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JIPMER Jipmer Medical Solved Paper-2002

  • question_answer
    A ray of light enters from a rarer medium to a denser medium at an angle of incidence i. The reflected and refracted rays make an angle of \[90{}^\circ C\]with each other. The angles of reflection and refraction are r and r respectively. The critical angle of denser medium is:

    A)  \[\tan {{\,}^{-1}}(\sin \,i)\]         

    B)  \[\tan {{\,}^{-1}}(\sin \,i)\]         

    C)          \[{{\sin }^{-1}}\,{{(\tan \,i)}^{-1}}\]    

    D)                         \[\sin {{\,}^{-1}}(\tan \,r)\]

    Correct Answer: C

    Solution :

    It is quite clear \[r+r=90{}^\circ \] or            \[r=90{}^\circ -r\]             and  \[i=r\] The refractive index is given by \[\mu =\frac{\sin i}{\sin r}=\frac{\sin i}{\sin \,(90{}^\circ -r)}=\frac{\sin i}{\cos r}\] \[=\frac{\sin i}{\cos i}=\tan i\] Now      \[\frac{1}{\sin C}=\tan i\] \[\Rightarrow \]               \[\sin C={{(\tan i)}^{-1}}\] so,          \[C={{\sin }^{-1}}{{(\tan i)}^{-1}}\]


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