A microscope is a device used to see small object much magnified at the least distance of distinct vision.
Least distance of distinct vision : The minimum distance from the eye at which the objects are clearly visible is called the least distance of distinct vision. It is denoted by D. For a normal eye it is about 25 cm.
The two types of microscopes are discussed below :
1. Simple microscope or magnifying glass,
2. Compound microscope
1. Simple microscope or Magnifying glass
The size of an object depends upon the angle subtended by the object at the eye. The angle subtended depends upon the dimensions of the object and its distance from the eye. If the object is brought nearer, the angle subtended at the eye increases and the object appears bigger and more distinct. Thus to see san object distinctly, it should be moved very near to the eye. But if it is brought near the eye at a distance less than the least distance of distinct vision, it becomes indistinct. Thus to see the object distinctly, It should be moved very close to the eye but its image should be formed at the least distance of distinct vision.
An ordinary convex lens of small focal length kept close to the eye can be used as a simple microscope or magnifying glass.
Watch makers use a single convex lens to get a magnified view of the fine parts of the watch.
Magnifying Power : The magnifying power of a simple microscope is the ratio of the angle subtended at the eye by the image as seen through the lens to the angle subtended by the object at the unaided eye, when both are placed at the least distance of distinct vision, it is denoted by M.
The mathematical formula for Magnifying Power, M is
M = D/u
= 1+D/f
Where, D is the least distance of distinct vision and is equal to v.
D being constant, the magnifying power depends upon the focal length of the lens.
Smaller the focal length, greater will be the magnifying power of the lens.Compound microscope is an optical instrument which is used to obtain high magnification.
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/ p2We 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/p21/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 MeM = (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)
