How Does Light Refraction Affect the Diameter of a Light Cone in a Pool?

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SUMMARY

The discussion focuses on calculating the diameter of a light cone emerging from a swimming pool, specifically when light refracts from water to air. The pool is 70.0 cm deep, with a light source at the bottom measuring 10.0 cm in diameter, and an observer positioned 2.50 m away. The critical angle for this scenario is essential for determining the maximum angle of refraction, which directly influences the diameter of the light cone. The potential answers for the diameter are 1.60 m, 1.70 m, 1.75 m, and 1.80 m.

PREREQUISITES
  • Understanding of Snell's Law for light refraction
  • Knowledge of critical angles in optics
  • Ability to draw and interpret geometric diagrams
  • Familiarity with basic trigonometric principles
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  • Study Snell's Law and its application in light refraction scenarios
  • Learn how to calculate critical angles for different mediums
  • Explore geometric optics, focusing on light cones and their properties
  • Practice problems involving light refraction in various depths of water
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Students studying physics, particularly those focusing on optics, as well as educators looking for practical examples of light refraction in real-world scenarios.

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Homework Statement


At the shallow end of a swimming pool, the water is 70.0 cm deep. The diameter of the cone of the light emerging from the water into the air above, emitted by a light source 10.0 cm in diameter at the bottom of the pool and measured by an observer on the edge of the pool 2.50 m away, is
a) 1.60 m
b) 1.70 m
c) 1.75 m
d) 1.80 m


Homework Equations


nsin(angle)=nsin(angle)
nsin(criticalangle)=nsin90


The Attempt at a Solution


I am really confused, can anybody help me? I don't know where to start.

Thanks
 
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i don't sure the situation is clear. how tall is the observer?
 
This is a critical angle problem. Draw a diagram of the light (at the bottom of the pool) being emitted at all angles. Figure out the maximum angle that will be refracted--anything greater will just be reflected by the water surface--and use that to calculate the diameter of the cone.
 

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