A light wave is an electromagnetic wave that travels through the vacuum of outer space. Light waves are produced by vibrating electric charges. The nature of such electromagnetic waves is beyond the scope of The Physics Classroom Tutorial. For our purposes, it is sufficient to merely say that an electromagnetic wave is a transverse wave that has both an electric and a magnetic component.

It is possible to transform unpolarized light into polarized light. Polarized light waves are light waves in which the vibrations occur in a single plane. The process of transforming unpolarized light into polarized light is known as polarization. There are a variety of methods of polarizing light. The four methods discussed on this page are:

In day-to-day routine observations, many microscopists do not attempt to achieve the highest image resolution that is possible with their equipment. The resolving power of a microscope is the most important feature of the optical system and influences the ability to distinguish between fine details of a particular specimen. The primary factor in determining resolution is the objective numerical aperture, but resolution is also dependent upon the type of specimen, coherence of illumination, degree of aberration correction, and other factors such as contrast-enhancing methodology either in the optical system of the microscope or in the specimen itself.

The alignment of these molecules gives the filter a polarization axis. This polarization axis extends across the length of the filter and only allows vibrations of the electromagnetic wave that are parallel to the axis to pass through. Any vibrations that are perpendicular to the polarization axis are blocked by the filter. Thus, a Polaroid filter with its long-chain molecules aligned horizontally will have a polarization axis aligned vertically. Such a filter will block all horizontal vibrations and allow the vertical vibrations to be transmitted (see diagram above). On the other hand, a Polaroid filter with its long-chain molecules aligned vertically will have a polarization axis aligned horizontally; this filter will block all vertical vibrations and allow the horizontal vibrations to be transmitted.

Does the depth of fieldincrease or decreasewithmagnification

Polarization of light by use of a Polaroid filter is often demonstrated in a Physics class through a variety of demonstrations. Filters are used to look through and view objects. The filter does not distort the shape or dimensions of the object; it merely serves to produce a dimmer image of the object since one-half of the light is blocked as it passed through the filter. A pair of filters is often placed back to back in order to view objects looking through two filters. By slowly rotating the second filter, an orientation can be found in which all the light from an object is blocked and the object can no longer be seen when viewed through two filters. What happened? In this demonstration, the light was polarized upon passage through the first filter; perhaps only vertical vibrations were able to pass through. These vertical vibrations were then blocked by the second filter since its polarization filter is aligned in a horizontal direction. While you are unable to see the axes on the filter, you will know when the axes are aligned perpendicular to each other because with this orientation, all light is blocked. So by use of two filters, one can completely block all of the light that is incident upon the set; this will only occur if the polarization axes are rotated such that they are perpendicular to each other.

The numerical aperture of objectives increases with the magnification up to about 40x (see Tables 1 and 2), but levels off between 1.30 and 1.40 (depending upon the degree of aberration correction) for oil immersion versions. Presented in Table 2 are the calculated values for the resolution of objectives typically used in research and teaching laboratories. The point-to-point resolution at the specimen, d0, is listed in the table along with the magnified size of the image (D0) in the intermediate eyepiece plane (using green light of 550 nanometer wavelength). Also in the table, the value n represents the number of resolved pixels if they are organized in a linear array along the field diameter of 20 millimeters (20 millimeters/D0).

In the same manner, two Polaroid filters oriented with their polarization axes perpendicular to each other will block all the light. Now that's a pretty cool observation that could never be explained by a particle view of light.

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Polarization has a wealth of other applications besides their use in glare-reducing sunglasses. In industry, Polaroid filters are used to perform stress analysis tests on transparent plastics. As light passes through a plastic, each color of visible light is polarized with its own orientation. If such a plastic is placed between two polarizing plates, a colorful pattern is revealed. As the top plate is turned, the color pattern changes as new colors become blocked and the formerly blocked colors are transmitted. A common Physics demonstration involves placing a plastic protractor between two Polaroid plates and placing them on top of an overhead projector. It is known that structural stress in plastic is signified at locations where there is a large concentration of colored bands. This location of stress is usually the location where structural failure will most likely occur. Perhaps you wish that a more careful stress analysis were performed on the plastic case of the CD that you recently purchased.

