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  • A diverging lens of focal length –10 cm is moving towards right with a velocity 5 m/s.An object, placed on Principal axis is moving towards left with a velocity 3 m/s. Find the velocity of im

A diverging lens of focal length –10 cm is moving towards right with a velocity 5 m/s.An object, placed on Principal axis is moving towards left with a velocity 3 m/s. Find the velocity of image at the instant when the lateral magnification produced is 1/2. All velocities are with respect to ground.

Option: 1

3 m/s towards right


Option: 2

3 m/s towards left


Option: 3

7 m/s towards right


Option: 4

7 m/s towards left


Answers (1)

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\frac{\mathrm{dv}}{\mathrm{dt}}=\frac{\mathrm{v}^2}{\mathrm{u}^2} \cdot \frac{\mathrm{du}}{\mathrm{dt}}
(where \frac{\mathrm{dv}}{\mathrm{dt}}  denotes image speed w.r.t. lens and \frac{\mathrm{du}}{\mathrm{dt}}  denotes object speed w.r.t. lens)

=\mathrm{m}^2 \cdot \frac{\mathrm{du}}{\mathrm{dt}}=\frac{1}{4} \cdot 8=2.

Therefore image speed w.r.t. lens is 2 m/s Therefore image speed w.r.t. ground is 7 m/s towards right

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