A linear object AB is placed along the axis of a concave mirror. The object is moving towards the mirror with speed U. The speed of the image of the point A is $$4U$$ and the speed of the image of B is also $$4U$$ but in opposite direction. If the centre of the line AB is at a distanc e L from the mirror then find out the length of the object.

Question

Infinity Learn · Accepted Answer

For concave mirror, if x and y are object distance and image and distance, respectively, we have −$$1x$$−$$1y=$$−$$1$$|f|⇒ $$1x+1y=1$$|f|⇒ −$$1x2dxdt$$−$$1y2dydt=0$$⇒ $$VxVy=x2y2$$ For  $$VxVy=14$$,$$xy=$$±$$12$$              For  $$xy=12$$, we get $$x=3$$|f|$$2$$                [for point A]            and for $$xy=$$ $$-$$ $$12$$, we get  $$x=$$|f|$$2$$     [for point B] As the middle point happens to be focus of the mirror, we get|f| $$=$$ L

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