Question

What is the focal length of a concave mirror that magnifies, by a factor of +3.2, an object that is placed 30 cm from the mirror?
A. 23cm
B. 32cm
C. 44cm
D. 46cm

Answer 1

Answer:

C. 44 cm

Explanation:

We can solve the problem by using the lens equation:

$\frac{1}{f}=\frac{1}{p}+\frac{1}{q}$

where

f is the focal length

p = 30 cm is the distance of the object from the mirror

q is the distance of the image from the mirror

We also know that the magnification is

$M=-\frac{q}{p}=+3.2$

So

$q=-3.2p=-3.2(30)=-96 cm$

Substituting into the first equation, we find f:

$\frac{1}{f}=\frac{1}{30}-\frac{1}{96}=0.0229 cm^{-1} \rightarrow f=43.7 cm \sim 44 cm$