Calculating Apparent Depth: Air vs Water

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SUMMARY

The discussion confirms that the formula for calculating apparent depth, given by Apparent Depth = Actual Depth x (n air / n water), is valid for determining how objects appear submerged in water. This relationship derives from Snell's Law and the small angle approximation, providing a straightforward method for solving problems related to optical depth perception in fluids. The consensus among participants is that this approach simplifies the calculation without compromising accuracy.

PREREQUISITES
  • Understanding of Snell's Law in optics
  • Familiarity with the concept of refractive indices (n air and n water)
  • Basic knowledge of geometry and angles
  • Experience with optical phenomena related to light refraction
NEXT STEPS
  • Study the derivation of Snell's Law and its applications in optics
  • Explore the concept of refractive index and its significance in different media
  • Investigate the small angle approximation and its relevance in physics
  • Practice problems involving apparent depth calculations in various fluids
USEFUL FOR

Students studying physics, particularly those focusing on optics, as well as educators looking for effective methods to teach concepts related to light refraction and apparent depth.

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Homework Statement


Instead of calculating apparent depth (for example, a penny in a glass of water appears to be closer to the surface than it actually is), instead of finding the angle of refraction and using snell's law, can I use the following:

Apparent Depth = Actual Depth x (n air / n water)
?
 
Physics news on Phys.org
Yes, that relationship will work for this situation. It comes ultimately from applying Snell's Law and the small angle approximation to the given problem.
 

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