Question

A spherical mirror is to be used to form an image 5.20 times the size of an object on a screen located 4.20 m from the object.

(a) Is the mirror required concave or convex?

concaveconvex    

(b) What is the required radius of curvature of the mirror?
m

(c) Where should the mirror be positioned relative to the object?
m from the object

Answer 1

Since the image has to be collected onto a screen it must be a real image.
A real image is always inverted, so magnification is negative:
M = -5.2
But M = - di/do, so
do = di / 5.2 = 4.2 / 5.2 = 0.8077 m

From conjugate points formula
1/f = 1/do + 1/di
f = do di / (do + di) = 0.8077 x 4.2 / (0.8077 + 4.2) = 0.6774 m

Therefore
(a)The mirror has a focal length of 0.6774 m

radius of curvature = 1.3488 m
(b) The object should be 0.8077 m in front of the mirror

positive focal length implies it is concave lens