The cornea behaves as a thin lens of focal length approximately 1.80 cm, althoug

Question

The cornea behaves as a thin lens of focal length approximately 1.80 cm, although this varies a bit. The material of which it is made has an index of refraction of 1.38, and its front surface is convex, with a radius of curvature of 5.00 mm.
(Note: The results obtained here are not strictly accurate, because, on one side, the cornea has a fluid with a refractive index different from that of air.) Q: If this focal length is in air, what is the radius of curvature of the back side of the cornea? The closest distance at which a typical person can focus on an object (called the near point) is about 25.0 cm, although this varies considerably with age. Where would the cornea focus the image of an 5.00 mm-tall object at the near point?

Explanation / Answer

Use the lens makers equation: 1/f = ( n - 1 ) ( 1/R1 - 1/R2 ) They give you f =0.0180 n = 1.38 R1 =0.005 and you have to solve for R2 (notice I expressed f and R1 in meters...) So : 1/0.0180 = ( 1.38 - 1) ( 1/0.005 - 1/R2 ) Or: 55.556 = 0.38 *( 200 - 1/R2 ) Or: 146.2 = 200 -1/R2 or 1/R2 = 200 -146.2 = 53.8 invert both sides R2 = 0.0186 meters or R2= 1.86 cm = 18.6 mm so the front is curved outward with a radius of 5.00mm and the back is also curved outward with a radiusof 18.6 mm

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