question_answer

            Two similar thin equi-convex lenses, of focal length f each, are kept coaxially in contact with each other such that the focal length of the combination is \[{{F}_{1}}\]. When the space between the two lenses is filled with glycerin (which has the same refractive index \[(\mu =1.5)\] as that of glass) then the equivalent focal length is \[{{F}_{2}}\]. The ratio \[{{F}_{2}}\] :  \[{{F}_{1}}\]will be:                   [NEET 5-5-2019]

A) 2 : 3                 

B) 3 : 4

C) 2 : 1                             

D) 1 : 2

Correct Answer: D

Solution :

  \[\frac{1}{{{F}_{1}}}=\frac{1}{f}+\frac{1}{f}\]                        

\[{{F}_{1}}=f/2\]

\[\frac{1}{{{F}_{1}}}=\frac{1}{f}\left( -\frac{1}{f} \right)+\frac{1}{f}\] \[\frac{1}{{{F}_{2}}}=\frac{1}{f}\]                        

\[{{F}_{2}}=f\]

\[{{F}_{1}}:{{F}_{2}}=\frac{f}{2}:f=\frac{1}{2}:1=1:2\]