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The objective of a microscope has a focal length of 1 cm and diameter 0.5 cm. Using light of 6000 Å, is it possible to resolve the two point objects if they are separated by a distance of 10^(-6) m ? |
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Answer» Solution : Suppose the two objects are a distance `Delta x `apart. Since these objects are almost at the focal LENGTH of the objective, the angle SUBTENDED by `Delta x, i.e., Delta phi = (Delta x)/(f_0)` For the two objects to be clearly resolved ,` Delta phi GT Delta theta` `(Delta x)/(f_0) gt (1.22 lamda)/(a) (Delta theta = (1.22 lamda)/(a)) " or " Delta x gt (1.22 f_0 lamda)/(a)` `Delta x gt ((1.22)(1 xx 10^(-2) m)(6000 xx 10^(-10) m) )/((0.5 xx 10^(-2)m) ) = 1.46 xx 10^(-6) m` Because `10^(-6)m` is smaller than `1.46 xx 10^(-6)`m, the two objects will not be resolved . |
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