Index of refraction in an air bubble

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SUMMARY

The discussion centers on calculating the apparent depth of an air bubble within a 9.00 cm-diameter plastic ball, positioned 2.90 cm from the surface. The relevant equation used is the lensmaker's equation: n_1/s + n_2/s' = n_2-n_1/R. The correct solution for the apparent depth, s', is determined to be -0.024 m, indicating that the bubble appears virtually beneath the surface due to the refraction of light. The final value is confirmed as accurate, emphasizing the importance of sign conventions in optics.

PREREQUISITES
  • Understanding of the lensmaker's equation in optics
  • Familiarity with the concept of refraction and indices of refraction
  • Basic knowledge of virtual images in optical systems
  • Ability to perform unit conversions and calculations in physics
NEXT STEPS
  • Study the principles of refraction and Snell's Law
  • Learn about virtual images and their properties in optics
  • Explore the applications of the lensmaker's equation in real-world scenarios
  • Investigate the effects of different materials on the index of refraction
USEFUL FOR

Students studying optics, physics educators, and anyone interested in understanding the behavior of light in different mediums.

tiger1
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[SOLVED] Index of refraction

Homework Statement


An air bubble inside an 9.00 cm-diameter plastic ball is 2.90 cm from the surface.

As you look at the ball with the bubble turned toward you, how far beneath the surface does the bubble appear to be?


Homework Equations


n_1/s + n_2/s' = n_2-n_1/R


The Attempt at a Solution


1.59/.0290 + 1/s' = 1-1.5/.045
s'=1.52

I'm not sure why that isn't correct.

...

1.59/.0290+1/s' = 1.59-1/.045
s'=.024m <- correct
 
Last edited:
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Here s' is virtual. So it should be -ve.
Your value is correct.
 

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