Lens-Makers Equation: Finding Focal Length in Different Mediums

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SUMMARY

The lens-makers' equation is essential for calculating the focal length of a lens in different mediums, specifically when the index of refraction of the surrounding medium is considered. For a lens with a focal length of 92.6 cm in air and an index of refraction of 1.55, the correct approach involves using the modified equation 1/f = (n2/n1 - 1)(1/R1 - 1/R2). The index of refraction of water is 1.33, which must be incorporated correctly to find the new focal length. Misapplication of the equation can lead to incorrect results, as demonstrated in the discussion.

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  • Understanding of the lens-makers' equation
  • Knowledge of index of refraction concepts
  • Familiarity with focal length calculations
  • Basic principles of optics and lens design
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  • Study the derivation of the lens-makers' equation
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Students in optics, physics enthusiasts, and professionals in optical engineering who seek to understand the behavior of lenses in different mediums.

PhyHyped

Homework Statement


The lens-makers' equation applies to a lens immersed in a liquid if n in the equation is replaced by n2/n1. Here n2 refers to the index of refraction of the lens material and n1 is that of the medium surrounding the lens.
(a) A certain lens has focal length 92.6 cm in the air and index of refraction 1.55. Find its focal length in water.
(b) A certain mirror has focal length 92.6 cm in the air. Find its focal length in water.

Homework Equations


1/f = (n-1)(1/R1 - 1/R2)

The Attempt at a Solution


I'm not really sure how to set this up. Think it looks something like this f2/f1 =(n1-1)/(n2-1) index of refraction of water 1.33 plugged in the given variables and got 55.56 which was wrong.

Comments
Not sure what direction to go with this equation.

Any help would be greatly appreciated.
 
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PhyHyped said:
f2/f1 =(n1-1)/(n2-1)
That does not result from replacing n with n1/n2 in 1/f = (n-1)(1/R1 - 1/R2), as instructed.
 
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Likes   Reactions: PhyHyped
thanks! I figured it out earlier! Thanks for the reply though
 

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