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

  • question_answer
    A vertical microscope is focused on a point at the bottom of an empty tank. Water \[\left( \mu =\frac{4}{3} \right)\] is then poured into the tank. The height of the water column is 4 cm. Another lighter liquid, which does not mix with water and which has refractive index \[\frac{3}{2}\] is then poured over the water. The height of liquid column is 2 cm. What is the vertical distance through which the microscope must be moved to bring the object in focus again?

    A) 2.61 m

    B) 1.55 m

    C) 3.12 m

    D) 1.67 m

    Correct Answer: D

    Solution :

    [d] The apparent shift of the bottom point upwards will be
    \[x={{x}_{1}}+{{x}_{2}}\]
    \[={{t}_{1}}\left( 1-\frac{1}{{{\mu }_{1}}} \right)+{{t}_{2}}\left( 1-\frac{1}{{{\mu }_{2}}} \right)\]
    \[=4\left( 1-\frac{1}{4/3} \right)+2\left( 1-\frac{1}{3/2} \right)\]
    \[=4\left( 1-\frac{3}{4} \right)+2\left( 1-\frac{2}{3} \right)=1.67\,cm\]


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