question_answer

A converging beam of light forms a sharp image on a screen. A lens is placed 10 cm from the screen in the path of the beam. It was found that the screen has to be moved 8 cm further away to obtain the sharp image. Focal length of the lens is-

A) 6.43 cm                        

B) -2.5 cm

C) - 22.5 cm                      

D) 2.66 cm

Correct Answer: C

Solution :

Since the screen has to be moved away, the lens used should be concave.   \[\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\] \[\Rightarrow \,\,\,\frac{1}{f}=\frac{1}{18}-\frac{1}{10}\] \[f=\frac{180}{10-18}\,\,=\,\,-22.5\,cm\]