question_answer

A hollow double concave lens is made of very thin transparent material.  It can be filled with air or either of two liquids L1 and L2 having refractive indices n1 and n2 respectively (n2>n1>1).  The lens will diverge a parallel beam of light if it is filled with                                                     [IIT-JEE (Screening) 2000]

A)            Air and placed in air

B)            Air and immersed in L1

C)            L1 and immersed in L2       

D)            L2 and immersed in L1

Correct Answer: D

Solution :

                   \[\frac{1}{f}=\left( \frac{{{n}_{2}}}{{{n}_{1}}}-1 \right)\,\,\left( \frac{1}{{{R}_{1}}}-\frac{1}{{{R}_{2}}} \right)\] where \[{{n}_{2}}\] and \[{{n}_{1}}\] are the refractive indices of the material of the lens and of the surroundings respectively. For a double concave lens,                    \[\left( \frac{1}{{{R}_{1}}}-\frac{1}{{{R}_{2}}} \right)\] is always negative.            Hence \[f\] is negative only when \[{{n}_{2}}>{{n}_{1}}\]