A person lying at poolside looks over the edge of the pool and sees a bottle cap on the bottom, directly below. If the depth of the pool is 3.2 m, how far below the water surface does the bottle cap appear to be?
To find out how far below the water surface the bottle cap appears to be, we need to consider the concept of refraction. Refraction occurs when light travels from one medium to another, such as from air to water, causing the light rays to bend.
To calculate the apparent depth of an object submerged in water, we can use Snell's Law, which relates the angles of incidence and refraction to the refractive indices of the two media. However, in this case, we don't need to calculate the exact angles, as we are only interested in the apparent depth.
The apparent depth of an object submerged in a medium can be determined by applying the following formula:
Apparent depth = Actual depth / Refractive index
In this scenario, the person lying at the poolside is viewing the bottle cap through air, and the bottle cap is submerged in water. The refractive index of air is approximately 1.00, while the refractive index of water is approximately 1.33.
Using the formula, we can calculate the apparent depth:
Apparent depth = 3.2 m / 1.33 ≈ 2.41 m
Therefore, the bottle cap would appear to be approximately 2.41 meters below the water surface when viewed from the poolside.