where must the mirror be placed

Question

An incandescent lamp is located 2.4 m from a wall. It is desired to throw on the wall an image magnified three times the diameter, using a concave mirror. What must be the radius of curvature of the mirror? Where must it be placed?

 

I got the first part, what I need is where the mirror must be placed.

Answer 1

Assume that the mirror is placed at distance d m from mirror.

 

So distance of image from mirror = d + 2.4 m

 

Let's use cartesian sign convention in mirror equation:

u = -d, v = -(d+2.4)

 

The image is 3 times magnified. so  (d+2.4)/d = 3 or d = 1.2

 

So mirror must be placed 1.2m beyond the lamp.

 

1/u + 1/v = 1/f  or  - 1/1.2 + (-1/3.6) = 1/f or - 4/.3.6 = 1/f or f = -.9

Radius of curvature of the mirror is 2f = 1.8 m