Two similar thin equiconvex 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  then the equivalent  focal length is F_2 . The ratio F_1 : F_2 

  • Option 1)

    2 : 1 

  • Option 2)

    1 : 2 

  • Option 3)

    2 : 3 

  • Option 4)

    3 : 4 

Answers (1)

1 / f = ( u-1 ) \left ( \frac{1}{R_1}-\frac{1}{R_2} \right ) \\\\ R_1 =R_2 \\\\ 1/f = ( u-1 ) (2/ R ) \\\\ F_1 = f/2 \\ 1/ f' = ( u-1 ) \left ( \frac{1}{-R}- \frac{1}{R} \right ) \\\\ 1/ f' = - ( u-1)(2/R) = - 1/ f \\\\ 1/F_{ 2 } = 1/f + 1/f+ 1/ f' = 1/ f \\\\ \Rightarrow \frac{F_1}{F_2}= 1/2


Option 1)

2 : 1 

Option 2)

1 : 2 

Option 3)

2 : 3 

Option 4)

3 : 4 

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