Question

A beam of light appears to converge at a point $O$, behind a convex mirror of focal length $20\text{cm}$. Find the nature and position of the image, if the point $O$ is $10\text{cm}$ behind the mirror

• A. Image distance $|v|=20\text{cm}$
• B. Image is virtual and enlarged.
• C. Image is real and enlarged.
• D. Image distance is $|v|=\frac{20}{3}\text{cm}$

Answer 1

Answer: (A), (C)

Image is real and enlarged.

Here, in this case the object is virtual. So, for this we have
$u=+10\text{cm};f=+20\text{cm}$

Using mirror formula,

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

we get ,

$\frac{1}{v}=\frac{1}{f}-\frac{1}{u}=\frac{1}{+20}-\frac{1}{+10}=\frac{1-2}{20}=\frac{-1}{20}$

$\Rightarrow v=-20\text{cm}$

From definition of magnification$\left(m\right)$,
$m=-\frac{v}{u}=-\frac{(-20)}{10}=+2$

Since, the magnification is positive, image formed is enlarged.



Hence, the image formed will be real and enlarged, and at a distance of $20\text{cm}$ in front of the mirror as shown in the above schematic ray diagram.

Hence, options (a) and (c) are the correct answers.