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

[rabar789]

[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.

 

[rabar789]

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

 

[Moetasim]

Contact Lenses Problem [SOLVED]

After reviewing the given information and the thin lens equation, it seems that the 20.0 mm radius of curvature is for the inner surface of the lens. Since the focal length is positive, the lens is converging and therefore the outer surface should have a negative radius of curvature. Using this information, we can rearrange the thin lens equation to solve for R2:

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

Plugging in the given values, we get:

1/R2 = (1/0.26 - 1/0.02)/(1.58-1)

Simplifying, we get:

1/R2 = (1.58/0.52)/0.58

1/R2 = 3.04

R2 = 1/3.04 = 0.33 cm or 3.3 mm

Therefore, the radius of curvature of the outer surface of the contact lens is approximately 3.3 mm.