Polarization can also occur by the refraction of light. Refraction occurs when a beam of light passes from one material into another material. At the surface of the two materials, the path of the beam changes its direction. The refracted beam acquires some degree of polarization. Most often, the polarization occurs in a plane perpendicular to the surface. The polarization of refracted light is often demonstrated in a Physics class using a unique crystal that serves as a double-refracting crystal. Iceland Spar, a rather rare form of the mineral calcite, refracts incident light into two different paths. The light is split into two beams upon entering the crystal. Subsequently, if an object is viewed by looking through an Iceland Spar crystal, two images will be seen. The two images are the result of the double refraction of light. Both refracted light beams are polarized - one in a direction parallel to the surface and the other in a direction perpendicular to the surface. Since these two refracted rays are polarized with a perpendicular orientation, a polarizing filter can be used to completely block one of the images. If the polarization axis of the filter is aligned perpendicular to the plane of polarized light, the light is completely blocked by the filter; meanwhile the second image is as bright as can be. And if the filter is then turned 90-degrees in either direction, the second image reappears and the first image disappears. Now that's pretty neat observation that could never be observed if light did not exhibit any wavelike behavior.

How doeslightintensity affect resolution

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The numerical aperture of a microscope objective is the measure of its ability to gather light and to resolve fine specimen detail while working at a fixed object (or specimen) distance. Image-forming light waves pass through the specimen and enter the objective in an inverted cone as illustrated in Figure 1(a). White light consists of a wide spectrum of electromagnetic waves, the period lengths of which range between 400 and 700 nanometers. As a reference, it is important to know that 1 millimeter equals 1000 micrometers and 1 micrometer equals 1000 nanometers. Light of green color has a wavelength range centered at 550 nanometers, which corresponds to 0.55 micrometers. If small objects (such as a typical stained specimen mounted on a microscope slide) are viewed through the microscope, the light incident on these minute objects is diffracted so that it deviates from the original direction (Figure 1(a)). The smaller the object, the more pronounced the diffraction of incident light rays will be. Higher values of numerical aperture permit increasingly oblique rays to enter the objective front lens, which produces a more highly resolved image and allows smaller structures to be visualized with higher clarity. Illustrated in Figure 1(a) is a simple microscope system consisting of an objective and specimen being illuminated by a collimated light beam, which would be the case if no condenser was used. Light diffracted by the specimen is presented as an inverted cone of half-angle (α), which represents the limits of light that can enter the objective. In order to increase the effective aperture and resolving power of the microscope, a condenser (Figure 1(b)) is added to generate a ray cone on the illumination side of the specimen. This enables the objective to gather light rays that are the result of larger diffraction angles, increasing the resolution of the microscope system. The sum of the aperture angles of the objective and the condenser is referred to as the working aperture. If the condenser aperture angle matches the objective, maximum resolution is obtained.

You should not try to increase the overall magnification of a microscope by using eyepieces providing a high additional magnification (for example, 16x, 20x or 25x) or other optical after-burners if the objective does not supply enough pixels at a low numerical aperture. On the other hand, you will miss subtle nuances if the objective projects very fine details onto the intermediate image, and you are using an eyepiece with a low magnification. In order to observe fine specimen detail in the optical microscope, the minute features present in the specimen must be of sufficient contrast and project an intermediate image at an angle that is somewhat larger than the angular resolving power of the human eye. As previously mentioned, the overall combined magnification (objective and eyepiece) of a microscope should be higher than 500x, but less than 1000x the objective aperture. This value is known as the range of the useful magnification.

