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
$\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$
$\Rightarrow \frac{1}{2 f + x}+\frac{1}{v}=\frac{1}{f}$
$\Rightarrow \frac{1}{v}=\frac{1}{f}-\frac{1}{2 f + x}=\frac{f + x}{f \left(\right. 2 f + x \left.\right)}$
$\Rightarrow v=\frac{f \left(\right. 2 f + x \left.\right)}{f + x}$
It is given that $u+v=1.0 \, m$
$2f+x+\frac{f \left(\right. 2 f + x \left.\right)}{f + x}=\left(2 f + x\right)\left[1 + \frac{f}{f + x}\right] < 1.0$ m
Or $ \, \frac{\left(2 f + x\right)^{2}}{f + x} < 1.0$ m
Or $(2 f+x)^{2}<(f+x)$
This will be true only when $f < 0.25 \, m$