An object 115 cm tall is placed at the zero mark of a meters

An object 11.5 cm tall is placed at the zero mark of a meterstick. A spherical mirror located at some point on the meterstick creates an image of the object that is upright 4.00 cm tall, and located at the 38.0-cm mark of the meterstick.

(a) Is the mirror convex or concave?

convexconcave    

(b) Where is the mirror?

At the ___ cm mark.

(c) What is the mirror\'s focal length? ___ cm

Solution

a) concave

b) h_o = 11.5 cm, h_i = 4 cm

d_o + d_i = 38.0 cm

d_i   = 38 - d_o

M = h_i / h_o = - d _i / d_o

4 / 11.5 = - (38 - d_o ) /d_o

0.348 d_o = - 38 + d_o

d_o = 58.27 cm

c) image distance d_i = 58.27 - 38 = 20.27 cm

1 / f = 1 / d_o + 1 / d_i = 1 / 58.27 + 1 / 20.27

f = 15 cm