A convex mirror used as a rear-view mirror in a car has a radius of curvature of 3m. If a bus is located at a distance of 5m from this mirror, find the position of image. What is the nature of the image?
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R = 3m, u = 5m,$\frac{\text{R}}{2}=\frac{3}{2}=1.5\text{cm}$
We know that$\frac{1}{\text{v}}+\frac{1}{\text{u}}=\frac{1}{\text{f}}$
$\Rightarrow\frac{1}{\text{v}}+\frac{1}{-5}=\frac{1}{1.5}$
$\Rightarrow\frac{1}{\text{v}}=\frac{1}{-5}+\frac{2}{3}=\frac{3+10}{15}=\frac{13}{10}$
$\therefore \text{v}=\frac{15}{13}\text{m}=1.15\text{cm}$
The image is formed 1.15m behind the mirror. The image is virtual and erect.
We know that$\frac{1}{\text{v}}+\frac{1}{\text{u}}=\frac{1}{\text{f}}$
$\Rightarrow\frac{1}{\text{v}}+\frac{1}{-5}=\frac{1}{1.5}$
$\Rightarrow\frac{1}{\text{v}}=\frac{1}{-5}+\frac{2}{3}=\frac{3+10}{15}=\frac{13}{10}$
$\therefore \text{v}=\frac{15}{13}\text{m}=1.15\text{cm}$
The image is formed 1.15m behind the mirror. The image is virtual and erect.
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