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University of Wisconsin - Milwaukee

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Problem 67 Hard Difficulty

A Boy Scout starts a fire by using a lens from his eyeglasses to focus sunlight on kindling 5.0 $\mathrm{cm}$ from the lens. The Boy Scout has a near point of 15 $\mathrm{cm} .$ When the lens is used as a simple magnifier, (a) what is the maximum magnification that can be achieved and (b) what is the magnification when the eye is relaxed? caution: The equations derived in the text for a simple magnifier assume a "normal" eye.

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Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Andy C.

University of Michigan - Ann Arbor

LB
Liev B.

Numerade Educator

Meghan M.

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Video Transcript

So in this problem of Boy Scout is trying to start a fire by using his eyeglasses. The list is in focus on killing when he is keeping the lens five centimeter away from the killing. Therefore, when P equals in infinity, that is the distance between sun and lance que physicals five centimeter. And in this case, when P equals infinity and cuticles five centimeter, this basically gonna be cure equals f Rickles five centimeter. Right? And it is also given that the Boy Scout has the near point of 15 centimetre. So now the information we have here Lisk saw part of the problem in this part. When the lens is used as a magnifier, the maximum magnification is achieved when virtual and upright image is formed at his near point. That is when. Q because negative 15 centimetre, right? Therefore, the optic Descents for this case would be P cause Q times F over Q minus F. And we know the focal length. That is five centimeters. So it's gonna be a negative 15 times five over. Negative 15 minus five. This would give me 15 by four centimeter. I'm just gonna keep it this way. All right now, the maximum angler magnification in this case is going to be. And Max, there's going to be one plus 15 centimetre over f. All right, So you see the difference between the usual 25 centimeter and this one? It is because the eye, the near point of the Boy Scout, is 15 centimetre not normal near point, which is 25 centimeter. So we're using 15 centimetre here for that reason. So that's going to give us positive for So that's the maximum magnification. Now let's go Salt Part B of the problem. So in this case, in this part, when the man when the I is relaxed, we want to find the magnification of the eye for the relaxed case. Okay, So again, M is going to be 15 centimetre for the relax I over f. And it is for the same reason since the eyes near point is at 15 centimetre, not 25 centimeter, which is their normal near point. So this is going to give us 15 centimetre over five centimeter which will give me positive three. This is the magnification for the relax. I

University of Wisconsin - Milwaukee
Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Andy C.

University of Michigan - Ann Arbor

LB
Liev B.

Numerade Educator

Meghan M.

McMaster University