# Why Does Light Form a Cone When Refracted in a Swimming Pool?

• joelkato1605
In summary, the first sketch is what I assumed would happen, where the light beams bends. The second is meant to depict the light forming a cone, which I don't understand. Snell has to do with angles. Which angles in the picture ? forget the second picture - nobody understands it.
joelkato1605
Homework Statement
You are several meters under water (η = 1.33), swimming in a pool, and look skywards. Light from outside the pool will form a cone. Describe why and compute the
angle of the cone.
Relevant Equations
snell's law
The first sketch is what I assumed would happen, where the light beams bends. And the second is meant to depict the light forming a cone, which I don't understand.

[Mentors provided help re-posting the image that was missing]

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Thanks for the reply I edited my question, however I'm not sure where to start with a solution.

joelkato1605 said:
The first sketch is what I assumed would happen, where the light beams bends. And the second is meant to depict the light forming a cone, which I don't understand.
What do they look like ? Snell has to do with angles. Which angles in the picture ?

BvU said:
What do they look like ? Snell has to do with angles. Which angles in the picture ?
The refractive index of air is 1, so 1*sin( theta initial)=1.33*sin(theta cone) then maybe assume theta inital =90?

I'm not really sure but that is all I can think of.

Draw a picture with an eye below the surface of the water.

Draw a ray of light from air to the eye, passing through the water. Draw another ray at a different angle of incidence. And another. And another.

What happens as you change the angle of incidence of the ray?

Look up "total internal reflection" - at what angle does it occur?

What happens when you get total internal reflection?

Diagrams:

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• lightcone.pdf
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We have a picture !

Any description of what it represents ? Ah, yes:
joelkato1605 said:
The first sketch is what I assumed would happen, where the light beams bends. And the second is meant to depict the light forming a cone, which I don't understand.
Forget the second picture -- nobody understands it.

In the top picture, where are the angles we encounter in Snell's law ?

berkeman
So is it just the critical angle:
arcsin(1/1.33)?

You have part of the answer. I miss
Describe why and compute the angle of the cone.

Your diagram is not very good for doing an analysis. Where is the eye you were asked to put in? It's all about angles - how can you measure angles in your diagram?

Perhaps some was my error as, when I said draw a picture, I should have said draw a diagram.

You should have drawn a diagram like below where you are looking at a cross section through the experiment - it is a 2-dimensional diagram. Solve the problem in 2-D before generalising your solution to 3-D. Using the diagram:

1. Draw a ray of light going from B to the eye. Label the angle of incidence and the angle of refraction. To do that you will need to draw in the normal.

2. Draw a ray of light going from C to the eye. Label the angle of incidence and the angle of refraction.

3. Draw a ray of light going from D to the eye. Label the angle of incidence and the angle of refraction.

What do you notice is happening as the angle of incidence of the ray increases from B to C to D?

When you thoroughly understand what is happening in the diagram, think about what happens in 3-D.

#### Attachments

• diagram.png
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## What is refraction in a swimming pool?

Refraction in a swimming pool is the bending of light as it passes through the water. This is due to the change in speed and density of the light as it moves from air to water.

## Why does refraction occur in a swimming pool?

Refraction occurs because light travels at different speeds in different mediums. In this case, the light travels slower in water than in air, causing it to bend when it enters the water.

## How does refraction affect the appearance of objects in a swimming pool?

Refraction can make objects appear distorted or shifted when viewed from above the water. This is because the light rays are bending as they enter and exit the water, creating an illusion of the object being in a different location.

## What is the difference between refraction in a swimming pool and in a glass of water?

The principle of refraction is the same in both cases, but the amount of bending is different. The density and depth of the water in a swimming pool is much greater than a glass of water, resulting in a greater amount of refraction.

## Can refraction in a swimming pool be controlled or changed?

Refraction in a swimming pool cannot be controlled, but it can be minimized by using a pool with clear and still water. Additionally, objects can be viewed from different angles to reduce the effects of refraction.

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