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# An object is placed at a distance of 40cm in front of a convex mirror of radius of curvature 40cm. List** four characteristics **of the image formed by the mirror.

**Given:** An object is placed at a distance of 40cm in front of a convex mirror of radius of curvature of 40cm

So, $u = - 40 \ cm, \ R = + 40 \ cm$

**
**

**Focal length** $f = \frac{R}{2} = \frac{40}{2}$

**
**

**Using mirror formula:**

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

We can rewrite it as: $\frac{1}{v}=\frac{1}{f}-\frac{1}{u}$

Therefore, $\frac{1}{v}=\frac{1}{20}-\frac{1}{-40}=\frac{3}{40}$

So, $v=\frac{40}{3} \mathrm{cm}$

We also know **magnification**, $m = \frac{-v}{u}$

$m = \frac{-\frac{40}{3}}{- 40}$

So, $m = \frac{1}{3}$

From the values of $v$ and $m$, we can identify the following characteristics of the image:

- The image is
**virtual**as $v$ is positive - The image is
**erect**as $m$ is positive - The image is
**diminished**as $m - The image is
**between focus and pole**as $ 0

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