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Manipal Engineering Manipal Engineering Solved Paper-2011

  • question_answer
    A thin prism \[{{P}_{1}}\] of angle \[4{}^\circ \] and refractive index \[1.54{}^\circ \] is combined with another thin prism \[{{P}_{2}}\] of refractive index 1.72 to produce dispersion without deviation. The angle of \[{{P}_{2}}\] is

    A) \[4{}^\circ \]                                      

    B) \[5.33{}^\circ \]

    C) \[2.6{}^\circ \]

    D)        \[3{}^\circ \]

    Correct Answer: D

    Solution :

    Angle of deviation\[\delta =(n-1)A\] Dispersion produced by both the prisms will be equal.                 \[({{n}_{1}}-1){{A}_{1}}=({{n}_{2}}-1){{A}_{2}}\] \[\Rightarrow \]               \[{{A}_{2}}=\frac{({{n}_{1}}-1){{A}_{1}}}{({{n}_{2}}-1)}=\frac{(1.54-1)}{(1.72-1)}={{3}^{o}}\] Hence, the angle of prism\[{{P}_{2}}\]is\[{{3}^{o}}\].


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