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JEE Main & Advanced Sample Paper JEE Main Sample Paper-18

  • question_answer
    A convex lens of focal length\[f\]is placed somewhere in between an object and a screen. The distance between the object and the screen is\[x\]. If the magnification produced by the lens is\[m,\]the focal length of the lens is

    A)  \[\frac{mx}{{{(m+1)}^{2}}}\]                     

    B)  \[\frac{mx}{{{(m-1)}^{2}}}\]

    C)  \[\frac{{{(m+1)}^{2}}}{mx}\]                     

    D)  \[\frac{{{(m-1)}^{2}}}{mx}\]

    Correct Answer: A

    Solution :

     \[|u|+|v|\,=x\]  \[m=-\frac{v}{u}\] \[|v|\,=mu\] Using (i) and (ii), we get \[|u|+m|u|\,=x\] \[\Rightarrow \]               \[|u|\,=\frac{x}{1+m}\] and        \[|v|=\frac{mx}{1+m}\] Putting values of\[v\]and\[u\]in,\[\frac{1}{v}-\frac{1}{u}=\frac{1}{f},\]we get \[\frac{1+m}{mx}-\left[ -\left( \frac{1+m}{x} \right) \right]=\frac{1}{f}\] \[\Rightarrow \]               \[f=\frac{mx}{{{(1+m)}^{2}}}\]


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