How do I find the radius of curvature?

[Hawking Jr]

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

 

[Herman Trivilino]

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?

 

[Hawking Jr]

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.

 

[Herman Trivilino]

The image is virtual.

Correct. So what is the value of $q$?

 

[Hawking Jr]

I think it is 54.2 cm

 

[Herman Trivilino]

No. $q$ is negative when the image is virtual!

 

[Hawking Jr]

Oh! Give me a moment to do it over.

 

[Hawking Jr]

Okay I redid the problem and the answer I have now is 127.55 cm. Is it correct?