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Question

An object is to be seen through a simple microscope of focal length 12 cm. Where should the object be placed so as to produce maximum angular magnification? The least distance for clear vision is 25 cm.

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Solution

For the simple microscope, we have: Focal length, f = 12 cm Least distance of clear vision, d = 25 cm For maximum angular magnification, Image distance = Least distance of clear vision v = d = − 25 cm $\mathrm{The}\mathrm{lens}\mathrm{formula}\mathrm{is}\mathrm{given}\mathrm{by}\phantom{\rule{0ex}{0ex}}\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\phantom{\rule{0ex}{0ex}}⇒\frac{1}{u}=\frac{1}{v}-\frac{1}{f}$ On substituting the values, we get: $\frac{1}{u}=\frac{1}{-25}-\frac{1}{12}\phantom{\rule{0ex}{0ex}}\frac{1}{u}=-\frac{25+12}{300}=-\frac{37}{300}$ $⇒u=-\frac{300}{37}=-8.1\mathrm{cm}$ So, to produce maximum angular magnification, the object should be placed 8.1 cm away from the lens.

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