The position of image should be at 2F, since the image is real and same size.
It is given that the image of the needle is formed at a distance of 50 cm from the convex lens. Therefore, the needle is placed in front of the lens at a distance of 50 cm.
Object distance (u) = - 50 cm
Image distance, (v) = 50 cm
Focal length = f
According to the lens formula.
\( \frac{1}{u}-\frac{1}{u}=\frac{1}{f}\)
\( \frac{1}{f}=\frac{1}{50}-\frac{1}{-50}\)
\( =\frac{1}{50}+\frac{1}{50}=\frac{1}{25}\)
f = 25 cm = 0.25 m
Power of lens \( P = \frac{1}{f(in\, meters)}=\frac{1}{0.25}=+4D\)
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