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JEE Main & Advanced Physics Ray Optics Question Bank Refraction of Light at Plane Surfaces

  • question_answer
    Each quarter of a vessel of depth H is filled with liquids of the refractive indices \[{{n}_{1}},{{n}_{2}},{{n}_{3}}\,\,and\,\,{{n}_{4}}\] from the bottom respectively.  The apparent depth of the vessel when looked normally is        [AMU (Engg.) 2000]

    A) \[\frac{H({{n}_{1}}+{{n}_{2}}+{{n}_{3}}+{{n}_{4}})}{4}\]     

    B) \[\frac{H\left( \frac{1}{{{n}_{1}}}+\frac{1}{{{n}_{2}}}+\frac{1}{{{n}_{3}}}+\frac{1}{{{n}_{4}}} \right)}{4}\]

    C) \[\frac{({{n}_{1}}+{{n}_{2}}+{{n}_{3}}+{{n}_{4}})}{4H}\]     

    D) \[\frac{H\left( \frac{1}{{{n}_{1}}}+\frac{1}{{{n}_{2}}}+\frac{1}{{{n}_{3}}}+\frac{1}{{{n}_{4}}} \right)}{2}\]

    Correct Answer: B

    Solution :

    Apparent depth of bottom                    = \[\frac{H/4}{{{\mu }_{1}}}+\frac{H/4}{{{\mu }_{2}}}+\frac{H/4}{{{\mu }_{3}}}+\frac{H/4}{{{\mu }_{4}}}\]           \[=\frac{H}{4}\left( \frac{1}{{{\mu }_{1}}}+\frac{1}{{{\mu }_{2}}}+\frac{1}{{{\mu }_{3}}}+\frac{1}{{{\mu }_{4}}} \right)\]


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