Two thin lenses are of same focal lengths , but one is convex and the other one is concave. When they are placed in contact with each other, the equivalent focal length of the combination will be [2023]

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Solution

Q.
Two thin lenses are of same focal lengths $(f)$ , but one is convex and the other one is concave. When they are placed in contact with each other, the equivalent focal length of the combination will be [2023]

1 $f / 2$

2 infinite

3 zero

4 $f / 4$

Ans.
(2)

Let the focal length of the convex lens be $'f'$ .

When two lenses are placed in contact with each other, their power will be added.

$∴$ $P_{combination} = P_{convex} + P_{concave}$

$\frac{1}{f_{combination}} = \frac{1}{f_{convex}} + \frac{1}{f_{concave}} = \frac{1}{f} + \frac{1}{(- f)} = 0$

$∴$ $f_{combination} = \frac{1}{0} = \infty$

Hence, $f_{combination}$ will be infinite.

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