How far from a piece of paper must you hold your father’s 2.25 D reading glasses to try to burn a hole in the paper with sunlight?
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Final Answer

44.4 cm44.4 \textrm{ cm}

Solution video

OpenStax College Physics for AP® Courses, Chapter 25, Problem 43 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. We're going to hold these reading glasses some distance away from that piece of paper that will be placed here such that sunlight will burn a hole in the paper. Now sunlight has rays that are coming parallel because the light source is so far away that by this point when it reaches Earth all the rays are parallel. And so since the Rays are parallel when they go through the lens they will be focused on to the focal point because that's how the focal point is defined. It is the place where all parallel rays converge and that's going to be the spot that is the hottest. And so that's where you should put the paper to burn a hole in it. So in other words we need to figure out what is the focal length of this lens. Now we're given the power of it and the power is the reciprocal of the focal length. So he can raise both sides to the exponent negative one to solve for focal length. And it's the reciprocal of power so that's one over two and a quarter diopters which is 0.444 meters and so the paper should be 44.4 centimeters from the lens.