JEE Main & Advanced Sample Paper JEE Main Sample Paper-47

  • 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)  \[x=d-f,\]\[y=-f\,\theta \]

    Correct Answer: D

    Solution :

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

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