The transverse nature of an electromagnetic wave is quite different from any other type of wave that has been discussed in The Physics Classroom Tutorial. Let's suppose that we use the customary slinky to model the behavior of an electromagnetic wave. As an electromagnetic wave traveled towards you, then you would observe the vibrations of the slinky occurring in more than one plane of vibration. This is quite different than what you might notice if you were to look along a slinky and observe a slinky wave traveling towards you. Indeed, the coils of the slinky would be vibrating back and forth as the slinky approached; yet these vibrations would occur in a single plane of space. That is, the coils of the slinky might vibrate up and down or left and right. Yet regardless of their direction of vibration, they would be moving along the same linear direction as you sighted along the slinky. If a slinky wave were an electromagnetic wave, then the vibrations of the slinky would occur in multiple planes. Unlike a usual slinky wave, the electric and magnetic vibrations of an electromagnetic wave occur in numerous planes. A light wave that is vibrating in more than one plane is referred to as unpolarized light. Light emitted by the sun, by a lamp in the classroom, or by a candle flame is unpolarized light. Such light waves are created by electric charges that vibrate in a variety of directions, thus creating an electromagnetic wave that vibrates in a variety of directions. This concept of unpolarized light is rather difficult to visualize. In general, it is helpful to picture unpolarized light as a wave that has an average of half its vibrations in a horizontal plane and half of its vibrations in a vertical plane.

A ray of white light scatters into 7 colours when it passes through a prism. The different colours of light waves experience a different degree of deviation.

One way of increasing the optical resolving power of the microscope is to use immersion liquids between the front lens of the objective and the cover slip. Most objectives in the magnification range between 60x and 100x (and higher) are designed for use with immersion oil. Good results have been obtained with oil that has a refractive index of n = 1.51, which has been precisely matched to the refractive index of glass. All reflections on the path from the object to the objective are eliminated in this way. If this trick were not used, reflection would always cause a loss of light in the cover slip or on the front lens in the case of large angles (Figure 2).

Whenyou switch to highermagnificationwhatshouldyou do to thelightintensity

The first filter will polarize the light, blocking one-half of its vibrations. The second filter will have no affect on the light. Being aligned parallel to the first filter, the second filter will let the same light waves through.

which objective lensisusedwhenviewing bacteria?

Our model of the polarization of light provides some substantial support for the wavelike nature of light. It would be extremely difficult to explain polarization phenomenon using a particle view of light. Polarization would only occur with a transverse wave. For this reason, polarization is one more reason why scientists believe that light exhibits wavelike behavior.

