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RAJASTHAN PMT Rajasthan - PMT Solved Paper-2008

  • question_answer
    In a laboratory four convex lenses\[{{L}_{1}},\,{{L}_{2}},{{L}_{3}}\] and \[{{L}_{4}}\] of focal lengths 2, 4, 6 and 8 cm, respectively are available. Two of these lenses form a telescope of length 10 cm and magnifying power 4. The objective and eye lenses are respectively

    A)  \[\,{{L}_{2}},{{L}_{3}}\]                                

    B)  \[\,{{L}_{1}},{{L}_{4}}\]

    C)  \[\,{{L}_{1}},{{L}_{2}}\]                

    D)         \[\,{{L}_{4}},{{L}_{1}}\]

    Correct Answer: D

    Solution :

    Length of tube\[=10\,\,cm\]                 \[{{f}_{o}}+{{f}_{e}}=10\,\,cm\] Magnification\[m=\frac{{{f}_{o}}}{{{f}_{e}}}=4\]                 \[{{f}_{o}}=4{{f}_{e}}\] Putting in Eq. (i),                 \[5{{f}_{e}}=10\,\,cm\] or            \[{{f}_{e}}=2\,\,cm\] and        \[{{f}_{o}}=8\,\,cm\]                 \[{{f}_{o}}=8\,\,cm,\,\,{{f}_{e}}=2\,\,cm\] Hence, \[{{L}_{4}}\] and \[{{L}_{1}}\] will be used.


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