Optics Question: Object and Image. Check my work!?

Question

question: a concave makeup mirror is designed so the virtual image it produces is twice the size of the object when the distance between the object and the mirror is 14 cm. what is the radius of curvature of the mirror?

approach: i took half of do and got 7 cm. then, i plugged in numbers into 1/f = 1/do + 1/di with variables di = 14 cm, do = 7m. I got f = 4.7. I mult. by 2 of that to get radius and got R = 9.4 cm.

Did i read the question right?

Answer 1

Ok, if the image is virtual then the distance from the image to mirror is negative, so :

1 / p + 1 /q = 1 / f

q = image distance

p = object distance

q < 0

-q / p = 2

p = 14, then q = - 28

So, now :

1 / 14 - 1/28 = 2 / R

1 / 28 = 2 / R

R = 56 cm

Watch out with the signs of "p" and "q", because, the problem says a virtual image, if it's virtual then q is negative.

Hope that helps