How do I find the radius of curvature?

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Homework Help Overview

The discussion revolves around finding the radius of curvature in the context of optics, specifically relating to focal lengths and image characteristics.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the relationship between focal length and radius of curvature, questioning the implications of image type (real or virtual) on calculations.

Discussion Status

Participants are actively engaging with the problem, with some providing calculations and others correcting assumptions about the nature of the image. There is an ongoing exploration of the correct values and relationships involved.

Contextual Notes

There is a mention of the image being virtual, which affects the sign of certain values in the calculations. Participants are also addressing potential errors in previous calculations.

Hawking Jr
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Homework Statement
A concave makeup mirror is designed so that a person 29.3 in front of it sees an upright image at a distance of 54.2 cm behind the mirror.What is the radius of curvature of the mirror?
Relevant Equations
1/f=1/p + 1/q and 1/p +1/q = 2/R
I figured out that the focal distance is 19.01868
 
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And you want to know what? The radius of curvature? Do you know the relationship between the focal length and the radius of curvature?

And by the way, is the image real or virtual? And how did your answer to that question affect the way you did your calculation?
 
The focal length is half of the radius curvature. So I multiplied it by 2 and I still got it wrong. The image is virtual.
 
Hawking Jr said:
The image is virtual.

Correct. So what is the value of ##q##?
 
I think it is 54.2 cm
 
No. ##q## is negative when the image is virtual!
 
Oh! Give me a moment to do it over.
 
Okay I redid the problem and the answer I have now is 127.55 cm. Is it correct?
 

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