Question

The distance between an object and its real image formed by a convex lens cannot be

• A. greater than $2f$
• B. less than $2f$
• C. greater than $4f$
• D. less than $4f$

Answer 1

Answer: (D)

less than $4f$

Let $f$ be the focal length of convex lens.

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

As $u=-xv=D-x$

$\frac{1}{D-x}-\frac{1}{-x}=\frac{1}{f}⟹x^2-Dx+Df=0$

So, $x=\frac{-D\pm \sqrt{D^2-4Df}}{2}$

For $x$ to be real, $D^2-4Df\ge 0$

$⟹$ either $D<0ORD>4f$

But $D$ can't be < 0.

Thus $D>4f$