An object that is 47.5 cm tall forms an image that is 38.6 cm tall and 14.8 cm from a spherical mirror.How far is the object from the mirror?
A)124 cm
B)47.6 cm
C)18.2 cm
D)12.0 cm

Question

Quizplus · Accepted Answer

Using the mirror formula 1/f = 1/v + 1/u, where f is the focal length, v is the distance of the image from the mirror, and u is the distance of the object from the mirror.

We have: 
Height of object (h_u) = 47.5 cm 
Height of image (h_v) = 38.6 cm 
Distance of image from the mirror (v) = 14.8 cm

Now, using the magnification formula -v/u = m = h_v/h_u, we get: 
Distance of object from the mirror (u) = -m*v/(1-m) 
=-38.6/47.5*14.8/8.9
= 18.2 cm (approx)

Therefore, the distance of the object from the mirror is 18.2 cm. Thus, the best choice is C) 18.2 cm.

An Object That Is 47