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JEE Main & Advanced Physics Ray Optics Question Bank Total Internal Reflection

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    Material A has critical angle \[{{i}_{A}},\] and material B has critical angle \[{{i}_{B}}({{i}_{B}}>{{i}_{A}}).\] Then which of the following is true (i)       Light can be totally internally reflected when it passes from B to A (ii)      Light can be totally internally reflected when it passes from A to B (iii)     Critical angle for total internal reflection is \[{{i}_{B}}-{{i}_{A}}\] (iv)     Critical angle between A and B is \[{{\sin }^{-1}}\left( \frac{\sin {{i}_{A}}}{\sin {{i}_{B}}} \right)\] [UPSEAT 2004]

    A)            (i) and (iii)                              

    B)            (i) and (iv)

    C)            (ii) and (iii)                             

    D)            (ii) and (iv)

    Correct Answer: D

    Solution :

                       We know \[C={{\sin }^{-1}}\left( \frac{1}{\mu } \right)\] Given critical angle \[{{i}_{B}}>{{i}_{A}}\] So \[{{\mu }_{B}}<{{\mu }_{A}}\]i.e. B is rarer and A is denser. Hence light can be totally internally reflected when it passes from A to B                    Now critical angle for A to B                    \[{{C}_{AB}}={{\sin }^{-1}}\left( \frac{1}{_{B}{{\mu }_{A}}} \right)\]\[={{\sin }^{-1}}\left[ _{A}{{\mu }_{B}} \right]\]            \[={{\sin }^{-1}}\left[ \frac{{{\mu }_{B}}}{{{\mu }_{A}}} \right]\]\[={{\sin }^{-1}}\left[ \frac{\sin {{i}_{A}}}{\sin {{i}_{B}}} \right]\]


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