Question

What will be the image speed if:

(1)The object is moving toward the plane mirror with speed $v$?

(2)The plane mirror is moving toward the object with speed $v$?

Answer 1

Let the object and mirror distance be $x$ & $y$.

(i) We can write, as image and object distance are equal, [Ref. image (i)]

$x=-y\Rightarrow \frac{dx}{dt}=\frac{dy}{dt}{V}_i=-V_o$

(ii) mirror is moving with velocity $V_m$ [Ref. image (ii)]

We write, $\frac{dx}{dt}=-V_m\&\frac{dy}{dt}=V_i-V_m$ (row distance are changing)

as $\frac{dx}{dt}=-\frac{dy}{dt}\Rightarrow V_i=-2V_m$