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University of Wisconsin - Milwaukee

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Problem 65 Hard Difficulty

A cataract - impaired lens in an eye may be surgically removed and replaced by a manufactured lens. The focal length required for the new lens is determined by the lens - to - retina distance, which is measured by a sonar - like device, and by the requirement that the implant provide for correct distance vision. (a) If the distance from lens to retina is 22.4 mm, calculate the power of the implanted lens in diopters. (b) Since there is no accommodation and the implant allows for correct distance vision, a corrective lens for close work or reading must be used. Assume a reading distance of 33.0 cm, and calculate the power of the lens in the reading glasses.

Answer

a. 48.6 \text { diopter } s
b. -103 \mathrm{cm}

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Top Physics 103 Educators
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Video Transcript

So we have a case where a Catterick impair Liz is surgically removed and replaced by artificial lens. So in part A, it is given that the distance from the lens to Regina is 22.4 meter. This Mr Lin's should have emails distance of 22.4 meter when the object is a distant object. So that means when P equals infinity, Q is a 22 point for millimeter. All right, What I'm gonna do here is I'm gonna write down in terms off meter 22.4 times to do make it a three meter now for the infinite object like a DNR in front of distance. If we use the less Finland's equation, we're gonna get focal length it cause Q because 22.4 times 10 to the negative three. So from here, we can actually just find the power of the lends to be one of her F. And that's going to give me one of our 22.4 times sent in negative three. Remember, one over f has f has to be in meters for that, and this is going to give me positive 44.6 Stab tres. All right, so that's the power of the less. Now for part B. The power of the lens found in part, is on Lee for the distant vision. But to see the closer objects, the persons should use an additional corrective lis on top of the that's particularly more plants. What So now if the person wants to read at Pecos 33 centimeter? So if the person wants to read at 33 centimeter, then the corrective lens should produce parallel rays, that is. Q has to be called to infinity so that the artificial limbs can focus the maze of the parallel race in retina. All right, so in this case, P the power has to be one of her F because one of her P plus whatever Q. And remember one of accuse infinity. So it is basically one of her P right, So 1/0 0.33 and this would give me positive 3.3 doctors

University of Wisconsin - Milwaukee
Top Physics 103 Educators
Elyse G.

Cornell University

Andy C.

University of Michigan - Ann Arbor

Marshall S.

University of Washington

Zachary M.

Hope College