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

  • question_answer
    A glass slab has the left half of refractive index \[{{n}_{1}},\] and the right half of \[{{n}_{2}}=3{{n}_{1}}\]. The effective refractive index of the whole slab is

    A) \[\frac{{{n}_{1}}}{2}\]

    B) \[2n\]

    C) \[\frac{3{{n}_{1}}}{2}\]

    D) \[\frac{2{{n}_{1}}}{3}\]

    Correct Answer: C

    Solution :

    [c] Total time taken to travel distance d is:
    \[\frac{d}{2{{n}_{1}}}+\frac{d}{2{{n}_{2}}}=d\left( \frac{{{n}_{1}}+{{n}_{2}}}{2{{n}_{1}}{{n}_{2}}} \right)=\frac{d}{{{n}_{eff}}};\]
    \[{{n}_{2}}=3{{n}_{1}}\Rightarrow \,{{n}_{eff}}=\frac{3}{2}{{n}_{1}}\]
                            \[=\frac{6\times {{10}^{5}}cm}{1.0003-1}\]\[=0.2cm=2mm\]


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