A linear object AB is placed along the axis of a concave mirror. This 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 btu in opposite direction. If the center of the line AB is at a distance L from the mirror then find out the length of the object.

Options

A. `3L//2`
B. `5L//3`
C. L
D. None of these

Answer

c.

Explanation

For concave mirror, if x and y are object distance and image and distance, recpectivley, we have
`-(1)/(x)-(1)/(y)=-(1)/(|f|)`
`rArr(1)/(x)+(1)/(y)=(1)/(|f|)`
`rArr-(1)/(x)(dx)/(dt)-(1)/(y)(dy)/(dt)=0`
`rArr |(V_(x))/(V_(y))|=(x^(2))/(y^(2))`
For`rArr |(V_(x))/(V_(y))|=(1)/(4),(x)/(y)=+-2`
For `(x)/(y)=2` we get `x=(3|f|)/(2)` [for point A]
and For`(x)/(y)=-2`, we get `x=(|f|)/(2)` [for point B]
As the middle happens to be focus of the mirror, we get
`|f|=L`