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A convex mirror used for rear-view on an automobile has a radius of curvature of $15 m$ . If a bus of height $10 m$ is located at $5.00 m$ from this mirror, size of the image will be[[1]] $m$ .

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Detailed Solution

A convex mirror used for rear-view on an automobile has a radius of curvature of

15.00 m

. If a bus is located at

5.00 m

from this mirror, size of the image will be

6 m

.
It has been given that,
Object distance,

(u) = - 5 m

Radius of curvature,

(R) = 15 m

Focal length,

f = \frac{R}{2}

\Rightarrow f = \frac{15.00}{2}

\Rightarrow f = 7.50 m

Applying mirror formula,

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

Where

v

is the distance of the image from the mirror,

u

is the distance of the object from the mirror, and

f

is the focal length of the mirror.

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

\frac{1}{v} = \frac{1}{7.50} - \frac{1}{- 5.00}

v = 3 m

Magnification can be expressed as,

m = \frac{h'}{h}

Also,

m = \frac{- v}{u}

\Rightarrow \frac{- v}{u} = \frac{- 3.00 m}{- 5.00 m}

\Rightarrow m = - \frac{3}{5}

Now,

\frac{h'}{h} = \frac{- v}{u}

\Rightarrow h' = h \times \frac{- v}{u}

h' = 10 \frac{- 3}{- 5}

h^{'} = 6 m

Therefore the image of the bus is the same size as the actual size of the bus.

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