Compound Microscope

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Working Principle of a Compound Microscope

Optical system of a microscope includes

Objective lens
Eyepieces

During observation, specimen (object) is placed near the focal plane of the objective lens and a magnified real image of the specimen is first created near the focal plane of the eyepiece. Eyepiece then acts as a magnifier to further magnify the image. Finally a magnified, virtual, inverted image is seen by the observer.

➤ Compound Microscope forms a virtual, magnified and inverted image.

Magnification of a Microscope

In a microscope, each lens produces a magnification that multipies the height of the image (enlarges the image). It is apparent that the overall magnification, $m$ of the microscope is the product of the individual magnifications: $$ m = m_{o}m_{e} $$ where $m_{o} $ is the magnification of the objective and $m_{e} $ is the magnification of the eyepiece. Both objective and eyepiece contribute to the overall magnification.

➤ Magnification of a microscope, $\boldsymbol{m = m_{o}m_{e}} $

Resolution of a Microscope

Resolution of a microscope is its ability to clearly magnify two closeby objects. The spatial resolution of a well designed optical microscope is mainly determined by its objective lens and is given by the Rayleigh equation as follows; $$\Delta r_{0} = 0.62 \frac{\lambda }{n \sin \alpha}$$ where ($\lambda$), is the wavelength of the light source; $n$ is the refractive index of the medium between the specimen and the lens, $\alpha$ is half-angle aperature and $n \sin \alpha$ is the numerical aperature (NA) of the objective lens.

➤ Resolution of a microscope depends on $\lambda$ and $n$ for a microscope of given numeric aperature, NA.

Practical limitations of a light microscope

Use of visible light with the wavelength between 390 nm and 790 nm.
Maximum reachable aperature with the haif-angle of 70-75 degree.
Requirement to use immersion methods with water or oil to increase the refractive index.

➤ Resolution of a conventional light microscope cannot exceed 200 nm.

Electron Microscope

As the wavelength of electronic beam is much shorter than the visible light in several orders of magnitude, the resolution of a microscope using electronic beam can reach $\sim 0.3$ nm. For this reason, electron microscope build on the principles of electronic optics, has very high magnification power and can image the fine structures of objects.

Comparison of resolution

➤ Eye $\sim 0.1$ mm,
➤ Light microscope $\sim 0.2$ µm,
➤ Electron microscope $\sim 0.3$ nm.