Light Reflection: Path Length Difference?

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SUMMARY

The path length difference when light reflects from a thin film back toward the source is equal to twice the thickness of the film multiplied by the refractive index of the film. This conclusion is based on the understanding that the optical path length difference accounts for the phase change of 180 degrees that occurs upon reflection from an optically denser medium. The angle of incidence is approximately 90 degrees, reinforcing the calculation of the path length difference as twice the film thickness.

PREREQUISITES
  • Understanding of thin film interference
  • Knowledge of optical path length concepts
  • Familiarity with refractive index
  • Basic principles of light reflection
NEXT STEPS
  • Study the principles of thin film interference in detail
  • Learn about the effects of refractive index on light behavior
  • Explore the concept of phase change upon reflection
  • Investigate applications of thin films in optics and coatings
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Students studying optics, physics educators, and anyone interested in the principles of light behavior in thin films.

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Homework Statement



When light reflects from a thin film back toward the source, what is the path length difference?


The Attempt at a Solution



A. It is equal to twice the thickness of the film.
B. It is equal to the thickness of the film.
C. It is equal to half the thickness of the film.

I have rules out C. I think the answer is A but I'm not sure.
 
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I'm leaning towards A now. Anyone have any ideas?
 


Tell us why you are leaning towards A and we can help you evaluate that thought process.
 


I guess the path length difference is between the rays reflected from the two surfaces of the film. When light reflects from a "thin" film back toward the source, the angle of incidence is approximately 90 degree. So, the optical path length difference is twice the film thickness times the refractive index of the film. One also has to take into account the fact that a phase change of 180 degree occurs upon reflection from an optically denser medium.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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