Question

In the figure shown in thin parallel beam of light is incident on a plane mirror $m_1$ at small angle ${}^{\prime }{\theta }^{\prime }{m}_2$ is a concave mirror of focal length ${}^{\prime }{f}^{\prime }$. After three successive reflections of this beam the $x$ and $y$ coordinates of the image is :

• A. $x=f-d,y=f\theta$
• B. $x=f+d,y=f\theta$
• C. $x=f-d,y=-f\theta$
• D. $x=d-f,y=-f\theta$

Answer 1

The correct option is A $x=f-d,y=f\theta$

$\to$ After $I^{st}$ reflection (from plane mirror) parallel beam of light strick on a concave mirror

$\to$ After $I{I}^{nd}$ reflection (from concave mirror) image is formed at focus and shifted by a distance $f\theta$ (perpendicular to principal axis)

$\to$ For $II{I}^{rd}$ reflection object is placed at a distance $|f-d|$ from a plane mirror.

So, $x=f-d,y=f\theta$