Ray Optics

JEE Main level, single correct, medium

36 of 295

Question 36 of 295

Car BB overtakes another car AA at a relative speed of 40ms−140{ms}^{-1}. How fast will the image of car BB appear to move in the mirror of focal length 10cm10cm fitted in car AA, when the car BB is 1.9m1.9m away from the car AA?

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Answer: (A) 0.1ms−10.1{ms}^{-1}

Object distance, u=−1.9m=190cmu=-1.9m=190cm
Focal length, f=10cmf=10cm
Magnification, m=ff−u=1010−(−190)m=\dfrac{f}{f-u}=\dfrac{10}{10-(-190)}
Therefore, m=10200=120m=\dfrac{10}{200}=\dfrac{1}{20}
Image velocity, VI=−m2V0=−(120)2×40{V}_{I}=-{m}^{2}{V}_{0}=-{\left(\dfrac{1}{20}\right)}^{2}\times 40
Hence, VI=−0.1ms−1{V}_{I}=-0.1m{s}^{-1}
Magnitude of velocity =0.1ms−1=0.1m{s}^{-1}

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