Question

A concave mirror has a focal length of 20 cm. Find the position or positions of an object for which the image-size is double of the object-size.

Answer 1

Using sign conventions, given,
Focal length of the concave mirror:
f = −20 cm
As per the question,
Magnification (m) is:
\[m =  - \frac{v}{u} = 2\] 
⇒ v = −2u

 Case I (Virtual image):

Using mirror formula,

\[\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\] 

\[ \Rightarrow    - \frac{1}{2u} - \frac{1}{u} = \frac{1}{f}\] 

\[ \Rightarrow   \frac{3}{2u} = \frac{1}{f}\] 

\[ \Rightarrow   u = \frac{3f}{2} = 30  \text{ cm }\]
Hence, the required positions of objects are 10 cm or 30 cm from the concave mirror.