A screen is placed at 90 cm away from the object. The image of the object on the screen is formed by a convex lens at two different locations separated by 20 cm. What is the focal length of the lens?

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42.8 cm

21.4 cm

10.7 cm

5.5 cm

answer is B.

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Detailed Solution

Concept: Using the formula, we can easily determine the focal length of the lens. The distance between the screen and the object, as well as the distance between two image spots, are provided, allowing us to quickly determine the focal length of the lens.
For two-positions of convex lens, the image of the object can be located on the screen by exchanging u and v.
The distance between two lens positions is d= 20 cm.
From the figure,

Solving,

From lens formula,

Hence, option 2 is correct.

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