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The Hale Telescope The 200 -inch-diameter concave mirror of the Hale telescope on Mount Palomar has a focal length of 16.9 $\mathrm{m}$ .An astronomer stands 20.0 $\mathrm{m}$ in front of this mirror. (a) Where isher image located? Is it in front of or behind the mirror? (b) Is herimage real or virtual? How do you know? (c) What is the magnification of her image?

(a) 110 $\mathrm{m}$(b) real(c) $-5.5$

Physics 103

Chapter 26

Geometrical Optics

Wave Optics

Cornell University

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Simon Fraser University

University of Sheffield

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Okay, So for this question, we are asked to find where her image with images located ISAT in front or behind the mirror. Is the image real or virtual? And then what the magnification of the image would be. So we're given that the focal length for the concave mirror that we have in question, which is the focal ache, this f So we have focal lengths steen 0.9 meters and we know that this is between the astronomer and the mirror. It's 20 meters. We'll find that as distance not equals 20 going zero meters. So the first question we want to find out where is her limit? Where's the image locators in front or behind the mirror? So for the first part, we're going to use an equation which is one over F equals one over the initial distance Initial distance plus one over d I. And then if we rearrange, it listens for the image. So we therefore the distance for the image we get the following equation. Ah, do you not over 80 knots minus f and then we plug everything in. So you have g I equals the focal length. 16.9 multiplied by 20 all that divided by 20 minus 16 99. And when we do this, we get that the distance of the image is 109 0.8 meters, which is approximately 110 meters, which is the answer, which is a distance of the image. And we're just going to be in front of the mirror since the image is since the distance is positive now, the second part, we want to see if the images real or virtual, we're going to say, since we have a positive distance for the image and since it is in front of the mirror when I say that the images, the image, Israel stands there for the second part and then, for the third part, identify the magnification for the image to find magnification used a formula for magnification, which is the negative distance of the image over the distance of the object, which equals negative 110 which is what we calculated and then the 20 readers was given to us. Therefore, the magnification of the image is negative. Five point five

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