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Question

A light source is placed 100 cm away from a screen. A converging lens placed at a certain position between the source and the screen focuses the image of the source on the screen. The lens is moved a distance of 40 cm and it is found that it again focuses the image of the source on the screen. The focal length of the lens is :

A
21 cm
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B
30 cm
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C
40 cm
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D
67 cm
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Solution

The correct option is C 21 cm
Answer is A.
The expression for focal length by displacement method is given as follows.
f=D2x24D
where,
D - the distance between the object and screen
x - the distance between the two positions of the lens.
Here, D = 100 cm and x = 40 cm.
So, f=D2x24D=10024024×100=21cm.
Hence, the focal length of the lens is 21 cm.

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