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JEE Main & Advanced Physics Ray Optics Question Bank Self Evaluation Test - Ray Optics and Optical Instruments

  • question_answer
    A piano convex lens fits exactly into a piano concave lens. Their plane surface are parallel to each other. If the lenses are made of different materials of refractive indices \[{{\mu }_{1}}\] & \[{{\mu }_{2}}\] and R is the radius of curvature of the curved surface of the lenses, then focal length of combination is            

    A) \[\frac{R}{{{\mu }_{1}}-{{\mu }_{2}}}\]

    B) \[\frac{2R}{{{\mu }_{1}}-{{\mu }_{2}}}\]

    C) \[\,\frac{R}{2\left( {{\mu }_{1}}-{{\mu }_{2}} \right)}\]

    D) \[\,\frac{R}{2-\left( {{\mu }_{1}}+{{\mu }_{2}} \right)}\]

    Correct Answer: A

    Solution :

    [a]  \[\frac{1}{F}=\frac{1}{{{f}_{1}}}+\frac{1}{{{f}_{2}}}\] \[\frac{1}{F}=\left( {{\mu }_{1}}-1 \right)\left( \frac{1}{\infty }+\frac{1}{R} \right)+\left( {{\mu }_{2}}-1 \right)\left( \frac{1}{-R}-\frac{1}{\infty } \right)\] \[=\frac{{{\mu }_{1}}-{{\mu }_{2}}}{R}\] \[F=\frac{R}{{{\mu }_{1}}-{{\mu }_{2}}}\]


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