Question

In Fig., shown $AB$ is the principal axis of the concave mirror. A point object moves on the line $PQ$ which makes small angle ${}^{\prime }{\theta }^{\prime }$ with the principal axis. Show that image also moves in straight line making same angle $\theta$ with principle axis.

Answer 1

Let $\tan \theta =a$ then equation of the line $PQ$ is
$y=-ax...\left(i\right)$
Let $y=y-coordinate$ of the image and
$x^{\prime }=x-coordinate$ of image. By using the formula of magnification, $\frac{y^{\prime }}{y}=-\frac{x^{\prime }}{x}$
$\Rightarrow y^{\prime }=-\frac{y}{x}{x}^{\prime }=-(-a)x^{\prime }=a{x}^{\prime }$
$\Rightarrow y^{\prime }=a{x}^{\prime }$
This is equation of a straight line, making angle ${}^{\prime }{\theta }^{\prime }$ with the principal axis. (hence, proved.)