• # question_answer In the figure shown, a thin parallel beam of light is incident on a plane mirror ${{m}_{1}}$ at small angle $\theta ,\,\,{{m}_{2}}$ is a concave mirror of focal length f. After three successive reflections of this the $x$ and $y$ coordinates of the image is                      A)  $x=f-d,\,\,y=f\,\theta$           B)  $x=d+f,\,\,y=f\,\theta$ C)  $x=f-d,\,\,y=-f\theta$           D)  $x=d-f,$$y=-f\,\theta$

From diagram, $\int_{A}^{B}{{{B}_{P}}dI+}\int_{B}^{C}{{{B}_{P}}di+}\int_{C}^{D}{{{B}_{P}}dI}+\int_{D}^{A}{{{B}_{P}}dI}$ $+\int_{A}^{B}{{{B}_{Q}}dI+}\int_{B}^{C}{{{B}_{Q}}dI}+\int_{C}^{D}{{{B}_{Q}}dI}+\int_{D}^{A}{{{B}_{Q}}dI}={{\mu }_{0}}\,(2I-I)$$(-{{\mu }_{0}}-2{{\mu }_{0}}-{{\mu }_{0}}-2{{\mu }_{0}})\,+(2{{\mu }_{0}}+4{{\mu }_{0}}+2{{\mu }_{0}}+4{{\mu }_{0}})$$={{\mu }_{0}}I$ $\Rightarrow$            $I=12-6=6A$