Ray Refraction: Finding the depth of a pool

In summary, a 4.0m wide swimming pool is filled to the top and becomes completely shaded in the afternoon when the sun is 20 degrees above the horizon. By using the Law of Refraction (Snell's Law), a ray of light coming up from the bottom of the pool can be traced to the surface at a 45 degree angle, indicating a depth of 4m. The accuracy of this solution cannot be confirmed without the answer to the problem.
  • #1
KEØM
68
0

Homework Statement


A 4.0m wide swimming pool is filled to the top. The bottom of the pool becomes completely
shaded in the afternoon when the sun is 20 degrees above the horizon. How deep is the pool?


Homework Equations


[tex]\theta[/tex] = arcsin(n2/n1)
n1sin[tex]\theta[/tex]1= n2sin[tex]\theta[/tex]2




The Attempt at a Solution


The main thing that I don't understand about this problem is that if the bottom of the pool
is shaded then that means light is not reaching the bottom right? I have only seen problems where something under the surface emitting light has total internal reflection.
Could somebody please explain this to me.

Thanks in advance.
 
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  • #2
Sketch a ray coming up from the far end of the bottom of the pool to the surface at the near end, refracting (angle change) at the surface and heading off at an angle of 20 degrees above the water/ground. Beginning with the 20 degrees and using the Law of Refraction (Snell's Law) you can deduce the angle in the water and then the depth.
 
  • #3
Ok, so using snells law I found the angle to be 45 degrees and then using trigonometry I found the height to be 4m. Is this right? I don't have the answer to the problem so I don't know.

Thanks a bunch for your help delphi.
 

Related to Ray Refraction: Finding the depth of a pool

1. What is ray refraction?

Ray refraction is the phenomenon in which light travels through a medium at different speeds, causing the light to bend or change direction.

2. How is ray refraction used to find the depth of a pool?

By measuring the angle at which a light ray enters and exits the water, and knowing the refractive index of water, the depth of the pool can be calculated using the laws of refraction.

3. What factors affect ray refraction in a pool?

The refractive index of water, the angle at which the light enters and exits the water, and the shape and curvature of the pool all play a role in ray refraction.

4. Can ray refraction be used to find the depth of any body of water?

Yes, ray refraction can be used to find the depth of any body of water as long as the refractive index is known and the angle of incidence and refraction can be measured accurately.

5. Are there any limitations to using ray refraction to find the depth of a pool?

Yes, ray refraction can be affected by factors such as water temperature and impurities in the water, which can alter the refractive index and affect the accuracy of the calculations.

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