# Finding magnification, object distance from the mirror, and radius of curvature

## Homework Statement

You placed a 10cm high object in front of a mirror and got 5cm high virtual image at (-30cm). (Hint: watch the sign convention)
a. Find the magnification
b. Find the object distance from the mirror
c. Find the radius of curvature of the mirror

then I have to know if the mirror is convex or concave and if it is upright or inverted, but I think I can figure that out if I find the solutions to these problems.

## Homework Equations

I've figured out from the information that Ho= 10cm, Hi= 5cm, I think f= -30cm
For object distance, I can't figure out how I can possibly figure that out without any distances given. I'm not supplied with distance from focal point.
Any ideas on what I'm doing wrong?

and for radius, I have no idea where to begin.

## The Attempt at a Solution

for part a. M=Hi/Ho=5cm/10cm=1/2cm ? So does Magnitude equal 1/2cm?

I am not good at science, I am taking this as my gen-ed required science for my major. PLEASE help however you can.
Thanks so much :-)

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Hello,

let s= object distance=x, s'=image distance=-30cm, h= object height=10cm, h'=image height=5cm, f=focal length=y and R=Radius of curvature=z

For part A you have the right answer as m=-$\frac{s'}{s}$ Except you thought -30 is focal length which it is not, its where the image appears to be.

For part B you can use the following equation $\frac{1}{f}$=$\frac{1}{s}$+$\frac{1}{s'}$. You don't know object distance but you can work it out from magnification equation, m=-$\frac{s'}{s}$ we also know |m|=$\frac{h'}{h}$ so you can work out what s is.

For part C Radius of curvature is simply 2x Focal length.

Hope this helps

that helps so much! thank you!