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KVPY Sample Paper KVPY Stream-SX Model Paper-9

  • question_answer
    The focal length of a convex lens of refractive index 1, 5 is 2 cm. The focal length of the lens when immerged in liquid spirit of refractive index 1.25 is

    A) 5 m

    B) 2.5 cm

    C) 4 cm    

    D) 5 cm

    Correct Answer: D

    Solution :

    \[\frac{1}{f}=({{\mu }_{rd}}-1)\,\,\left( \frac{1}{{{R}_{1}}}-\frac{1}{{{R}_{2}}} \right]\]
    \[\frac{1}{2}=(1.5-1)\,\,\left[ \frac{1}{{{R}_{1}}}-\frac{1}{{{R}_{2}}} \right]\]    \[\therefore \]      \[\left[ \frac{1}{{{R}_{1}}}-\frac{1}{{{R}_{2}}} \right]=1\]
    now in medium
    \[\frac{1}{f}=\left( \frac{1.5}{1.25}-1 \right)\,\,\left( \frac{1}{{{R}_{1}}}-\frac{1}{{{R}_{2}}} \right]\]
    \[\frac{1}{f}=\frac{0.25}{1.25}\times 1\]             \[\therefore \]      \[{{f}_{2}}=5\,\,cm\]


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