1. ## Mirrors

A concave spherical mirror can be used to
project an image onto a sheet of paper, allow-
ing the magnified image of an illuminated real
object to be accurately traced.
a) If you have a concave mirror with a focal
length of 12 cm, where would you place a
sheet of paper so that the image projected
onto it is twice as far from the mirror as the
object is? Answer in units of cm.

Okay. So I got it down to:
1/f = 1/(2p) + 1/p
which is:
1/12 = p/2 + 1/p

I'm pretty sure you just need to solve for "p" and then "q" would be twice of "p".

"p" = distance of object from mirror
"q" = distance of image from mirror

How do I solve for "p"? I can't believe I forgot how to do this. T_T

2. Originally Posted by iEricKim
...
a) If you have a concave mirror with a focal
length of 12 cm, where would you place a
sheet of paper so that the image projected
onto it is twice as far from the mirror as the
object is? Answer in units of cm.

Okay. So I got it down to:
1/f = 1/(2p) + 1/p

...
$\displaystyle \dfrac1{2p}+\dfrac1p=\dfrac1f~\implies~\dfrac1{2p} +\dfrac2{2p}=\dfrac1{12} ~\implies~\dfrac3{2p}=\dfrac1{12}~\implies~\dfrac{ 2p}3=12~\implies~\boxed{p=18}$

Can you take it from here?