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JEE Main & Advanced Sample Paper JEE Main Sample Paper-21

  • question_answer
    A fish in a lake (refractive index 4/3 for water) is viewed through a convex lens. From water surface, the lens is placed in air at half of the distance of the fish from the water surface, so that the image is formed at the fish itself. The focal length of the lens is how many times the depth of fish in water?

    A)  4                                

    B)  6

    C)  7.5                              

    D)  9

    Correct Answer: C

    Solution :

    For plane water surface. \[\frac{1}{v}\,-\frac{4/3}{(-u)}\,=\frac{1-4/3}{\infty }=0\] Or \[v=/00.75\,u\] For convex lens \[{{\mu }_{1}}=1,\,\,{{\mu }_{2}}=1\] \[{{u}_{1}}=-(0.75+0.5)\,u\] \[=-0.25\,u\] \[{{v}_{1}}=-(u+0.5u)\,=-1.5u\] Rays coming from air and viewed through air From \[\frac{1}{{{v}_{1}}}-\frac{1}{{{u}_{1}}}\,=\frac{1}{f}\] \[\frac{1}{1.5u}\,-\frac{1}{(-1.25u)}=\frac{1}{f}\] Or \[f=7.5\,u\]


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