Question

derivation for simple microscope

Answer 1

Mgnifying power of magnifying glass\M = b/a ---------(1) a and b are small angles, therefore we can take:a = tan a.

and.

b = tan b-------------------(2)Consider an object OP placed at a distance "p" within the focal length of a magnifying glass such that an erect ,virtual and magnified image IQ is produced at 25 cm from the eye.In right angled triangle DABE:tana = AB/EB-----ORtana = AB/d---------(a)In right angled triangle DOPE:tanb = OP/PE-----tanb = OP/p-------(b)-----Since OP = AB = height of objecttanb = AB/p-------(c)-----Putting the values of tana and tanb in equation (2)M = (AB/p)/(AB/d)M = d/p -----------------(d)Using thin lens formulaHere P = + p, q = - d and f = + f1/f = 1/-d + 1/p

1/f = -1/d + 1/p

Multiplying both sides by "d"

d/f = -d/d + d/p

d/f = -1 + d/p

1 + d/f = d/p

or 

d/p = 1 + d/f-----(e)

Comparing equation (e) and (d)

                                       M=1=d/f

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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