In the diagram given below, there are three lenses formed. Considering negligible thickness of each of them as compared to [] and [], i.e., the radii of curvature for upper and lower surfaces of the glass lens, the power of the combination is [20

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Solution

Q.
In the diagram given below, there are three lenses formed. Considering negligible thickness of each of them as compared to [ $R_{1}$ ] and [ $R_{2}$ ], i.e., the radii of curvature for upper and lower surfaces of the glass lens, the power of the combination is [2025]

1 $- \frac{1}{6} (\frac{1}{| R_{1} |} + \frac{1}{| R_{2} |})$

2 $- \frac{1}{6} (\frac{1}{| R_{1} |} - \frac{1}{| R_{2} |})$

3 $\frac{1}{6} (\frac{1}{| R_{1} |} + \frac{1}{| R_{2} |})$

4 $\frac{1}{6} (\frac{1}{| R_{1} |} - \frac{1}{| R_{2} |})$

Ans.
(2)

$\Rightarrow P_{eq} = P_{1} + P_{2} + P_{3}$

$\Rightarrow P_{1} = (\frac{4}{3} - 1) (\frac{1}{\infty} - \frac{1}{- | R_{1} |})$

$\Rightarrow P_{1} = (\frac{1}{3 | R_{1} |})$

$\Rightarrow P_{2} = (\frac{1}{2}) (\frac{1}{- | R_{1} |} - \frac{1}{- | R_{2} |})$

$\Rightarrow P_{2} = \frac{1}{2} (\frac{1}{| R_{2} |} - \frac{1}{| R_{1} |})$

$\Rightarrow P_{3} = (\frac{1}{3}) (\frac{1}{- | R_{2} |} - \frac{1}{\infty}) = - \frac{1}{3 | R_{2} |}$

$\Rightarrow P_{e q} = \frac{1}{3} (\frac{1}{| R_{1} |} - \frac{1}{| R_{2} |}) - \frac{1}{2} (\frac{1}{| R_{1} |} - \frac{1}{| R_{2} |})$

$= - \frac{1}{6} (\frac{1}{| R_{1} |} - \frac{1}{| R_{2} |})$

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