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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.

     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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Since the image formed by the lens is real and inverted it is formed on the side opposite to the one where object is placed.

Image position v = 50 cm

Let the object position be u.

Since image formed is inverted and the size image is equal to the size of the object, magnification (m) = -1.

\\m=\frac{v}{u}\\ -1=\frac{v}{u}\\ u=-v\\ u=-50\ cm

The needle is placed 50 cm in front of the lens

Using lens formula we have

\\\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\\ \frac{1}{f}=\frac{1}{50}-\frac{1}{-50}\\ \frac{1}{f}=\frac{2}{50}\\ f=25\ cm

Power of the lens P is given by

\\P=\frac{1}{f}\\ P=\frac{1}{25\times 10^{-2}}\\ P=4\ D

The power of the lens P is 4 Dioptre.

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