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

[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]

 

[BvU]

Hello @joelkato1605 , !

"I have no idea" does not count as an attempt at solution:
https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

How is Snell connected to this problem ?

Can you post a sketch of the situation ??

 

[joelkato1605]

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

 

[BvU]

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 ?

 

[joelkato1605]

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.

 

[Frodo]

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?

 

[joelkato1605]

Diagrams:

 

[BvU]

We have a picture !

Any description of what it represents ? Ah, yes:

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 ?

Now follow Frodo's advice

 

[joelkato1605]

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

 

[BvU]

You have part of the answer. I miss

Describe why and compute the angle of the cone.

 

[Frodo]

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.