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 distance 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 distance, respectively, we have−$$1x$$−$$1y=$$−$$1f$$⇒$$1x+1y=$$−$$1f$$ ⇒−$$1x2dxdt$$−$$1y2dydt=0$$⇒$$VxVy=x2y2For$$, $$VxVy=14$$,$$xy=$$±$$2For$$ $$x/y=2$$, we get $$x=3f/2$$ [for point A] and for $$x/y=$$−$$2$$, 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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