Question

A Convex lens of focal length $f$ produces a real image, $x$ times the size of an object, then find the distance of the object from the lens.

• A.
  $\left(\right(x+1\left)/x\right))2f$
• B.
  $\left(\right(x+1\left)/2x\right))f$
• C.
  $\left(\right(2x+1\left)/x\right))f$
• D.
  $\left(\right(x+1\left)/x\right))2f$

Answer 1

The correct option is D

$\left(\right(x+1\left)/x\right))2f$
For Real image,
$m=\frac{v}{u}=-x$ Given

So, $v=-xu$

From lens formula

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

$\Rightarrow \frac{1}{-xu}-\frac{1}{u}=\frac{1}{f}$

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

So, object should be placed at a distance $\frac{(x+1)}{x}.f$ from the lens.