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KVPY Sample Paper KVPY Stream-SX Model Paper-4

  • question_answer
    On a hypotenuse of a right prism \[(30{}^\circ -60{}^\circ -90{}^\circ )\] of refractive index \[1.50,\] a drop of liquid is placed as shown in figure. Light is allowed to fall normally on the short face of the prism. In order that the ray of light may get totally reflected, the maximum value of refractive index is:

    A) 1.30                             

    B) 1.47

    C) 1.20                             

    D) 1.25

    Correct Answer: A

    Solution :

    [a] \[{{C}_{\max }}=60{}^\circ \] \[\therefore \]\[{}_{r}{{\mu }_{d}}=\frac{1}{\sin 60{}^\circ }\operatorname{or}\frac{{{\mu }_{g}}}{{{\mu }_{\ell }}}=\frac{2}{\sqrt{3}}\] \[\therefore \]\[{{\mu }_{\ell }}=\frac{\sqrt{3}}{2}{{\mu }_{g}}\frac{\sqrt{3}}{2}\times 1.5=1.3\]


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