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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.

Here v = +50cm
Because the real image is of the same size as the object,

$$\therefore m=\frac{h`}h=\frac{v}u=-1$$

or $$u= -v= -50cm$$

Now, $$\frac{1}f=\frac{1}v-\frac{1}u =\frac{+2}{50}=\frac{+1}{25}$$

or $$f=25cm$$ or $$0.25m$$

$$Power(P)=\frac{1}f= +\frac{1}{0.25}=+4D$$