question_answer

The focal length of a piano convex lens is and its refractive index is 1.5. It is kept over a plane glass plate with its curved surface touching the glass plate. The gap between the lens and the glass plate is filled with a liquid. As a result, the effective focal length of the combination becomes 2f. Then the refractive index of the liquid is

A)  1.5      

B)  2    

C)  1.25    

D)  1.33

Correct Answer: C

Solution :

[c]: According to lens makers formula The focal length of piano convex lens is \[\frac{1}{f}=(n-1)\left( \frac{1}{\infty }-\frac{1}{-R} \right)\] \[\frac{1}{f}=\left( \frac{3}{2}-1 \right)\left( \frac{1}{R} \right)=\frac{1}{2R}\]or\[R=\frac{f}{2}\]               ?.(i) The focal length of liquid lens is \[\frac{1}{{{f}_{1}}}=({{n}_{l}}-1)\left( \frac{1}{-R}-\frac{1}{\infty } \right)\] \[\frac{1}{{{f}_{l}}}=-\frac{({{n}_{l}}-1)}{R}\] \[\frac{1}{{{f}_{l}}}=-\frac{2({{n}_{l}}-1)}{f}\]                                    (Using (i)) Effective focal length of the combination is \[\frac{1}{2f}=\frac{1}{f}+\frac{1}{{{f}_{1}}}\] \[\frac{1}{2f}=\frac{1}{f}-\frac{2({{n}_{l}}-1)}{f}\] \[{{n}_{l}}=\frac{5}{4}=1.25\]