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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 34

  • question_answer
    A transparent glass slab (G) of thickness \[6\text{ }cm\]is held perpendicular to the principal axis of a convex lens (L) as shown in the figure. The refractive index of the material 3 of the glass is \[\frac{3}{2}\]and its nearer face is at a distance \[40cm\] from the lens. Focal length of the lens is\[20\text{ }cm\]. Find the thickness of the glass slab as observed through the lens.

    A) \[3.3\text{ }cm\]            

    B) \[\text{2 }cm\]   

    C) \[\text{1}\text{.5 }cm\]                     

    D) \[\text{4}\text{.2 }cm\]

    Correct Answer: A

    Solution :

    [a] Image of the front face is formed at a distance of 40 cm on the other side of the lens. The rear face of the glass slab appears to be shifted by \[s=t\left( 1-\frac{1}{\mu } \right)=6\left( 1-\frac{1}{3/2} \right)=2cm\] nearer to the lens. For lens the distance of rear face of the slab is \[40+6-2=44\,cm.\]Its image is formed at a distance v from lens given by             \[\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\frac{1}{v}-\frac{1}{-44}=\frac{1}{20}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\frac{1}{v}=\frac{1}{20}-\frac{1}{44}=\frac{11-5}{220}=\frac{3}{110}\] \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,v=\frac{110}{3}=36.7\,cm\] \[\therefore \] Thickness of slab in the image formed by the lens is\[=40-36.7=3.3\text{ }cm\].


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