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Question

To form an image twice the size of the object, using a convex lens of focal length 20 cm, the object distance must be

A

< 20 cm

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B

> 20 cm

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C

< 20 cm and between 20 cm and 40 cm

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D

equal to 20 cm

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Solution

The correct option is C < 20 cm and between 20 cm and 40 cm Let object distance be u image distance be v and focal length be f Given that the image is twice the size of the object which means we want a magnified image. As per the different cases of ray diagrams, we know that A convex lens forms real and inverted image till the object is brought from infinity to focus. So u>f for a real image. The convex lens produces magnified real image when the object is placed between f and 2f. Also, a convex lens forms virtual, magnified and erect image when the object is placed between the pole and the focus. So u<f for a virtual image. So for a virtual magnified image, object distance should be less than 20 cm and for real magnified image, object distance must be between 20 cm and 40 cm.

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