Lens-Makers Equation: Finding Focal Length in Different Mediums

  • Thread starter PhyHyped
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In summary, the lens-makers' equation can be applied to a lens immersed in a liquid by replacing n with n2/n1, where n2 is the index of refraction of the lens material and n1 is the index of refraction of the surrounding medium. Using this equation, the focal length of a lens with a focal length of 92.6 cm in air and an index of refraction of 1.55 can be found in water. Similarly, the focal length of a mirror with a focal length of 92.6 cm in air can be found in water using the same equation.
  • #1
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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  • #2
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 PhyHyped
  • #3
thanks! I figured it out earlier! Thanks for the reply though
 

1. What is the lens-maker's equation?

The lens-maker's equation is a formula used to calculate the focal length of a lens in different mediums. It takes into account the refractive index of the lens material and the surrounding medium, as well as the curvature of the lens surfaces.

2. How is the lens-maker's equation derived?

The lens-maker's equation is derived from the laws of refraction and Snell's law, which describe how light bends when passing through different mediums. It also takes into account the geometry of the lens and the principle of thin lenses.

3. What do the variables in the lens-maker's equation represent?

The variables in the lens-maker's equation represent the following: f is the focal length of the lens, n1 is the refractive index of the lens material, n2 is the refractive index of the surrounding medium, and R1 and R2 are the radii of curvature of the two lens surfaces.

4. Can the lens-maker's equation be used for all types of lenses?

Yes, the lens-maker's equation can be used for all types of lenses, including both convex and concave lenses. It is a fundamental formula in optics and is applicable to all types of lenses, as long as the lens materials and surrounding mediums are known.

5. How accurate is the lens-maker's equation?

The lens-maker's equation is a simplified model and does not take into account factors such as lens thickness and aberrations. Therefore, it may not be 100% accurate in all cases. However, it is a good approximation and is commonly used in lens design and calculations.

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