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.


Image formed is real and inverted

∴ Magnifications (m) = -1

Since the image is real, image distance is a positive value.

Image distance (v) = 50 cm

Let the object distance be u

Magnification in a lens (m) = v/u

-1 = 50/u

u = -50 cm

The needle is placed 50 cm in front of the convex lens.

Need to find the focal length (f)

According to the lens formula,

1/f = 1/v – 1/u

1/f = 2/50

1/f = 1/25

f = 25cm

Power of the lens p = 1/f

P = 1/25cm-1

P = 1/25 × 10-2 m-1

P = 4m-1

Since 1m-1 = 1D

∴ P = 4D

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