In this section you will learn:


the relationship between the aperture and resolving power of an optical instrument,


the similarities and differences between optical and electron microscopes, and


and the basic working principle of a transmission electron microscope.


Different tools were invented to help mankind in resolving the details of tiny objects. Magnifying glass was the first tool invented by making use of simple optics principle. Later, sophisticated optical microscope was developed to increase the resolution even higher, up to 200 times greater than that of the magnifying glass. However, the story does not end here. The desire to see further drove the invention of electron microscope which finally reached an insurmountable level of resolution of around 2 million times better than that of the human eye! This level is so high that even individual atoms and how they are arranged in a solid can be pictured with great details. These current imaging technologies make use of the extraordinary wave properties of electrons. In this section, we will explore the basic principle of a transmission electron microscope and see how electron wave can be used for exceedingly high resolution imaging.

Our eyes have a certain ability to distinguish objects that are close together. Consider a boy looking at two ants which are separated by a small distance a. When his eye is at a distance L from the ants (Fig. 2a), he sees the ants separated by an angle

q  =   a

This angle is called angular separation. The angular separation q decreases as the boy move away from the ants. At sufficiently large distances L, q will become so small that the boy can no longer distinguish two ants with his bare eyes (Fig. 2b). The angular resolution or resolving power of an imaging instrument is the smallest angular separation that the instrument can resolve. A smaller value of the angular resolution means that the instrument can resolve finer details. In order words, the instrument has a higher resolving power.

What determines the angular resolution of an optical instrument? Advanced optics theory shows that diffraction will limit the angular resolution of an optical instrument, and the theoretical angular resolution is given by Rayleigh's criterion:

angular resolution  =   1.22l

where l is the wavelength of light and D is the aperture diameter of the instrument. For example, the pupil of your eye has a diameter of about 5 mm. Taking the average wavelength of light to be 550 nm,

angular resolution  =   1.22 × 550 × 10-9    0.000134 radian

This should be taken as the ideal value only. Owing to various defects in our eyes, the actual value of the angular resolution may be much larger than this. An optical microscope certainly has a better angular resolution than our eyes and can therefore measure much smaller angular separation. In the following animation, you can vary the aperture diameter of an optical instrument to see if it agrees with Rayleigh's criterion:

Animation: Rayleigh's criterion

In Activity 1, you have a chance to estimate the angular resolution of your eyes! In Activity 2, you will do an interesting experiment on Rayleigh's criterion using laser beams.

What makes electron microscopes so powerful? The secret is that electron wave can have very small "wavelengths". Hence according to Rayleigh's criterion, electron wave can be used to resolve very small angular separations. This is why electron microscopes have extremely high resolving powers. In fact, the "wavelength" l of an electron wave, known as the de Broglie wavelength, is related to the momentum mv of the electron by

l  =   h

where h = 6.63 × 10-34 J s is called the Planck constant. Electrons can be easily accelerated to high velocities by electric fields. Take v = 3 × 106 ms-1 (i.e., 1% the speed of light) for example,

l  =   h  =   6.63 × 10-34  =  2.43 × 10-10 m
 mv  9.11 × 10-31 × 3 × 106

This is more than two thousand times smaller than the wavelength of light! The extremely small de Broglie wavelengths make it possible for us to probe into atomic structures using electrons. This is the basic principle of electron microscopy. You will go through a more detailed comparison between optical microscopes and electron microscopes in Activity 3.

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