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define the magnifying power of a simple microscope and derive an expresion for it.

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Vaishali Deshmukh asked in Physics

define the magnifying power of a simple microscope and derive an expresion for it.

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Nitish Kumar Gupta answered this
790 helpful votes in Physics, Class XII-Science

Simple Microscope:

When image is formed at the near point



The angular magnification of a simple microscope is the ratio of the angle β subtended at the eye by the image at the near point and the angle αsubtended at the unaided eye by the object at the near point.



Now,and

Since the angles are small,







This gives the linear magnification produced by the lens.

It can be proved that

We know that,





v = − D



In case the eye is placed behind the lens at a distance ‘a’, then



When the image is formed at infinity



In this case,and





Answer 2

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$\huge\mathfrak\purple{simple\:microscope}$

(See fig 1st)
It is used for observing magnified images of objects. It is consists of a converging lens of small focal length.

Magnifying Power

(i) When final image is formed at least distance of distinct vision (D), then M=1+d/f

where, f= focal length of the lens.

(ii) When final image is formed at infinity, then M = D/f


$\huge\mathfrak\purple{Compound\:Microscope}$

(See fig. 2nd)
It is a combination of two convex lenses called objective lens and eye piece separated by a distance. Both lenses are of small focal lengths but fo < fe, where fo and feare focal lengths of objective lens and eye piece respectively

Magnifying Power

M = vo / uo {1 + (D/fo)

Where vo= distance of image, formed by objective lens and
uo = distance of object from the objective

(ii) When final image is formed at infinity, then
M = vo/uo . D/fe

$\huge\mathfrak\purple{Astronomical\:microscope}$

(See fig. 3rd)
It is also a combination of two lenses, called objective lens and eye piece, separated by a distance. It is used for observing distinct images of heavenly bodies like stars, planets etc

Magnifying Power

(i) When final image is formed at least distance of distinct vision (D), then M = fo/fe {1+ (D/fe)} where foand fe are focal lengths of objective and eyepiece respectively.

Length of the telescope (L) = (fo + ue)

where, ue = distance of object from the eyepiece.

(ii) When final image is formed at infinity, then M = fo/fe

Length of the telescope (L) = fo + fe

For large magnifying power of a telescope fo should be large and feshould be small.

For large magnifying power of a microscope; fo < fe should be small.


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