What is the radius of curvature of the mirror

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?

Answer 1

Let the distance between the lamp and the vertex of the mirror be x, and the focal length of the mirror be f.

 

The imaging  equation,  1/f = 1/p + 1/q,   then reads

 

  1/f  = 1/x + 1/(x + 2.4).   

 

   The magnification , m,    is m = q/p  =  (x + 2.4 )/ x.      Since m = 3, this gives  x = 1.2

 

Substituting back into the imaging  equation gives  1/f =  1.111   So  f = .9

 

Since the focal length of a concave mirror is 1/2 the radius of curvature,  the radius of curvature is 1.8 m