Figure A shows two identical plano-convex lenses in contact as shown.The combination has local length 24 cm.Figure B shows the same with a liquid introduced between them.If refractive index of glass of the lenses is 1.50 and that of the liquid is 1.60 , the focal length of the system in figure B will be

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Answer 1

Let radius of the convex side be $R$ .
By lens makers' formula,
So focal length of 2 identical plano-convex lens is given by, $\frac{1}{f} = \frac{1}{2 4} = (1.5 - 1) (\frac{1}{\infty} - \frac{1}{- R}) + (1.5 - 1) (\frac{1}{R} - \frac{1}{\infty}) ⟹ R = 24 c m$

The total focal length of the lens combination can be given as,
$\frac{1}{f _{t}} = (1.5 - 1) (\frac{1}{\infty} - \frac{1}{- R}) + (1.6 - 1) (\frac{1}{- R} - \frac{1}{R}) + (1.5 - 1) (\frac{1}{R} - \frac{1}{\infty})$

$⟹ \frac{1}{f _{t}} = \frac{- 0 . 2}{R} ⟹ f_{t} = - 120 c m$

Option A is correct

Answer 2

Let radius of the convex side be

R

.

By lens makers' formula,

So focal length of 2 identical plano-convex lens is given by,

\frac{1}{f} = \frac{1}{2 4} = (1.5 - 1) (\frac{1}{\infty} - \frac{1}{- R}) + (1.5 - 1) (\frac{1}{R} - \frac{1}{\infty}) ⟹ R = 24 c m

The total focal length of the lens combination can be given as,

\frac{1}{f _{t}} = (1.5 - 1) (\frac{1}{\infty} - \frac{1}{- R}) + (1.6 - 1) (\frac{1}{- R} - \frac{1}{R}) + (1.5 - 1) (\frac{1}{R} - \frac{1}{\infty})

⟹ \frac{1}{f _{t}} = \frac{- 0 . 2}{R} ⟹ f_{t} = - 120 c m

Option A is correct