Question

A diminished image of an object is to be obtained on a screen 1.0 m away from it. This can be achieved by approximately placing

• A. A convex mirror of suitable focal length
• B. A concave mirror of suitable focal length
• C. A convex lens of focal length less than 0.25 m
• D. A concave lens of suitable focal length

Answer 1

Answer: (C)

Image can be formed on the screen if it is real. Real image of reduced size can be formed by a concave mirror or a convex lens
Let $u=2f+x$ , then
$\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$
$\Rightarrow \frac{1}{2f+x}+\frac{1}{v}=\frac{1}{f}$
$\Rightarrow \frac{1}{v}=\frac{1}{f}-\frac{1}{2f+x}=\frac{f+x}{f(2f+x)}$
$\Rightarrow v=\frac{f(2f+x)}{f+x}$
It is given that $u+v=1.0m$
$2f+x+\frac{f(2f+x)}{f+x}=\left(2f+x\right)\left[1+\frac{f}{f+x}\right]<1.0$ m
Or $\frac{{\left(2f+x\right)}^2}{f+x}<1.0$ m
Or $(2f+x{)}^2<(f+x)$
This will be true only when $f<0.25m$