The radius of curvature of a convex mirror used as a rear view mirror in a moving car is 2.0m. A truck is coming from behind it at a distance of 3.5m. Calculate (a) position, and (b) size, of the image relative to the size of the truck. What will be the nature of the image?
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R = 2m,$\text{f}=\frac{\text{R}}{2}=1\text{m}$
u = -3.5m We konw that
$\Rightarrow\frac{1}{\text{v}}=1+\frac{1}{3.5}=1+\frac{10}{30}=1+\frac{2}{7}=\frac{9}{7}$
$\therefore \text{v}=\frac{7}{9}=0.77\text{m}$
$\text{u}=-2\text{v}=-2\times10=-20\text{cm}$
So, the image is fomed 0.77m in behind the mirror.
u = -3.5m We konw that
- $\frac{1}{\text{v}}+\frac{1}{\text{u}}=\frac{1}{\text{f}}$
$\Rightarrow\frac{1}{\text{v}}=1+\frac{1}{3.5}=1+\frac{10}{30}=1+\frac{2}{7}=\frac{9}{7}$
$\therefore \text{v}=\frac{7}{9}=0.77\text{m}$
$\text{u}=-2\text{v}=-2\times10=-20\text{cm}$
So, the image is fomed 0.77m in behind the mirror.
- Now, $\text{m}=\frac{\text{v}}{\text{u}}=\frac{0.77}{(-3.5)}=\frac{\frac{7}{9}}{3.5}=\frac{1}{4.5}$
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