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A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it. Where is the needle placed in front of the convex lens if the image is equal to the size of the object? Also, find the power of the lens.

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A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it. Where is the needle placed in front of the convex lens if the image is equal to the size of the object? Also, find the power of the lens.

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Given: v = 50 cm, u = ?, P = ?

Since the image is equal to the size of the object, so the object is placed at a distance twice the focal length of the lens, i.e.

-u = v = 2f = 50 cm

∴ u = -50 cm and f = 25 cm

Hence, the needle is placed at a distance of 50 cm in front of the lens.

Now power, P = \(\frac{100}{f(cm)}\) = \(\frac{100}{25}\) = +4D

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