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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2007

  • question_answer
    A prism of a certain angle deviates the red and blue rays by \[{{8}^{o}}\] and \[{{12}^{o}}\] respectively. Another prism of the same angle deviates the red and blue rays by \[{{10}^{o}}\] and \[{{14}^{o}}\] respectively. The prisms are small angled and made of different materials. The dispersive powers of the materials of the prisms are in the ratio

    A)  \[5:6\]                                 

    B)  \[9:11\]

    C)  \[6:5\]                                 

    D)  \[11:9\]

    Correct Answer: C

    Solution :

    Dispersive power, \[\omega =\frac{{{\delta }_{B}}-{{\delta }_{R}}}{\delta }\] For 1st prism,     \[{{\omega }_{1}}=\frac{{{\delta }_{B}}-{{\delta }_{R}}}{\delta }=\frac{{{12}^{o}}-{{8}^{o}}}{{{10}^{o}}}=\frac{2}{5}\] where                   \[\delta =\frac{{{\delta }_{B}}+{{\delta }_{R}}}{2}\] Similarly, for 2nd prism,                 \[{{\omega }_{2}}=\frac{{{14}^{o}}-{{10}^{o}}}{12}=\frac{1}{3}\] \[\therefore \]  \[\frac{{{\omega }_{1}}}{{{\omega }_{2}}}=\frac{2}{5}\times \frac{3}{1}=\frac{6}{5}\]


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