Question

A man uses a concave mirror for shaving. He keeps his face at a distance of 25 cm from the mirror and gets an image which is 1.4 times enlarged. Find the focal length of the mirror. (The man does not see his face flipped upside down.)

• A. 36.8 cm
  
• B. 87.5 cm
  
• C. 75.6 cm
  
• D. 99.4 cm
  

Answer 1

The correct option is B 87.5 cm


Let's draw the schematic first.

Writing with sign convention:
u=−25 cm
m=+1.4
Let's apply the magnification formula first.
$m=\frac{-v}{u}$
We get
$1.4=\frac{-v}{-25}$
v=35 cm. ( A positive value of v means the image is behind the mirror or to the right side of it.)
Now we have both object and image distance and we need the focal length. Let's apply the mirror formula for it.
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
Or
$\frac{1}{35}+\frac{-1}{25}=\frac{1}{f}$
On solving we get,
f=−87.5 cm, so, focal length is 87.5 cm and the focus lies in front of the mirror.