Question

A convex lens of focal length f produces a real image n times the size of an object, then 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

Answer: (C)

$\left(\frac{n+1}{n}\right)f$

Magnification $m=\frac{-v}{u}=n$
$⟹v=-nu$
Using lens formula:
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\frac{1}{-nu}-\frac{1}{u}=\frac{1}{f}$

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

$u=-\left(\frac{n+1}{n}\right)f$
Thus distance between lens and object is $\left(\frac{n+1}{n}\right)f$