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

  • question_answer
    Two point light sources are 24 cm apart. Where should a convex lens of focal length 9 cm be put in between them from one source so that the images of both the sources are formed at the same place

    A) 6 cm

    B) 9 cm

    C) 12 cm

    D) 15 cm

    Correct Answer: A

    Solution :

    [a] The given condition will be satisfied only if one source \[({{S}_{1}})\] placed on one side such that \[u<f\] (i.e., it lies under the focus). The other source (5y is placed on the other side of the lens such that \[u>f\] (i.e., it lies beyond the focus).
    If \[{{S}_{1}}\] is the object for lens, then
    \[\frac{1}{f}=\frac{1}{-y}-\frac{1}{-x}\,\,\Rightarrow \,\,\frac{1}{y}=\frac{1}{x}-\frac{1}{f}\] ....(i)
    If \[{{S}_{2}}\] is the object for lens, then
    \[\Rightarrow \]            \[\frac{1}{y}=\frac{1}{y}-\frac{1}{(24-x)}\] ...(ii)
    From (i) and (ii),
    \[\Rightarrow \]   \[\frac{1}{x}+\frac{1}{(24-x)}=\frac{2}{f}=\frac{2}{9}\]
    \[\Rightarrow \]   \[{{x}^{2}}-24x+108=0\]
    On solving the equation, \[x=18\text{ }cm,\text{ }6\text{ }cm\]

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