MAGNIFYING GLASS OR SIMPLE MICROSCOPE
 
 
 
The apparent size of an object depends upon its visual angle subtended on the eye . The greater is the visual angle ,the larger is the apparent size of the object. In order to increase the visual angle ,the distance between the object and eye must be smaller but normal human eye can not see clearly an object if it is closer than the least distance of distinct vision i.e at 25cm or 250 mm.
In a number of cases one wishes to see the details of smaller object like a watch maker, finger print expert and writing expert etc. For this purpose a convex lens of short focal length is used to see the details of an object with in 25 cm. Such a lens is called magnifying glass or simple microscope .A magnifying glass forms an image at the least distance of distinct vision i.e 25cm from the eye and the object looks like a big sized object.
Magnifying power of magnifying glass
By definition magnifying power or angular magnification of magnifying glass is the ratio of visual angle subtended by the image seen through a magnifying glass to visual angle subtended by the object when placed at the least distance of distinct vision ,when see through the naked eye.
M = b/a ---------(1)
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since 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-----
OR
tana = AB/d---------(a)
In right angled triangle DOPE:
tanb = OP/PE-----
tanb = OP/p-------(b)-----
Since OP = AB = height of object
tanb = 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 formula
Here P = + p, q = - d and f = + f
1/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)
This expression indicates that for high magnification, focal length of magnifying glass should be small.
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