

n₂ is the refractive index of medium 1 = 1.33 for water

now,

1 × sin 67.75° = 1.33 × sin(r)

or

r = 44.09°

Now,  

the distance of googles = 2.2 + d×tan(r)  = 2.2 + (3.2 × tan(44.09°) = 5.30 m

Hence, the distance of the goggle from the edge is 5.30 m