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A shaving/makeup mirror produces an erect image that is magnified by a factor of 2.2 when your face is 25 $\mathrm{cm}$ from the mirror.What is the mirror's radius of curvature?

$\therefore$ Radius of curvature of the mirror is 92 $\mathrm{cm} .$

Physics 103

Chapter 26

Geometrical Optics

Wave Optics

Rutgers, The State University of New Jersey

University of Washington

University of Sheffield

McMaster University

Lectures

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(II) When walking toward a…

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An object is placed 15 $\m…

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You're asked to desig…

02:22

An object $15 \mathrm{cm}$…

01:04

You are looking for a mirr…

01:34

(II) The image of a distan…

A concave shaving mirror h…

02:47

(II) A shaving or makeup m…

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A concave mirror has a foc…

05:06

01:22

Shaving/makeup mirrors typ…

So for this problem were given that the magnification is 2.2 on the object distances 25 centimeters and we were asked to find the radius of curvature, which is capital are. So first we're gonna find a distance of the image by using the magnification formula, which is, um, equals de this is of the image gyrated distance of the object and rearranging it for the distance of the image we get that the distance of the image equals negative magnification, times the distance of the object plug in the values that have been getting to us. The in negative two point true multiplied by 25 and therefore we get the distance of the image is equivalent to negative 55 centimeters. Now we will use the mirror equation, which is one over the focal length equals one over a distance of the object, plus one over distance of the image. And here we can. This is also equivalent to distance of the object distance of the image over a distance of the object, Plus that this is the image. And since we know all this information, we just plug in. So we have 25 since the object times the distance of the image negative 55 divided by 25 plus negative five which is gonna become minus, and we get that The focal lengths is approximately 45 points 83 centimeters. We also know that there is a relationship between the radius of curvature, the focal lengths. The that relationship is that the radius of curvature is equivalent to two times the focal length. So to find the radius of curvature, we just do two times local ankle, just 45.83 centimeters and we get that this equals to 91.67. This equals 91.67 centimeters, which is approximately 92 centimeters, which is our answer for this problem.

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