Question

A concave mirror produces a real image that is three times as large as the object. If the object is 20 cm in front of the mirror, what is the image distance? What is the focal length of this mirror?

Answer 1

Answer:

The image is produced 60 cm behind the mirror

The focal length of the mirror is 30 cm

Explanation:

u = Object distance =  20 cm

v = Image distance

f = Focal length

m = Magnification = 3

$m=-\frac{v}{u}\\\Rightarrow 3=-\frac{v}{20}\\\Rightarrow v=-3\times 20\\\Rightarrow v=-60\ cm$

The image is produced 60 cm behind the mirror

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\\\Rightarrow \frac{1}{f}=\frac{1}{20}+\frac{1}{-60}\\\Rightarrow \frac{1}{f}=\frac{1}{30}\\\Rightarrow f=\frac{30}{1}=30\ cm$

The focal length of the mirror is 30 cm