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A car is fitted with a convex mirror of ...

A car is fitted with a convex mirror of focal length 20 cm. Another car is 6 m away from the first car. Find the position of the second car as seen in the mirror of the first. What is the size of the image if the second car is 2 m broad and 1.6 m high?

Text Solution

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Focal length `= 20` cm (convex mirror)
Object distance `= -6 m = - 600 cm`
Image distance `v=?`
`(1)/(f) = (1)/(u) + (1)/(v)`
`(1)/(20) = (1)/(- 600) + (1)/(v)`
`(1)/( v) = (1)/(20 ) (1)/(-600) = (1)/(20) + (1)/(600) = (30+ 1)/(600) = (31)/(600)`
`v= (600)/(31) = 19.35` cm
(b) Size of the image
`m = (-v)/(u ) = (v)/((-u)) = -(600)/(31) xx (1)/(-600) = (1)/(31)`
Breadth of image `= (1)/(31) xx 200 cm = 6.45 cm`
Height of image ` - (1)/(31) xx 160 cm = 5.16 cm`
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