In the figure shown here, what is the equivalent focal length of the combination of lenses (Assume that all layers are thin)? [2023]

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Solution

Q.
In the figure shown here, what is the equivalent focal length of the combination of lenses (Assume that all layers are thin) [2023]

1 –100 cm

2 –50 cm

3 40 cm

4 –40 cm

Ans.
(1)

From lens maker's formula,

$\frac{1}{f_{1}} = (1.6 - 1) (\frac{1}{\infty} - \frac{1}{20}) = - \frac{0.6}{20}$

$f_{1} = \frac{- 100}{3} cm; \frac{1}{f_{2}} = (1.5 - 1) (\frac{1}{20} + \frac{1}{20})$

$f_{2} = 20 cm$

$f_{3} = f_{1} = \frac{- 100}{3} cm; \frac{1}{f_{net}} = \frac{1}{f_{1}} + \frac{1}{f_{2}} + \frac{1}{f_{3}} = \frac{- 3}{100} + \frac{1}{20} - \frac{3}{100} = \frac{- 1}{100}$

$f_{net} = - 100 cm$

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