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].