What is the Radius of Curvature of the Outer Surface of a Contact Lens?

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SUMMARY

The radius of curvature of the outer surface of a contact lens made of plastic with an index of refraction of 1.58 and a focal length of +26.0 cm is calculated using the thin lens equation. Given that the inner surface has a radius of curvature of +20.0 mm, the outer surface's radius of curvature (R1) is determined to be 1.768 cm. The solution confirms that both radii should be treated as positive values in this context, adhering to the sign conventions for lenses.

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  • Understanding of the thin lens equation
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  • Knowledge of sign conventions in lens optics
  • Basic algebra for solving equations
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Students studying optics, optical engineers, and professionals involved in lens design and manufacturing will benefit from this discussion.

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[SOLVED] Contact Lenses Problem

Homework Statement



A contact lens is made of plastic with an index of refraction of 1.58. The lens has a focal length of +26.0 cm, and its inner surface has a radius of curvature of +20.0 mm. What is the radius of curvature of the outer surface?

Homework Equations



The "thin lens equation"
1/f = (n-1)(1/R1 - 1/R2)

The Attempt at a Solution



This seems like a basic, out-of-the-book problem at first glance, but I can't get it. I've tried it several times, solving for R1 and R2 because I don't know which radius of curvature the 20.0 mm is. I think my main problems are probably sign errors and where to put the 20.0 mm (I don't know the rules for sign conventions in lenses, etc). Could someone point me in the right direction? Thanks.
 
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Nevermind, I figured out my answer; I might as well post the solution here for reference for others!

1/f = (n-1)(1/R1 - 1/R2)
(In this case, both R's should be positive.)
0.038 = (0.58)(1/R1 - 1/2)
0.038 = (0.58/R1) - 0.29
(Solve for R1)
R1 = 1.768 cm
 

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