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University of Wisconsin - Milwaukee

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Problem 19 Easy Difficulty

A nearsighted woman can’t see objects clearly beyond 40.0 cm (her far point). If she has no astigmatism and contact lenses are prescribed, what power and type of lens are required to correct her vision?

Answer

-2.50 \text { diopter } s

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Top Physics 103 Educators
Andy C.

University of Michigan - Ann Arbor

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Video Transcript

in this problem, a woman with near sightedness has a fire point at 40 centimeter. And if she wants to wear a pair of contact lenses, a virtual and upright image should form at the image distance, which is also equal to negative value of the 40 centimeter. So Q has to be equal to negative 40 centimeter to able to be able to see an object at infinity. So from here, if we use the lens equation, whatever Africa was one of her P plus one of our cue, one of her pee is gonna be called one of infinity. Plus one of Acute is going to be called to one of our negative forties and do better one of our infinity and zero. So that means we actually get F equals minus 40 centimeter. All right, now we have the focal length, which is negative 40 centimeter. Now we want to find out the power of the lens. So the power of the less I'm gonna put this Capital P here he is actually the reciprocal of difficult length of the lens. So that's gonna be won over negative 40 centimeter. But be careful here. We have to convert centimeter in two meters. So if we do that, we have negative zero point for meter. And this will be called Thio. Negative 2.5 Diop Tres. All right. Now, if you look at the power, you can see this negative sign here. This actually indicates that the lens is the lenses can give or divers ing.

University of Wisconsin - Milwaukee
Top Physics 103 Educators
Andy C.

University of Michigan - Ann Arbor

LB
Liev B.

Numerade Educator

Farnaz M.

Other Schools

Aspen F.

University of Sheffield