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KVPY Sample Paper KVPY Stream-SX Model Paper-24

  • question_answer
    A piano convex lens of refractive index \[{{\mu }_{1}}\] and length \[{{f}_{1.}}\] is kept in contact with another plano  concave lens  of refractive index \[{{\mu }_{2}}\] and focal length \[{{f}_{2}}.\] If the  radius of curvature of their spherical faces is  R each and \[{{f}_{1}}=2{{f}_{2}},\] then \[{{\mu }_{1}}\] and \[{{\mu }_{2}}\] are related as:

    A) \[{{\mu }_{1}}+{{\mu }_{2}}+=3\]    

    B) \[2{{\mu }_{1}}+{{\mu }_{2}}+=1\]

    C) \[3{{\mu }_{1}}+{{\mu }_{1}}+=1\]

    D) \[2{{\mu }_{2}}+{{\mu }_{1}}+=1\]

    Correct Answer: A

    Solution :

    \[\frac{1}{{{f}_{1}}}=(\mu -1)\left( \frac{1}{R}-\frac{1}{\infty } \right);\]
    \[\frac{1}{{{f}_{2}}}=({{\mu }_{2}}-1)\left( \frac{1}{\infty }-\frac{1}{R} \right)\]
    \[\frac{1}{{{f}_{1}}}=\frac{(\mu -1)}{R};\frac{1}{{{f}_{2}}}=-\left( \frac{{{\mu }_{2}}-1}{R} \right)\]
    \[{{f}_{2}}=2{{f}_{1}};\frac{1}{{{f}_{1}}}=\frac{2}{{{f}_{2}}}\]
    \[\frac{{{\mu }_{1}}-1}{R}=\frac{-2({{\mu }_{1}}-1)}{R}\]
    \[{{\mu }_{1}}+2{{\mu }_{2}}=3.\]


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