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JEE Main & Advanced Physics Ray Optics Question Bank Critical Thinking

  • question_answer
    An achromatic prism is made by crown glass prism \[({{A}_{c}}={{19}^{o}})\] and flint glass prism \[({{A}_{F}}={{6}^{o}})\]. If \[^{C}{{\mu }_{v}}=1.5\] and \[^{F}{{\mu }_{v}}=1.66\], then resultant deviation for red coloured ray will be

    A)            1.04°                                        

    B)            5°

    C)            0.96°                                        

    D)            13.5°

    Correct Answer: D

    Solution :

                       For achromatic combination\[{{\omega }_{C}}=-{{\omega }_{F}}\]                    \[{{[({{\mu }_{v}}-{{\mu }_{r}})A]}_{C}}=-{{[({{\mu }_{v}}-{{\mu }_{r}})A]}_{F}}\]                    \[\Rightarrow \]\[{{[{{\mu }_{r}}A]}_{C}}+{{[{{\mu }_{r}}A]}_{F}}={{[{{\mu }_{v}}A]}_{C}}+{{[{{\mu }_{v}}A]}_{F}}\]                    \[=\] \[1.5\times 19+6\times 1.66=38.5\]                    Resultant \[\delta ={{[({{\mu }_{r}}-1)Al]}_{C}}+{{[({{\mu }_{r}}-1)A]}_{F}}\]            \[=\] \[{{[{{\mu }_{r}}A]}_{C}}+{{[{{\mu }_{r}}A]}_{F}}-({{A}_{C}}+{{A}_{F}})\]=\[38.5-(19+6)={{13.5}^{o}}\]


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