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University of Wisconsin - Milwaukee

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Problem 20 Easy Difficulty

A person sees clearly wearing eyeglasses that have a power of 24.00 diopters when the lenses are 2.00 cm in front of the eyes. (a) What is the focal length of the lens? (b) Is the person nearsighted or farsighted? (c) If the person wants to switch to contact lenses placed directly on the eyes, what lens power should be prescribed?

Answer

a. 25.0 \mathrm{cm}
b. \text { nearsighted }
c. -3.70 \text { diopters }

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Top Physics 103 Educators
LB
Liev B.

Numerade Educator

Farnaz M.

Other Schools

Aspen F.

University of Sheffield

Jared E.

University of Winnipeg

Video Transcript

So, first of all, I should let you know that I'm trying to be consistent with the textbook in this problem because under computer screen for this problem, you can see that power is given as 24 doctors. But in textbook problems, it is actually negative. Ford actor. So I'm using negative four adapters, So let's start. So here, the power of the eyeglasses that are worn to senator in front off the I is negative four adapters. So for part A, we just want to find out the focal length, which is F is going to be reciprocal of the power. Sorry, this negative sign does not exist here, which is going to one over negative for, and this is going to give me negative 0.25 meter, which is 25 centimeter negative, 25 centimeter. Two. So for part B, since the person is wearing a negative focal length eyeglass, he must be able. He must be nearsighted says, for a distant objects, which is when P because infinity then Q has to be called a focal length, which is 25 centimeter. His immense distances at 21 centimeter and actual hiss actually his Farpoint is 25 plus two because there's a difference between the islands and the glasses he's wearing. So that's gonna be negative. 27 centimeter now for Parsi. If contact lenses are to be worn instead of eyeglasses, then there's no gap between the eyes and the context. Therefore, in this case, Q is going to be equal to F with these. The fire point negative 27 centimeter. And I'm just gonna ride this stone negative 0.27 meter. So the power would be one of her eth, which is one over negative 0.27 meter, and that would give us negative 3.7 chapters.

University of Wisconsin - Milwaukee
Top Physics 103 Educators
LB
Liev B.

Numerade Educator

Farnaz M.

Other Schools

Aspen F.

University of Sheffield

Jared E.

University of Winnipeg