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

  • Thread starter Thread starter rabar789
  • Start date Start date
  • Tags Tags
    Contact Lenses
AI Thread Summary
The discussion revolves around calculating the radius of curvature of the outer surface of a contact lens with a given focal length and inner surface radius. The lens has an index of refraction of 1.58 and a focal length of +26.0 cm, with the inner radius of curvature specified as +20.0 mm. The thin lens equation is applied, leading to confusion regarding sign conventions for the radii. After some attempts and clarification on the positive signs for both radii, the correct outer radius of curvature is determined to be 1.768 cm. The solution is shared for the benefit of others facing similar problems.
rabar789
Messages
21
Reaction score
0
[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.
 
Physics news on Phys.org
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
 
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
Back
Top