Optics Problems: Submerged light

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Homework Help Overview

The problem involves a green light submerged 2.30 m beneath the surface of a liquid with an index of refraction of 1.39, and it asks for the radius of the circle from which light escapes into the air above the surface.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the critical angle and its implications for the radius of the escape circle. There are attempts to clarify the relationship between the critical angle and the geometry of the situation, including questions about the meaning of the radius and the calculations involved.

Discussion Status

Some participants have provided guidance on visualizing the problem and interpreting the geometry, while others express uncertainty about their calculations and the definitions involved. There is an ongoing exploration of the correct approach to determine the radius.

Contextual Notes

Participants note potential confusion regarding the hypotenuse of the triangle versus the leg of the triangle that is relevant to the problem. There are also mentions of the limitations of relying on attachments for clarification.

yuvlevental
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Homework Statement


A green light is submerged 2.30 m beneath the surface of a liquid with an index of refraction 1.39. What is the radius of the circle from which light escapes from the liquid into the air above the surface?

Homework Equations


Critical angle: Sin(AngleCritical)=(n2/n1), n1>n2
Well I think...

The Attempt at a Solution


Is the radius a direct line of light from the light to the water's surface?
If so: sin-1(1.39/1) = 46 cos(46)*2.3=ans
 
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You seem to have the critical angle correct. Draw a picture of the situation. The light source (which I take it you are to treat as a point) would have rays reaching the surface from 2.3 meters below. At the surface, the rays just at the critical angle which define the radius of this circle make a 46º angle to the perpendicular. What angle do they make to the line going straight up from the source to the surface? If the distance up to the surface is 2.3 m, what would the radius of the circle be?
 
Last edited:
I got 3.31m, but I know that I am wrong. It the hypothenuse in the attatched picture the one that the problem meant?
 

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yuvlevental said:
I got 3.31m, but I know that I am wrong. It the hypothenuse in the attatched picture the one that the problem meant?

That sounds like you found the diameter of the circle. How did you calculate this value?

BTW, attachments can take hours to be cleared on this board. They should not be relied upon if you want a quick reply...
 
i did 2.3/cos(46) to find the length between the point of light and where the light meets the water. Also, I did 3.31/2, but the answer is still wrong. I'm not sure what the circle is. Can you describe it to me?
 
yuvlevental said:
i did 2.3/cos(46) to find the length between the point of light and where the light meets the water. Also, I did 3.31/2, but the answer is still wrong. I'm not sure what the circle is. Can you describe it to me?

You don't want the hypotenuse of the triangle, as that traces the ray of light itself. You are interested in the leg of the triangle perpendicular to the vertical leg, which is the distance along the surface of the water from the point directly above the light source. The other end of that leg is the point where the light ray traveling at the critical angle emerges from the water. What would be the length of that leg?
 
thank you very much good madam/sir, you are my hero :-DDDDD
 

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