Resolution can be calculated according to the famous formula introduced by Ernst Abbe in the late 19th Century, and represents a measure of the image sharpness of a light microscope: Resolutionx,y = λ / 2[η • sin(α)](2) Resolutionz = 2λ / [η • sin(α)]2(3) where λ is the wavelength of light, η represents the refractive index of the imaging medium as described above, and the combined term η • sin(α) is known as the objective numerical aperture (NA). Objectives commonly used in microscopy have a numerical aperture that is less than 1.5, restricting the term α in Equations (2) and (3) to less than 70 degrees (although new high-performance objectives closely approach this limit). Therefore, the theoretical resolution limit at the shortest practical wavelength (approximately 400 nanometers) is around 150 nanometers in the lateral dimension and approaching 400 nanometers in the axial dimension when using an objective having a numerical aperture of 1.40. Thus, structures that lie closer than this distance cannot be resolved in the lateral plane using a microscope. Due to the central significance of the interrelationship between the refractive index of the imaging medium and the angular aperture of the objective, Abbe introduced the concept of numerical aperture during the course of explaining microscope resolution. The diffraction rings in the Airy disk are caused by the limiting function of the objective aperture such that the objective acts as a hole, behind which diffraction rings are found. The higher the aperture of the objective and of the condenser, the smaller d0 will be. Thus, the higher the numerical aperture of the total system, the better the resolution. One of the several equations related to the original Abbe formula that have been derived to express the relationship between numerical aperture, wavelength, and resolution is: Resolutionx,y or d0 = 1.22λ / [NAObj + NACon](4) Where λ is the imaging wavelength of light, NACon is the condenser numerical aperture, and NAObj equals the objective numerical aperture. The factor 1.22 has been taken from the calculation for the case illustrated in Figure 4 for the close approach of two Airy disks where the intensity profiles have been superimposed. If the two image points are far away from each other, they are easy to recognize as separate objects. However, when the distance between the Airy disks is increasingly reduced, a limit point is reached when the principal maximum of the second Airy disk coincides with the first minimum of the first Airy disk. The superimposed profiles display two brightness maxima that are separated by a valley. The intensity in the valley is reduced by approximately 20 percent compared with the two maxima. This is just sufficient for the human eye to see two separate points, a limit that is referred to as the Rayleigh criterion. A comparison may help to make this easier to understand. It is most unlikely that a telephone cable would be used for the electronic transfer of the delicate sound of a violin, since the bandwidth of this medium is very restricted. Much better results are obtained if high-quality microphones and amplifiers are used, the frequency range of which is identical to the human range of hearing. In music, information is contained in the medium sound frequencies; however, the fine nuances of sound are contained in the high overtones. In the microscope, the subtleties of a structure are coded into the diffracted light. If you want to see them in the imaging space behind the objective, you must make sure that they are first gathered by the objective. This becomes easier with a higher aperture angle and thus an increased numerical aperture. The numerical aperture of objectives increases with the magnification up to about 40x (see Tables 1 and 2), but levels off between 1.30 and 1.40 (depending upon the degree of aberration correction) for oil immersion versions. Presented in Table 2 are the calculated values for the resolution of objectives typically used in research and teaching laboratories. The point-to-point resolution at the specimen, d0, is listed in the table along with the magnified size of the image (D0) in the intermediate eyepiece plane (using green light of 550 nanometer wavelength). Also in the table, the value n represents the number of resolved pixels if they are organized in a linear array along the field diameter of 20 millimeters (20 millimeters/D0). Resolution for Selected Objectives Objective/NA d0(μm) D0(μm) n 0.5x / 0.15 2.2 11.2 1786 10x / 0.30 1.1 11.2 1786 20x / 0.50 0.7 13.4 1493 40x / 0.75 0.45 17.9 1117 40x / 1.30 (oil) 0.26 10.3 1942 63x / 1.40 (oil) 0.24 15.1 1325 100x / 1.30 (oil) 0.26 25.8 775 Table 2 You should not try to increase the overall magnification of a microscope by using eyepieces providing a high additional magnification (for example, 16x, 20x or 25x) or other optical after-burners if the objective does not supply enough pixels at a low numerical aperture. On the other hand, you will miss subtle nuances if the objective projects very fine details onto the intermediate image, and you are using an eyepiece with a low magnification. In order to observe fine specimen detail in the optical microscope, the minute features present in the specimen must be of sufficient contrast and project an intermediate image at an angle that is somewhat larger than the angular resolving power of the human eye. As previously mentioned, the overall combined magnification (objective and eyepiece) of a microscope should be higher than 500x, but less than 1000x the objective aperture. This value is known as the range of the useful magnification. In day-to-day routine observations, many microscopists do not attempt to achieve the highest image resolution that is possible with their equipment. The resolving power of a microscope is the most important feature of the optical system and influences the ability to distinguish between fine details of a particular specimen. The primary factor in determining resolution is the objective numerical aperture, but resolution is also dependent upon the type of specimen, coherence of illumination, degree of aberration correction, and other factors such as contrast-enhancing methodology either in the optical system of the microscope or in the specimen itself. back to top ^Practical Hints to Increase Resolving Power Modern microscope objectives permit the theoretical resolving power to be realized in practice provided that suitable specimens are being observed. However, there are several hints that can be followed to ensure success. These are listed below. Are the objective and specimen clean? A fingerprint on the front lens of an air objective may be sufficient to affect the high-contrast image reproduction of a specimen as a result of unwanted scattered light. The same caveats apply to immersion objectives that are soiled with residues of resin or emulsions (such as oil and water). In these cases, careful cleaning of the objective front lens element using a soft cloth and lens cleaner or pure ethanol should alleviate problems. Do the cover slips have the correct thickness? It is of critical importance that cover slips matched to objectives of high aperture (greater than 0.65) have the standard thickness of 170 micrometers due to the fact that cover slip thickness is taken into consideration when the objectives are designed. Therefore, if a cover slip of different thickness (less than 165 or more than 175 micrometers) is used, the quality of the optical image visibly suffers. In general, the rule of thumb for objectives having a numerical aperture of 0.7 or higher is that they can tolerate a variation of 10 micrometers, whereas lower numerical aperture objectives (0.3 to 0.7) can tolerate a higher level of deviation, usually up to 30 micrometers. Are you using the correct immersion oil? All objectives having a numerical aperture greater than 0.95 are designed for use with immersion media (usually oil of refractive index 1.515). Immersion oil is free of polychlorinated biphenyls and exhibits hardly any autofluorescence. The image will be markedly impaired if air bubbles are introduced into the immersion layer, so oil must be carefully applied to avoid bubbles. Air bubbles can be readily visualized by removing the eyepiece and examining the objective rear focal plane through the microscope observation tubes (or using a Bertrand lens). If air bubbles are observed, the objective and specimen slide should be cleaned and the oil carefully re-applied. Contributing Authors Rudi Rottenfusser - Zeiss Microscopy Consultant, 46 Landfall, Falmouth, Massachusetts, 02540. Erin E. Wilson and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310. Back to Microscopy Basics

