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A concavemirror produces a virtual image that is three times as tall as the object. (a)Ifthe object is 16 $\mathrm{cm}$ in front of the mirror, what is theimage distance? (b) What is the focal length of this mirror?

(a) Thus, the image distance is $[-48 \mathrm{cm}]$(b) Thus, the focal length of the concave mirror is $[24 \mathrm{cm}]$

Physics 103

Chapter 26

Geometrical Optics

Wave Optics

Rutgers, The State University of New Jersey

University of Washington

Simon Fraser University

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Okay, So for this question, we know that in a conclave mirror, when the objects will be on the center of curvature, a real image is going to be formed that is basically reduced in size and inverted relative to the object. And when the object this placed between the focal point of the center of curvature or real images formed, that would be in Lord and inverted relative to the object. And when the object is located between the con Cape mirror and its focal point in large, upright and virtual images produced. So for port A, we have a concave mirror produces a virtual image that is three times as tall as the object. So the magnification of the mirrors three the information that is produced by the mirror we know by the following equation em He was the distance image led by distance of the object negative. And we here we would have to solve for the d I the distance of the object. Therefore we rearrange and we get that the distance with the object equals the Magnifico negative magnification distance of the on here. We substance to what we have in, so we know that we know that the magnification is three. Look in three and that the distance of the object is 16 centimeters. And therefore, when we do this, you know the distance of the image is negative. 48 centimeters and then for part B, we are going to find the focal length of this mirror, so we would go ahead. And for part B, you would use the following equation. One over the focal length equals one over the distance of the object Los one over the distance of the image. And here we would just plug in what we know. But we can really combined these terms and therefore have that one over F. He calls distance of the image close distance of the object, divided by distance of the inimitable deployed by the distance of the object. And then, since we have the inversion, what the focal length we would have, The focal length is equal to distance of the image times the distance of the object, divided by distance of the image, plus the distance of the object. And now we would go ahead and plug in all the values that we know, So we would plug in the F equals life equals 16 centimeters multiplied by the negative 48 wintry, calculated before divided by a negative 48 plus 16. Not only do this mass, we get that the focal, like of the conclave mirror in question is 24 centimeters.

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