# Determine the radius of curvature of the cornea for the case p = 32.0 cm and M = 0.0150.

To fit a contact lens to a patient's eye, a "keratometer" can be used to measure the curvature of the front surface of the eye, the cornea. This instrument places an illuminated object of known size at a known distance p from the cornea. The cornea reflects some light from the object, forming an image of the object. The magnification M of the image is measured by using a small viewing telescope that allows comparison of the image formed by the cornea with a second calibrated image projected into the field of view by a prism arrangement. Determine the radius of curvature of the cornea for the case p = 32.0 cm and M = 0.0150
cm

asked Apr 9, 2012 in Physics

To solve this problem you need to use two equations.

The first is the equation for Magnification which is:

M = -q / p

and the second equation is the mirrior equation which is:

1/p + 1/q = 2/R

R is the radius of curvature, and q is the image distance.

First step is to solve for q, which is:

q = -M*p

Next, you can plug p and into the mirror equation and solve for R.

R = 2/ (1/p + 1/q)

**note R is positive

answered Apr 11, 2012 by ~Expert~ (3,856 points)
selected Apr 11, 2012 by Gummmys