A 184 cm tall boy is standing 518 m in front of a large sphe

A 184 cm tall boy is standing 5.18 m in front of a large spherical mirror. He sees an inverted image of himself 2 times smaller. The mirror is concave and the image is real and inverted.

(a) Where is the image located? (Your answer should be positive if the image is in front of the mirror and negative if the image is behind it.)
_____________ m
(b) What is the focal length of the mirror?
______________m
(c) What is the radius of curvature of the mirror?
_____________m

Solution

Object height O = 184 cm

Distance of the object u = 5.18 m

Magnification m = 1/2

We know m = v / u

So, v/u = 1/2

v = u/2

= 5.18 m/ 2

   = 2.59 m     

the image is in front of the mirror.

From the relation (1/u) +(1/v) =(1/f)

                        (1/5.18) +(1/2.59)=(1/f)

                          (1+2)/5.18 = 1/f

                                        3/5.18 = 1/f

From this focal length f = 5.18 m / 3

                                  = 1.726 m

Radius of curvature of the mirror R =2f = 3.453 m