Question

An expensive spotlight dinner is located at the bottom of a gold-plated swimming pool of depth d = 2.80 m. Determine the diameter of the circle from which light emerges from the tranquil surface of the pool.

Answer 1

The diameter of the circle from which light emerges at the surface of the pool is approximately D ≈ 6.62 m.

Step-by-step explanation:

The diameter of the circle from which light emerges at the surface of the pool can be determined using the concept of refraction. The formula to calculate the diameter (D) is given by:

D = 2 . r = 2 . {n^2 . d^2 - (n^2 - 1) . r^2}^1/2

where:

- D is the diameter,

- r is the radius of the circle,

- d is the depth of the pool,

- n is the refractive index of water.

For water, the refractive index (n) is approximately 1.33.

Substitute the values into the formula and solve for D:

D = 2 . {(1.33)^2 . (2.80)^2 - ((1.33)^2 - 1) . r^2}^1/2

Since the spotlight is at the bottom of the pool, r is equal to d.

D = 2 . {(1.33)^2 . (2.80)^2 - ((1.33)^2 - 1) . (2.80)^2}^1/2

Now, calculate the value of D.

D ≈ 6.62 m.