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Q.

A double convex lens forms a real image of an object on a screen which is fixed. Now the lens is given a constant velocity 0.5 m/s along its axis and away from the screen. For the purpose of forming a sharp image always on the screen, the object is also required to be given an appropriate velocity. The velocity of the object at the instant the size of the image is half the size of the object.

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a

2 m/s

b

1.5 m/s

c

1 m/s

d

4 m/s

answer is C.

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Detailed Solution

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$\overset{⇀}{v_{i / l}} = m^{2} \overset{⇀}{v_{o / l}} \overset{⇀}{v_{o}} = \overset{⇀}{v_{l}} (1 - \frac{1}{m^{2}})$

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A double convex lens forms a real image of an object on a screen which is fixed. Now the lens is given a constant velocity 0.5 m/s along its axis and away from the screen. For the purpose of forming a sharp image always on the screen, the object is also required to be given an appropriate velocity. The velocity of the object at the instant the size of the image is half the size of the object.