Question

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

• A. a concave mirror of suitable focal length
• B. a convex 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

The correct option is C a convex lens of focal length less than 0.25 m

Image can be formed on the screed if it is real. Real image of reduced size can be formed can be formed by a concave mirror or a convex lens.

The object is beyond $2f$.

So let $u=2f+x$

And using lens formula we have

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

or

$\frac{1}{2f+x}+\frac{1}{v}=\frac{1}{f}$

or

$\frac{1}{v}=\frac{1}{f}-\frac{1}{2f+x}$

Solving we get

$v=\frac{f(2f+x)}{f+x}$

We have $u+v=1$

or

$2f+x+\frac{f(2f+x)}{f+x}=1$

or

$\frac{(2f+x{)}^2}{f+x}<1$

$(2f+x{)}^2<(f+x)$

This is valid only when $f<0.25m$