Question

The maximum and minimum distance between a convex lens and an object, for the magnification of a real image to be greater than one are

• A. $2f$ and $f$
• B. $f$ and zero
• C. $\infty$ and $2f$
• D. $4f$ and $2f$

Answer 1

The correct option is A $2f$ and $f$

For magnification of real image to be greater than 1 for lens,

$-\infty <\frac{v}{u}<-1$ (Magnification=$\frac{v}{u}$)

From lens equation, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$⟹v=\frac{uf}{u+f}$

$⟹-\infty <\frac{f}{u+f}<-1$

Reciprocating the inequality,

$0>\frac{u}{f}+1>-1$

$⟹-1>\frac{u}{f}>-2$

Hence $-2f<u<-f$