COMPOUND MICROSCOPE
Compound microscope is an optical instrument which is used to obtain high
magnification.
Construction
It consists of two converging lenses:
Objective
Eye piece
Objective
The lens in front of object is called objective. Its focal length f1= fo is taken to be
very small .The objective forms a real, inverted, and magnified image of the object
placed just beyond the focus of objective.
Eye piece
The lens towards the observer's eye is called piece .Focal length of eye piece is
greater than the focal length of objective. Eye piece works as a magnifying glass.
Working
The objective is so adjusted that the object is very closed to its focus. The
objective forms a real,
inverted and magnified image of the abject beyond 2fo on the right hand side. The
eye piece is so adjusted that it forms a virtual image at the least distance of
distinct vision "d" .The final image is
highly magnified.
Magnifying power
In order to determine the magnifying power of a compound microscope ,we
consider an object oo' placed in front of objective at a distance p1. Objective
forms an inverted image II' at a distance of q1 from objective.
Magnification produced by the objective is given by:
Mo= size of image / size of object
Mo= q1/ p1--------------- (1)
Eye piece works as a magnifying glass. It further magnifies the first image formed
by objective. Magnification produced by the eye piece is given by:
Me= size of image / size of object
Me= q2/ p2
We know that the eye piece behaves as a magnifying glass therefore the final
image will be formed at least distance of distinct vision i.e at 25 cm from the eye.
Hence q2 = d
Me= d / p2--------------- (2)
Using thin lens formula for eye piece :
1/f2 = 1/q2 + 1/p2
Here f2 = fe, q2 = - d and p = p2
1/fe = 1/-d + 1/p2
1/fe = -1/d + 1/p2
Multiplying both sides by "d"
d/fe = -d/d + d/p2
d/fe = -1 + d/p2
1 + d/fe = d/p2
d/p2 = 1 + d/fe----------------(3)
Comparing equation (2) and (3)
Me = 1 + d/fe--------(4)
Total magnification is equal to the product of the magnification produced by the
objective and the eye piece.
M =Mo X Me
M = (q1/p1)(1 + d/fe)
In order to get maximum magnification, we must decrease p1 and increase q1
.Thus maximum possible
value of p1 is fo i.e p = fo and maximum possible value of q1 is the length of
microscope i.e q1 = L
Therefore the magnification produced by a compound d microscope is given by:
M = (L/fO)(1 + d/fe)