KVPY Sample Paper KVPY Stream-SX Model Paper-29

  • question_answer
    A lens is placed between a source of light and a wall. It forms images of area \[{{A}_{1}}\] and \[{{A}_{2}}\] on the wall, for its two different positions. The area of the source of light is (source and wall are fixed)-

    A) \[{{({{A}_{1}}{{A}_{2}})}^{1/2}}\]

    B) \[\frac{{{A}_{1}}+{{A}_{2}}}{2}\]

    C) \[{{\left( \frac{1}{{{A}_{1}}}+\frac{1}{{{A}_{2}}} \right)}^{-1}}\]     

    D) \[{{\left( \frac{\sqrt{{{A}_{1}}}+\sqrt{{{A}_{2}}}}{2} \right)}^{2}}\]

    Correct Answer: A

    Solution :

    From Nerwton's equation of lens
    size of object  = \[{{O}^{2}}={{l}_{1}}{{l}_{2}}\]
    where \[{{l}_{1}}\] is size of image of object and \[{{l}_{2}}\]is size of image when positions of object & image are interchanged
    So \[{{A}^{2}}={{A}_{1}}{{A}_{2}}\Rightarrow \mathbf{A}=\sqrt{{{A}_{1}}{{A}_{2}}}\]

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