Question

At what distance from a concave lens of focal length 20 cm a 6 cm tall object be placed so as to obtain its image at 15 cm from the lens? Also calculate the size of the image formed.
Draw a ray diagram to justify your answer  for the above situation and label it.

Answer 1

\[f = - 20 cm\]
\[ h_0 = 6 cm \]
\[ h_i = ?\]
\[v = - 15 cm \]
\[u = ?\]
We know, 
\[\frac{1}{v} - \frac{1}{u} = \frac{1}{f}\]
\[ \Rightarrow \frac{1}{u} = \frac{1}{v} - \frac{1}{f}\]
\[ \Rightarrow \frac{1}{u} = \frac{1}{- 15} - \frac{1}{- 20} = - \frac{1}{60}\]
\[ \Rightarrow u = - 60 cm\]
Also. magnification, m can be calculated as: 

\[\frac{v}{u} = \frac{h_i}{h_0}\]
\[ \Rightarrow h_i = \frac{v}{u} \times h_0 \]
\[ \Rightarrow h_i = \frac{- 15}{- 60} \times 6 = 1 . 5 cm\]