Question

Having a really hard time with this question!

To fit a contact lens to a patient's eye, a keratometer can be used to measure the curvature of the cornea-the front surface of the eye. This instrument places an illuminated object of known size at a known distance p from the cornea, which then reflects some light from the object, forming an image of it. The magnification M of the image is measured by using a small viewing telescope that allows a 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 when p = 34.0 cm and M = 0.0200.

Answer 1

When a patient is being fitted with contact lenses, the curvature of the patient's cornea is measured with an instrument known as a keratometer. A lighted object is held near the eye, and the keratometer measures the magnification of the image formed by reflection from the front of the cornea. If an object is held 11.5 cm in front of a patient's eye, and the ratio of the height of the reflected image to that of the object is 0.028, what is the radius of curvature of the patient's cornea?

A:Since this is dealing with refections we use the mirror equation for magnification

M = d(i)/d(o)= h(i)/h(o)

M = 0.028
d(o) =11.5 cm

This will let us calculate the image distance d(i)

d(i) = Md(o) = (0.028)(11.5cm) = .322 cm

Now we can calculate the radius of curvature

1/f =2/R= 1/do + 1/di

2/R = (1/11.5 ) + (1/.322) = 0.0869565217 + 3.10559006

2/R = 3.19254658

R/2 = 1/3.19254658 = 0.313229572

R = 0.626459144 cm