A truck uses a convex mirror as a viewfinder whose radius of curvature is 2.0m. A Maruti car is coming behind the truck at a distance of 10 m. Magnification of the image of the car will be

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A truck uses a convex mirror as a viewfinder whose radius of curvature is $2.0 m$ . A Maruti car is coming behind the truck at a distance of $10 m$ . Magnification of the image of the car will be

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\frac{1}{11}

\frac{2}{11}

\frac{11}{2}

\frac{1}{2}

answer is A.

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Detailed Solution

A truck uses a convex mirror as a viewfinder whose radius of curvature is

2.0 m

. A Maruti car is coming behind the truck at a distance of

10 m

. Magnification of the image of the car will be

\frac{1}{11}

.
Given,
Object distance,

u = - 10 m

Radius of curvature,

R = 2 m

We know that, focal length,

f = \frac{R}{2}

\Rightarrow f = 1.0 m

Using mirror formula,

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

\frac{1}{v} = \frac{1}{f} - \frac{1}{u}

\Rightarrow \frac{1}{1.0} + \frac{1}{10} = \frac{11}{10}

v = \frac{10}{11} m

magnification,

m = \frac{- v}{u}

\Rightarrow \frac{- \frac{10}{11}}{- 10} = \frac{1}{11}

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