Question

A beam of light converges towards 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 $30\text{cm}$ behind the mirror.

• A. $|v|=12\text{cm};\text{Real, erect \& enlarged}$
• B. $|v|=60\text{cm};\text{Real, erect \& enlarged}$
• C. $|v|=12\text{cm};\text{Virtual, inverted \& enlarged}$
• D. $|v|=60\text{cm};\text{Virtual, inverted \& enlarged}$

Answer 1

The correct option is D $|v|=60\text{cm};\text{Virtual, inverted \& enlarged}$

Given,

$u=+30\text{cm};f=+20\text{cm}$

Since, the incident rays are converging behind the mirror, object is a virtual object and the image formed by this virtual object is virtual and inverted as $u>f.$

Using mirror formula,

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f},$ we get

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

Substituting the given data we get,

$\frac{1}{v}=\frac{1}{20}-\frac{1}{30}=\frac{3-2}{60}=\frac{1}{60}$

$\Rightarrow v=60\text{cm}$



Now, magnification from a convex mirror
$m=-\frac{v}{u}=-\frac{60}{30}=-2$

Hence, the image formed will be virtual, inverted and enlarged, and at a distance of $60\text{cm}$ behind the mirror.

Thus, option (d) is the correct answer.