(a) Draw the ray diagram showing the formation of image by a compound microscope.
(b) Show that in order to achieve large magnification in a compound microscope the magnitude of focal length of objective and eye piece should be small.

Question

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Answer 1

(A) : Compound microscope is consist of two convex lenses, one object of very small focal length with short aperture and one eyepiece, $E$ of moderate focal length and large aperture. The ray diagram showing the formation of image by a compound microscope is shown in the diagram.

(B) : The Magnifying power, $M = m_{e} \times m_{o}$ where $m_{e}$ and $m_{o}$ are the individual magnifying powers o objective and eye lens.
$M = \frac{v _{0}}{u _{0}} (1 + \frac{D}{f _{e}})$ --------- (1) when the final image is at near point.

$M = \frac{v _{0}}{u _{0}} \times \frac{D}{f _{e}}$ -----------(2) when the final image is at the infinity.
From the equations (1) and (2) it is clear that for achieving a large magnification the focal length $f_{e}$ must be small. Hence the answer.

Answer 2

(A) : Compound microscope is consist of two convex lenses, one object of very small focal length with short aperture and one eyepiece,

E

of moderate focal length and large aperture. The ray diagram showing the formation of image by a compound microscope is shown in the diagram.

(B) : The Magnifying power,

M = m_{e} \times m_{o}

where

m_{e}

and

m_{o}

are the individual magnifying powers o objective and eye lens.

M = \frac{v _{0}}{u _{0}} (1 + \frac{D}{f _{e}})

--------- (1) when the final image is at near point.

M = \frac{v _{0}}{u _{0}} \times \frac{D}{f _{e}}

-----------(2) when the final image is at the infinity.

From the equations (1) and (2) it is clear that for achieving a large magnification the focal length

f_{e}

must be small. Hence the answer.