Question

A concave lens of focal length f produces an image equal to $\frac{1}{n}$ of the size of the object, the distance of the object from the lens is:

• A. $(n-1)f$
• B. $(n+1)f$
• C. $\left(\frac{n-1}{n}\right)f$
• D. $\left(\frac{n+1}{n}\right)f$

Answer 1

The correct option is A $(n-1)f$

Magnification, $m=\frac{I}{O}=\frac{v}{u}=\frac{1}{n}$, where I = image height, O = Object height, v = image distance, u = Object distance

$\Rightarrow v=\frac{u}{n}$

Now, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\Rightarrow \frac{1}{f}=-\frac{1}{u}+\frac{n}{u}=\frac{(n-1)}{u}$

$\therefore u=(n-1)f$