Practicing Success
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If initially the objective ( focal length F) forms the image at distance vo then $v_0 = \frac{u_0.f_0}{u_0 - f_0} = \frac{3 \times 2}{3 - 2} = 6cm$ $\text{For lenses in contact } \frac{1}{F_0} = \frac{1}{f_1} + \frac{1}{F'_0}$ $\text{If one of the lenses is removed then Focal length of remaining system is } $ $ \frac{1}{F'_0} = \frac{1}{F_0} - \frac{1}{f_1} = \frac{1}{2} - \frac{1}{10}$ $\Rightarrow F'_0 = 2.5 cm$ $\text{This lens will form the image of same object at a distance }$ v0′ $\text{such that}$ $v'_0 = \frac{u_0.F'_0}{u_0 - F'_0} = \frac{3 \times 2.5}{3 - 2.5} = 15 cm$ So to refocus the image, eye-piece must be moved by the same distance through which the image formed by the objective has shifted i.e. 15−6=9 cm.
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