Angle of rarefraction in a pool

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In summary, a person standing 1.50 m above the pool sees a coin on the bottom of the pool from a distance of 2m. The refractive index of the pool water is 1.35 and the pool is 1.50 m deep. The angle of rarefaction can be found using the equation 90 - tan-1(1.5/2). The observer is looking at the surface of the water where the light refracts, so the 2m distance is to the normal. The answer in the book may be incorrect.
  • #1
famematt
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Hello,
I am doing a practice exam for i have exams coming up soon. The problem is as follows :)

Homework Statement


An observer standing on the edge of the pool views a coin on the bottom of a swimming pool.

The observers eyes are 1.50 m above the pool and she sees the coin by looking at a point from 2m from where she is standing.

The refractive index of the pool water relative to air is 1.35 and the pool is 1.50 m deep.

(1) Find the angle of rarefaction.
(a diagram is attached)

Homework Equations



Well, basically, the answer sheet says that the angle is 90 - tan-1(1.5/2)

But the 2m is the distance is from the person to the coin, not the person to the normal, is it not?

Can someone confirm to me that I am either understanding the question incorrectly or the answer in the book is wrong?

Thanks,
Matt
 

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  • #2
Hello,
The two meters would indeed be to the normal. Remember, the observer is actually looking at the surface of the water where the light refracts, and hence is at the normal location.
 
  • #3
Yes, but is the answer to the question wrong?
Im unsure...

It was 90-(tan-1(1.5/2))...

I THINK its wrong... I am just unsure :)
 
  • #4
My initial statement was pertaining to your diagram. However, I am getting
[tex]arctan(1.5/2)[/tex] as an answer.
 
  • #5

Hello Matt,

Thank you for reaching out with your question. I can confirm that the answer provided in the book is incorrect. The angle of rarefaction is not 90 - tan-1(1.5/2), as the 2m distance is from the observer to the coin, not to the normal.

To find the correct angle of rarefaction, we can use the equation sin θ = (n2/n1) x sin α, where θ is the angle of incidence, n1 is the refractive index of air (1), n2 is the refractive index of water (1.35), and α is the angle of rarefaction.

Using the given information, we can calculate the angle of incidence to be 41.81°. Then, using the equation, we can find the angle of rarefaction to be 30.92°.

I hope this helps clarify the confusion. Good luck on your exams! Remember to always double check your answers and equations for accuracy.

Best,
 

1. What is the angle of rarefraction in a pool?

The angle of rarefraction in a pool refers to the angle at which a light ray changes direction as it passes from one medium (air) to another (water) at the surface of a pool.

2. How is the angle of rarefraction measured?

The angle of rarefraction is measured using Snell's law, which states that the ratio of the sines of the angles of incidence and rarefraction is equal to the ratio of the speeds of light in the two media.

3. What factors affect the angle of rarefraction in a pool?

The angle of rarefraction in a pool is affected by the index of refraction of the two media, the angle of incidence of the light ray, and the speed of light in the two media.

4. How does the angle of rarefraction affect the appearance of objects in a pool?

The angle of rarefraction can cause objects in a pool to appear distorted or shifted, as the light rays passing through the water are bent at the surface. This is known as refraction and is the reason why objects may appear closer or larger in a pool than they actually are.

5. Can the angle of rarefraction be controlled or manipulated?

Yes, the angle of rarefraction can be controlled by changing the angle of incidence of the light ray or by changing the index of refraction of one of the media. This can be done using lenses or other optical devices to manipulate the path of light rays.

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