Question

An object is placed in front of a concave mirror of radius of curvature $40\text{cm}$ at a distance of $10\text{cm}$ from pole. Find the nature and magnification of the image.

• A. $|m|=1.5;$ Nature :- virtual, erect & enlarged
• B. $|m|=2;$ Nature :- real, inverted & enlarged
• C. $|m|=2;$ Nature :- virtual, erect & enlarged
• D. $|m|=1.5;$ Nature :- real, inverted & enlarged

Answer 1

The correct option is C $|m|=2;$ Nature :- virtual, erect & enlarged

Given,
For a concave mirror,

$R=-40\text{cm};u=-10\text{cm}$

Using mirror formula,

$\frac{1}{v}=\frac{1}{f}-\frac{1}{u}$ and $f=\frac{R}{2}$

and substituting the given data we get,

$\frac{1}{v}=\frac{2}{R}-\frac{1}{u}=\frac{2}{(-40)}-\frac{1}{(-10)}=\frac{1}{-20}+\frac{1}{10}$

$\Rightarrow \frac{1}{v}=\frac{-10+20}{200}=\frac{10}{200}=\frac{1}{20}$

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



Image is formed behind the mirror, so image formed is virtual in nature.

Magnification$\left(m\right)$ from a concave mirror,

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

Since, the magnification is positive, image is erect and enlarged.

$\therefore$Image is formed at $v=20\text{cm}$ is virtual , erect and enlarged.

Thus, option (c) is the correct answer.