Question

A lens forms a virtual, diminished image of an object placed at $2\text{m}$ from it. The size of image is half of the object. Which one of the following statements is correct regarding the nature and focal length of the lens?

• A. Concave, $|f|=1\text{m}$
• B. Convex, $|f|=1\text{m}$
• C. Concave, $|f|=2\text{m}$
• D. Convex, $|f|=2\text{m}$

Answer 1

The correct option is C Concave, $|f|=2\text{m}$

Given, object distance, $u=-2\text{m}$,

magnification, $|M|=\frac{1}{2}$,

Let, the image distance is $v$.

Since image is virtual, so $v<0$

We know that,
$M=\frac{v}{u}$

$\Rightarrow \frac{1}{2}=\frac{v}{-2}$

$\therefore v=0.5u=0.5\times (-2)=-1$

Applying lens formula,

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

$\Rightarrow \frac{1}{-1}-\frac{1}{-2}=\frac{1}{f}$

$\Rightarrow \frac{1}{-2}=\frac{1}{f}$

$\therefore f=-2$

$|f|=2\text{m}$.

Since, $f<0$ and the image is virtual as well as diminished which is possible only in concave lens. Therefore the lens is concave.