the objective lens collects a cone of light rays to create an image the condenser lens focuses a cone of light rays onto each point of the specimen RESOLUTION: the resolving power of the microscope depends on the width of the cone of illumination and therefore on both the condenser and the objective lens. It is calculated using the formula 0.61 ˛ where: ˜ = half the angular width of the cone of rays collected by the objective lens from a typical point in the central region of the specimen (since the maximum width is 180o, sin ˜ has a maximum value of 1) n = the refractive index of the medium (usually air or oil) separating the specimen from the objective and condenser lenses ˛ = the wavelength of light used (for white light a fgure of 0.53 µm is commonly assumed)
NUMERICAL APERTURE: n sin ˜ in the aperture, the greater the resolution and the equation above is called the numerical aperture brighter the image (brightness is important in of the lens and is a function of its light-fuorescence microscopy). However, this advancollecting ability. For dry lenses this cannot be tage does necessitate very short working distances more than 1, but for oil-immersion lenses it can and a very small depth of feld. be as high as 1.4. The higher the numerical specimen are accurately determined based on the distribution of these particles at the detector. However, with smaller numbers of particles, the structural details of the specimen are obscured by the statistical fluctuations in the numbers of particles detected in each region, which give the image a speckled appearance and limit its precision. The term noise describes this random variability.
Living Cells are seen Clearly in a phase-Contrast or a  Differential-interference-Contrast Microscope
There are many ways in which contrast in a specimen can be generated (Figure 9–7A). While fixing and staining a specimen can generate contrast through color, microscopists have always been challenged by the possibility that some components of the cell may be lost or distorted during specimen preparation. The only certain way to avoid the problem is to examine cells while they are alive, without fixing or freezing. For this purpose, light microscopes with special optical systems are especially useful.
In the normal bright-field microscope, light passing through a cell in culture forms the image directly. Another system, dark-field microscopy, exploits the fact that light rays can be scattered in all directions by small objects in their path. If oblique lighting from the condenser is arranged, which does not directly enter the objective, focused but unstained objects in a living cell can scatter the rays, some of which then enter the objective to create a bright image against a black background (Figure 9–7B).
When light passes through a living cell, the phase of the light wave is changed according to the cell’s refractive index: a relatively thick or dense part of the cell, such as a nucleus, slows the light passing through it. The phase of the light, consequently, is shifted relative to light that has passed through an adjacent thinner region of the cytoplasm (Figure 9–7C). The phase-contrast microscope and, in a more complex way, the differential-interference-contrast microscope increase these phase differences so that the waves are more nearly out of phase, producing amplitude differences when the sets of waves recombine, thereby creating an image of the cell’s structure. Both types of light microscopy are widely used to visualize living cells (see Movie 17.2). Figure 9–8 compares images of the same cell obtained by four kinds of light microscopy.