Microscope Resolving Power

In the case of a telescope the smallest permissible angular separation between two distant objects at an unknown distance, determines the limit of resolution when the images appear just resolved. But, in the case of a microscope, the object is very near the objective of the microscope (just beyond the focus of the objective) and the objects subtend a large angle at the objective. The limit of resolution of a microscope is determined by the least permissible linear distance between the two objects so that the two images appear just resolved.

In fig. MN is the aperture of the objective of the microscope and A and B are two object points at a distance d apart. A’ and B’ are the corresponding Fraunhofer diffraction patterns of the two images. A’ is the position of the central maximum of B. A’ and B’ are surrounded by alternate dark and bright diffraction rings. The two images are said to be just resolved if the position of the central maximum B’ also corresponds to the first minimum of the image A’.

The path difference between the extreme rays from the point B and reaching A’ is given by

(BN + NA’) – (BM + MA’)

But NA’ = MA

∴ Path difference = BN – BM

In fig. AD is perpendicular to DM and AC is perpendicular to BN.

∴ BN – BM = (BC + CN) – (DM – DE)

But CN = AN = AM = DM

∴ Path difference = BC + DB

From the Δs ACB and ADB

BC = AB sin = d sin

and DB = AB sin = d sin

Path difference = 2d sin

If this path difference 2d sin = 1.22 λ, then, A’ corresponds to the first minimum of the image B’ and the two images appear just resolved.

∴ 2d sin = 1.22 λ



Equation (i) derived above is based on the assumption that the object points A and B are self-luminous. But actually, the objects viewed with a microscope are not self-luminous but are illuminated with light from a condenser. It is found that the resolving power depends on the mode of illumination. According to Abbe, the least distance between two just resolvable object points is given by



where λ₀ is the wavelength of light through vacuum and is the refractive index of the medium between the object and the objective. The space between the object and the objective is filled with oil (cedar wood oil) in microscopes of high resolving power. Two advantages. Firstly the loss of light by reflection at the first lens surface is decreased and secondly the resolving power of the microscope is increased. The expression sin in equation (ii) is called the numerical aperture of the objective of the microscope and is a characteristic of the particular objective used. The highest value of numerical aperture obtainable in practice is about 1.6. taking the effective wavelength of white light as 5500 Å and sin = 1.6,

where d is the linear distance between two just resolvable object points. It is clear from equation (ii), that decrease of λ₀ and increase of numerical aperture of the objective decreases the value of d and hence the resolving power of the microscope is increased.

An oil immersion objective has higher numerical aperture than an ordinary objective. The resolving power of a microscope can be considerably increased by decreasing the value of λ₀. Thus, by using ultraviolet light and quartz lenses, the resolving power of the microscope can be increased further. In this case the image is photographed. Such a microscope is called an ultra microscope.

The magnifying power of a microscope is said to be normal if the diameter of the exit pupil is equal to the diameter of the pupil of the eye. If the magnifying power is higher than the normal, it does not correspondingly help in observing better details of the object. If the magnifying power of the microscope is less than the normal, then this means that full advantage of the available resolving power of the microscope objective is not taken.

The theory of the electron microscope is given in an electron microscope, a beam of electrons emitted from or transmitted through the different parts of the object is focused by electric and magnetic fields. Electrons behave like waves the wavelength depends on the voltage through which the electron beam is accelerated. For an accelerating voltage of 10000 volts, λ₀ is of the order of 0.12 Å. This wavelength is more than thousand times smaller than the wavelength of visible light. Hence, the resolving power of an electron microscope is much higher than an ordinary microscope. However, the numerical aperture of an electron microscope is smaller than ordinary microscope.

Services: - Microscope Resolving Power Homework | Microscope Resolving Power Homework Help | Microscope Resolving Power Homework Help Services | Live Microscope Resolving Power Homework Help | Microscope Resolving Power Homework Tutors | Online Microscope Resolving Power Homework Help | Microscope Resolving Power Tutors | Online Microscope Resolving Power Tutors | Microscope Resolving Power Homework Services | Microscope Resolving Power