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

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 =

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