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Fitting Contact Lenses with a Keratometer When a patient isbeing fitted with contact lenses, the curvature of the patient'scornea 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 10.0 $\mathrm{cm}$ in front of apatient's eye, and the reflected image is magnified by a factor of$0.035,$ what is the radius of curvature of the patient's cornea?

7.3 $\mathrm{mm}$

Physics 103

Chapter 27

Optical lnstruments

Wave Optics

Cornell University

University of Michigan - Ann Arbor

Simon Fraser University

University of Sheffield

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Okay, So in this problem, we have a light foreign object, reflects off the front of the cornea, as if were a convex mirror and produce a reduce retour image. And we want to calculate the radius of curvature off the corn ear. So what we have we must know First of all, that radios. Of course. Richard defined two times the focal lens off the Cory. Therefore, if we discover the focal Lynch, we discovered the reaches a curvature. So what? We know off this problem, we know that the distance off the object is just let's see. 10 same team enters. We know the magnification, which is miners, you know, 0.0 35. And that's it is the only thing we know about this problem. So knowing that we have the magnification in the distance of the object, we know that to discover, in order to discover the focal length, gonna have to use the fuel ins equation, which is one divided by zero plus one divided by the I all to the bar of miners one. But the problem here is we don't have a distance of the image. So let's find out first the distance of the image using the magnification because we know the distance of the images. Just the magnification, times the distance of the object. So this is going to be a loss. Actually, magnification is positive in here, so position gonna be negative. Negative. Do you know 0.0 35 time, Stan. So this is just miners, you know, point 35 ST. Team enters. Okay, Well, now that we have the distance of the image, let's calculate the focal length, which should be one divided by 10 plus one divided by minors. You know, 10.35 minus one. So this is your smile is you know, point 36 tree. Same team enters. So now that we have a focal lens, the curvature radius of curvature, Cher's going to be That's pointing here. Just going to be two times zero point 363 So this is just 7.3 me limiters, and that's a final instructor. Just problem. Thanks.

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