Light in Underwater Pool Refraction Problem

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Homework Help Overview

The problem involves a small underwater pool light located 1 meter below the surface of a swimming pool, focusing on the radius of the circle of light that emerges at the surface due to refraction and reflection of light. The subject area includes concepts of optics, specifically Snell's Law and critical angles.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the nature of the light source, considering it as a point source. There is an emphasis on determining the critical angle for total internal reflection and the implications for light escaping the water.

Discussion Status

Some participants have provided insights into the critical angle and its relevance to the problem. There is an acknowledgment of the relationship between the critical angle and the radius of the light circle, though not all aspects of the problem have been fully explored or agreed upon.

Contextual Notes

Participants note the absence of the radius of the light source itself, which may affect the overall understanding of the problem setup.

JSGandora
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Homework Statement


A small underwater pool light is 1 meter below the surface of a swimming pool. What is the radius of the circle of light on the surface, from which light emerges from the water?

Homework Equations


Snell's Law
Fermat's Principle

The Attempt at a Solution

I have no idea about how to approach the first part because we're not given the radius of the light.
 
Last edited:
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JSGandora said:
A small underwater pool light is 1 meter below the surface of a swimming pool. I also have no idea how to approach the first part because we're not given the radius of the light.

It is small. Consider it a point source of light. It will illuminate the surface: the light rays cross the water surface and arrive to the eyes of the observer. But not all rays can escape from the water: Find the angle where the rays incident on the surface of the water totally reflect. Make a drawing!

ehild
 
Ohh, thank you so much. It's just the critical angle, or 48.6 degrees, making the radius to be 1/tan(48.6)=1.13m.
 
It is correct.

ehild
 

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