Question

A light bulb is 3.00m from a wall. You are to use a concave mirror to project an image of the bulb on the wall, with the image 3.50 times the size of the object.

HOW FAR IS THE MIRROR FROM THE WALL?

WHAT IS THE RADIUS OF CURVATURE?

Answer 1

The mirror equation is
1/do + 1/di = 1/f
Where
do = distance of the image from the mirror
di = distance of the object from the mirror
f = focal length

Note that concave mirror (or lens) produces a virtual image, so the distance is negative.
Solving f,
1/3 + 1/(-3.50) = 1/f
1/f = 1/21
f = 21 m

The radius of curvature is twice the focal length, that is
R = 2f = 2*21 = 42 m