Apparent depth with multiple indices of refraction

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SUMMARY

The apparent depth of a penny located at the bottom of a 1m deep barrel of water with a 20cm layer of oil on top is calculated using Snell's Law. The refractive indices are 1.33 for water and 1.5 for oil. The apparent depth when viewed through just the water is 0.75m. To generalize for the oil layer, Snell's Law must be applied at both the water-oil and oil-air boundaries, requiring a two-step calculation.

PREREQUISITES
  • Understanding of Snell's Law in optics
  • Knowledge of refractive indices (n values)
  • Familiarity with ray diagrams for light refraction
  • Basic principles of light behavior at interfaces
NEXT STEPS
  • Study the application of Snell's Law in multi-layer media
  • Explore ray diagram techniques for complex refraction scenarios
  • Learn about the effects of different refractive indices on apparent depth
  • Investigate practical examples of refraction in everyday materials
USEFUL FOR

Students in physics or optics courses, educators teaching light refraction concepts, and anyone interested in understanding the behavior of light through different media.

KBriggs
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Homework Statement


A penny is located at the bottom of a barrel of water 1m deep. There is a 20cm thick layer of oil on top of the water. To an observer at normal incidence, what is the apparent depth of the penny. n for water is 1.33, for oil it is 1.5


Homework Equations


Snell's law, lots of ray diagrams


The Attempt at a Solution


I have already shown that to an observer looking through just the water, the apparent depth is 0.75m. I am just not sure how to generalize this for the other layer. Can someone point me in the right direction?
 
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The method is the same, only you have to use Snell's law twice, at the water oil, and oil/air boundaries.
 

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