question_answer

A concave lens forms the image of an object such that the distance between the object and the image is 10 cm and the magnification produced is 1/4. The focal length of the lens is:

A)  8.6 cm                       

B)  6.2 cm

C)  10 cm                        

D)  4.4 cm

Correct Answer: D

Solution :

Concave lens forms the virtual image of a real object. So let \[u=-4x\]and \[v=-x\]then \[3x=10\,cm\]or \[x=\frac{10}{3}\,cm\] \[\therefore \]\[u=\frac{-40}{3}cm\]and \[v=-\frac{10}{3}\,cm\] Substituting in \[\frac{1}{f}=\frac{1}{v}-\frac{1}{u},\]we get \[\frac{1}{f}=-\frac{3}{10}+\frac{3}{40}\]or \[f=-\frac{40}{9}=-4.4\,cm.\] Hence, the correction option is [d].