1. Draw a labelled ray diagram showing the formation of a final image by a compound microscope at least distance of distinct vision. 2. The total magnification produced by a compound microscope is 20. The magnification produced by the eye piece is 5. The microscope is focussed on a-certain object. The distance between the objective and eyepiece is observed to be 14 cm. If least distance of distinct vision is 20 cm, calculate the focal length of the objective and the eye piece.

For eyepiece m_ e = v_ e u_ e u_ e = v_ e m_ e = -20 5 cm = - 4 cm Also, 1 f_ e = 1 v_ e - 1 u_ e 1 f_ e = -1 20 + 1 4 f_ e = 5 cm m = m_ e m_ o -20 = 5 m_ o = > m_ 0 = -4 Also, |v_ o | + |u_ e | = 14 = > v_ o = (14 – 4) cm = 10 cm m_ 0 = 1- v_ o f_ 0 = > -4= 1-10 f_ o = > f_ o = 2 cm where subscripts e and o are used for eyepiece and objective respectively.

1. Draw a labelled ray diagram showing the formation of a final i…

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Question

Draw a labelled ray diagram showing the formation of a final image by a compound microscope at least distance of distinct vision.
The total magnification produced by a compound microscope is 20. The magnification produced by the eye piece is 5. The microscope is focussed on a-certain object. The distance between the objective and eyepiece is observed to be 14 cm. If least distance of distinct vision is 20 cm, calculate the focal length of the objective and the eye piece.

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Answer

For eyepiece $\text{m}_{e} = \frac{\text{v}_{e}}{\text{u}_{e}}$
$\text{u}_{e} = \frac{\text{v}_{e}}{\text{m}_{e}} = \frac{-20}{5}\text{cm} = - 4 \text{cm}$
Also, $\frac{1}{\text{f}_{e}}= \frac{1}{\text{v}_{e}} - \frac{1}{\text{u}_{e}}$
$\frac{1}{\text{f}_{e}} = \frac{-1}{20} + \frac{1}{4}$
$\text{f}_{e} = 5 \text{cm}$
$\text{m} = \text{m}_{e}\times \text{m}_{o}$
$-20 = 5 \times \text{m}_{o} = > \text{m}_{0} = -4$
Also, $|\text{v}_{o}| + |\text{u}_{e}| = 14$
$= > \text{v}_{o}= (14 – 4) \text{ cm} = 10\text{ cm}$
$\text{m}_{0} = 1-\frac{\text{v}_{o}}{\text{f}_{0}} = > -4= 1-\frac{10}{\text{f}_{o}}$
$= > \text{f}_{o} = 2\text{ cm}$
where subscripts e and o are used for eyepiece and objective respectively.

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