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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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