question_answer

A thin convex lens of focal length T is put on a plane mirror as shown in the figure. When an object is kept at a distance 'a' from the lens - mirror combination, its image is formed at a distance\[\frac{a}{3}\]in front of the combination. The value of 'a' is : [JEE Main Online Paper (Held On 11 April 2015)]  

A)  f

B)  2f

C)  3f

D)  \[\frac{3}{2}f\]

Correct Answer: B

Solution :

  This combinations will behave like a mirror of power. \[{{P}_{eq}}=2{{P}_{L}}+{{P}_{M}}\] \[{{P}_{eq}}=2\frac{1}{f}+0\] \[{{F}_{eq}}=-\frac{f}{2}\] so the behaviour will be like a mirror of focal length \[-\frac{f}{2}\] Using mirror equation\[\frac{1}{V}+\frac{1}{U}=\frac{1}{{{f}_{eq}}}\] \[\frac{1}{{{-}^{{}^{9}/{}_{3}}}}+\frac{1}{-a}=\frac{-1}{{}^{f}/{}_{2}}\] \[\frac{1}{a}=\frac{-2}{f}\] \[\]