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The near point of an eye is 75.0 cm. (a) What should be the power of a corrective lens prescribed to enable the eye to see an object clearly at 25.0 cm? (b) If, using the corrective lens, the person can see an object clearly at 26.0 cm but not at 25.0 cm, by how many diopters did the lens grinder miss the prescription?

a. 37.5 \mathrm{cm}

b. 0.16 \text { diopters too low }

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Numerade Educator

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Hope College

University of Winnipeg

So in this problem, the near point. Often I is 75 centimeter. So for part A If we want to find the corrective lens to be able to see at normal near point of 25 centimeter, then when the object distances that normal near point was his 25 centimeter or 0.25 meter. Then the Emmys distance has to be at negative. 75 centimeter negative. 75 centimeter. Okay, which is negatives 0.75 meter. No. The image of the reason why you see this negative here is because the inmates form is going to be first of all and upright. Right? So from here, we can actually find the power of the list. That corrective Lis is going to be won over F because one of her p plus one of a cue this is going to give me que plus p over cute RP and this is gonna be negative. 0.75 plus 0.25 over negative 0.75 times 0.25 and this would be positive 2.67 doctors. So, in part B, the person who made the list mess it up. Okay. And the Liz had different focal. And instead, and he was able to see the person who had the new point at 75 Centimetre was able to see on Lee at the object like the near his near point was at 26 centimeter instead of being 25 centimeter. So we want to find out what the error in power was. All right? So when the object, his near point was at 26 David, then that means this is 0.26 meter than the actual power of the lens Waas, one of the F, which is going to be que plus p over Cube Duh p. I'm gonna call this P prime and set. Okay, So that one and now p prime is 0.26 meter. So from here, we can actually see that this is going to be positive. 2.51 Dieters. Okay. Now, to find the error Delta P, which is the error in the power, it's going to be the absolute value off p minus p prime, which is going to be 2.67 minus 2.51 And this is going to give us your 0.16 doctors. So the power was sirrah 0.16 die after slower then the person who designed the lists actually wanted it to be.

University of Wisconsin - Milwaukee