### Magnification Of Microscopes

Microscope Resolution
The most important part of the microscope is the objective, which
must produce a clear image, not just a magnified one. Thus resolution
is extremely important. Resolution is the ability of a lens
to separate or distinguish between small objects that are close together.
Much of the optical theory underlying microscope design
was developed by the German physicist Ernst Abbé in the 1870s.
The minimum distance (d) between two objects that reveals them
as separate entities is given by the Abbé equation, in which
lambda () is the wavelength of light used to illuminate the specimen
and n sin  is the numerical aperture (NA).

The preceding equation indicates that a major factor in resolution
is the wavelength of light used. The wavelength must be
shorter than the distance between two objects or they will not be
seen clearly. Thus the greatest resolution is obtained with light of
the shortest wavelength, light at the blue end of the visible spectrum
(in the range of 450 to 500 nm).

The numerical aperture (n sin ) is more difficult to understand.
Theta is defined as 1
2 the angle of the cone of light entering
an objective.  Light that strikes the microorganism
after passing through a condenser is cone-shaped.
When this cone has a narrow angle and tapers to a sharp point,
it does not spread out much after leaving the slide and therefore
does not adequately separate images of closely packed objects.
The resolution is low. If the cone of light has a very wide angle
and spreads out rapidly after passing through a specimen,
closely packed objects appear widely separated and are resolved.
The angle of the cone of light that can enter a lens depends
on the refractive index (n) of the medium in which the
lens works, as well as upon the objective itself. The refractive
index for air is 1.00. Since sin  cannot be greater than 1 (the
maximum  is 90° and sin 90° is 1.00), no lens working in air
can have a numerical aperture greater than 1.00. The only practical
way to raise the numerical aperture above 1.00, and therefore
achieve higher resolution, is to increase the refractive index
with immersion oil, a colorless liquid with the same
refractive index as glass.  If air is replaced with immersion
oil, many light rays that did not enter the objective due
to reflection and refraction at the surfaces of the objective lens
and slide will now do so . An increase in numerical
aperture and resolution results.
r and its working distance smaller.