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 size of the object ? Also, find the power of the lens.

Explanation

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