Microscope!

The focal lengths of the eye-piece and the objective of a compound microscope are 5 cm 5\text{ cm} and 1 cm 1\text{ cm} respectively and the length of the tube is 20 cm . 20\text{ cm}. Calculate the magnifying power of the microscope, when the final image is formed at infinity. The value of least distance of distinct vision is 25 cm . 25\text{ cm}.


The answer is 70.

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1 solution

As the final image is formed at infinity, the image would have been on focus of eyepiece, that is at a distance of 5 cm 5\text{ cm} from the eyepiece.

Image distance for the objective = Tube length(L) f e = 20 5 = 15 cm Using Cartesian sign convention for the objective lens, 1 u 0 = 1 v 0 1 f 0 1 u 0 = 1 15 1 1 = 14 15 u 0 = 15 14 cm . \large \displaystyle \therefore \text{Image distance for the objective } = \text{Tube length(L)} - f_e\\ \large \displaystyle = 20 - 5 = 15\text{ cm}\\ \large \displaystyle \text{Using Cartesian sign convention for the objective lens, }\\ \large \displaystyle \frac{1}{u_0} = \frac{1}{v_0} - \frac{1}{f_0}\\ \large \displaystyle \frac{1}{u_0} = \frac{1}{15} - \frac{1}{1} = -\frac{14}{15}\\ \large \displaystyle \therefore u_0 = -\frac{15}{14} \text{ cm}.

When the final image is formed at infinity, the magnifying power of the microscope will be,

m = v 0 u 0 × D f e = 15 15 14 × 25 5 m = 70 . \large \displaystyle m = \frac{v_0}{u_0} \times \frac{D}{f_e}\\ \large \displaystyle = \frac{15}{\frac{15}{14}} \times \frac{25}{5}\\ \large \displaystyle m = \color{#D61F06}{\boxed{70}}.

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