Light in Underwater Pool Refraction Problem

In summary, the conversation discusses the problem of determining the radius of the circle of light on the surface of a swimming pool, given that a small underwater pool light is 1 meter below the surface. The solution involves using Snell's Law and Fermat's Principle to find the critical angle at which light rays incident on the surface totally reflect, and using this angle to calculate the radius of the light on the surface.
  • #1
JSGandora
95
0

Homework Statement


A small underwater pool light is 1 meter below the surface of a swimming pool. What is the radius of the circle of light on the surface, from which light emerges from the water?

Homework Equations


Snell's Law
Fermat's Principle

The Attempt at a Solution

I have no idea about how to approach the first part because we're not given the radius of the light.
 
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  • #2
JSGandora said:
A small underwater pool light is 1 meter below the surface of a swimming pool. I also have no idea how to approach the first part because we're not given the radius of the light.

It is small. Consider it a point source of light. It will illuminate the surface: the light rays cross the water surface and arrive to the eyes of the observer. But not all rays can escape from the water: Find the angle where the rays incident on the surface of the water totally reflect. Make a drawing!

ehild
 
  • #3
Ohh, thank you so much. It's just the critical angle, or 48.6 degrees, making the radius to be 1/tan(48.6)=1.13m.
 
  • #4
It is correct.

ehild
 
  • #5
However, based on the given information, we can use Snell's Law to calculate the angle of refraction at the air-water interface. We can then use Fermat's Principle to determine the path of the light from the light source to the surface of the water and then to the air. From this, we can calculate the angle of incidence at the water-air interface and use Snell's Law again to calculate the angle of refraction at this interface. Using these angles and the known distance of 1 meter, we can use trigonometry to calculate the radius of the circle of light on the surface of the water.
 

Related to Light in Underwater Pool Refraction Problem

1. What causes the light to appear distorted in an underwater pool?

The distortion of light in an underwater pool is caused by the phenomenon of refraction, where light waves bend as they pass through different mediums with varying densities. In this case, the light waves travel from air to water, causing them to change direction and creating the distorted appearance.

2. Does the depth of the pool affect the refraction of light?

Yes, the depth of the pool does affect the refraction of light. The deeper the pool, the greater the distance light must travel through water, resulting in a more pronounced distortion. This is because the density of water increases with depth, causing a greater change in the direction of the light waves.

3. Can the temperature of the water impact the refraction of light in an underwater pool?

Yes, the temperature of the water can affect the refraction of light. Warmer water has a lower density than colder water, which can cause light to refract differently. This is why the distortion of light may appear different in a pool with warm water compared to one with cold water.

4. How does the shape of the pool impact the refraction of light?

The shape of the pool can also play a role in the refraction of light. The curvature of the pool's walls can cause light to bend in different directions, leading to a more complex and varied distortion of light. A pool with a curved or irregular shape may create more noticeable refraction effects compared to a rectangular pool.

5. Can the refraction of light in an underwater pool be prevented?

While the refraction of light in an underwater pool cannot be completely eliminated, there are some ways to minimize its effects. Using flat and clear pool walls can reduce the distortion, as well as keeping the water temperature consistent. Additionally, using polarized sunglasses when swimming in the pool can help reduce the appearance of refraction.

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