An object is placed between a plane mirror and a concave mirror of focal length 15 cm as shown in Figure . Find the position of the images after two reflections.

Options

A. image starts moving with `4cms^(-1)` away from the mirror
B. image starts moving with `4cms^(-1)` towards the mirror
C. image starts moving with `8ms^(-1)` towards the mirror
D. image starts moving with `8cms^(-1)` away from the mirror

Answer

d.

Explanation

Let `u=-x, v=-y`
`(dx)/(dt)=-2cms^(-1),(1)/(-y)+(1)/(-x)=(1)/(f)`
`rArr (1)/(y^(2))(dy)/(dt)+(1)/(x^(2))(dx)/(dt)=0`
`rArr (dy)/(dt)=-((y)/(x))^(2)(dx)/(dt)rArrv_(I)=-((60)/(30))^(2)(-2)=8cms^(-1)`