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JEE Main & Advanced Physics Ray Optics Question Bank Critical Thinking

  • question_answer
    The distance of the moon from earth is \[3.8\times {{10}^{5}}km.\] The eye is most sensitive to light of wavelength 5500 Å. The separation of two points on the moon that can be resolved by a 500 cm telescope will be [AMU (Med.) 2002]

    A)            51 m                                        

    B)            60 m

    C)            70 m                                        

    D)            All the above

    Correct Answer: A

    Solution :

                       As limit of resolution                    \[\Delta \theta =\frac{1}{Resolving\ Power(RP)}\];  and if x is the distance between points on the surface of moon which is at a distance r from the telescope.                    \[\Delta \theta =\frac{x}{r}\]                    So \[\Delta \theta =\frac{1}{RP}=\frac{x}{r}i.e.\ x=\frac{r}{RP}=\frac{r}{d/1.22\ \lambda }\]\[\Rightarrow x=\frac{1.22\ \lambda r}{d}\]            \[=\frac{1.22\times 5500\times {{10}^{-10}}\times (3.8\times {{10}^{8}})}{500\times {{10}^{-2}}}=51\ m\]


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