Question

Where must an object be placed in front of a convex lens so that the image formed is of same size as the object :

(Given focal length for lens $=F$)

• A. $F$
• B. $2F$
• C. $0$
• D. $\infty$

Answer 1

The correct option is B $2F$

When an object is placed at $2F$, it forms a real, inverted image of the same size.

Using, the lens' formula, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

We know that magnification $m=\frac{v}{u}=\frac{h_I}{h_O}$

Given that the size of image is same as that of the object, we have $v=u$

Also, since object is infront of the mirror $u=-v$, using sign convention

Substituting in the lens' formula, we have, $\frac{2}{v}=\frac{1}{f}$

Hence, $v=2f$

Since $u=-v$. Hence, $u=-2F$, i.e. the object must be placed at position $2F$ in front of the convex lens.

So, option B is correct