JEE Main & Advanced Physics Ray Optics Sample Paper Topic Test - Refraction of Light Through Curved Surfaces

  • 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 :

    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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