CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2011

  • question_answer
    A prism having refractive index 1.414 and refracting angle \[{{30}^{o}}\] has one of the refracting surfaces silvered. A beam of light incident on the other refracting surface will retrace its path, if the angle of incidence is

    A)  \[{{0}^{o}}\]                                     

    B)  \[{{30}^{o}}\]

    C)  \[{{60}^{o}}\]                                   

    D)  \[{{45}^{o}}\]

    Correct Answer: D

    Solution :

    At second surface, there is no refraction so                 \[{{r}_{2}}=0\] \[\therefore \]  \[{{r}_{1}}=A={{30}^{o}}\] From Snell?s law                 \[n=\frac{\sin {{i}_{1}}}{\sin {{r}_{1}}}\]                 \[n=\frac{\sin {{i}_{1}}}{\sin {{30}^{o}}}\]                 \[\sin {{i}_{1}}=\sqrt{2}\times \frac{1}{2}=\frac{1}{\sqrt{2}}\]                 \[\sin {{i}_{1}}=\frac{1}{\sqrt{2}}\]                 \[{{i}_{1}}={{45}^{o}}\] 


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