The light waves are refracted close refractionProcess by which a wave changes speed and sometimes direction upon entering a denser or less dense medium, eg a ...

where α equals one-half of the objective's opening angle and η is the refractive index of the immersion medium used between the objective and the cover slip protecting the specimen (η = 1 for air; η = 1.51 for oil or glass). By examining Equation (1), it is apparent that the refractive index is the limiting factor in achieving numerical apertures greater than 1.0. Therefore, in order to obtain higher working numerical apertures, the refractive index of the medium between the front lens of the objective and the specimen cover slip must be increased. The highest angular aperture obtainable with a standard microscope objective would theoretically be 180 degrees, resulting in a value of 90 degrees for the half-angle used in the numerical aperture equation. The sine of 90 degrees is equal to one, which suggests that numerical aperture is limited not only by the angular aperture, but also by the imaging medium refractive index. Practically, aperture angles exceeding 70 to 80 degrees are found only in the highest-performance objectives that typically cost thousands of dollars.

When light from the various points of a specimen passes through the objective and is reconstituted as an image, the various points of the specimen appear in the image as small patterns (not points) known as Airy patterns. This phenomenon is caused by diffraction or scattering of the light as it passes through the minute parts and spaces in the specimen and the circular rear aperture of the objective. The limit up to which two small objects are still seen as separate entities is used as a measure of the resolving power of a microscope. The distance where this limit is reached is known as the effective resolution of the microscope and is denoted as d0. The resolution is a value that can be derived theoretically given the optical parameters of the instrument and the average wavelength of illumination.

The resolution of an optical microscope is defined as the smallest distance between two points on a specimen that can still be distinguished as two separate entities. Resolution is directly related to the useful magnification of the microscope and the perception limit of specimen detail, though it is a somewhat subjective value in microscopy because at high magnification, an image may appear out of focus but still be resolved to the maximum ability of the objective and assisting optical components. Due to the wave nature of light and the diffraction associated with these phenomena, the resolution of a microscope objective is determined by the angle of light waves that are able to enter the front lens and the instrument is therefore said to be diffraction limited. This limit is purely theoretical, but even a theoretically ideal objective without any imaging errors has a finite resolution.

2. Light becomes partially polarized as it reflects off nonmetallic surfaces such as glass, water, or a road surface. The polarized light consists of waves vibrate in a plane that is ____________ (parallel, perpendicular) to the reflecting surface.

Whichmagnificationrequires most illumination

A Polaroid filter is able to polarize light because of the chemical composition of the filter material. The filter can be thought of as having long-chain molecules that are aligned within the filter in the same direction. During the fabrication of the filter, the long-chain molecules are stretched across the filter so that each molecule is (as much as possible) aligned in say the vertical direction. As unpolarized light strikes the filter, the portion of the waves vibrating in the vertical direction are absorbed by the filter. The general rule is that the electromagnetic vibrations that are in a direction parallel to the alignment of the molecules are absorbed.

Why does resolutiondecreaseasmagnificationincreases

Do the cover slips have the correct thickness? It is of critical importance that cover slips matched to objectives of high aperture (greater than 0.65) have the standard thickness of 170 micrometers due to the fact that cover slip thickness is taken into consideration when the objectives are designed. Therefore, if a cover slip of different thickness (less than 165 or more than 175 micrometers) is used, the quality of the optical image visibly suffers. In general, the rule of thumb for objectives having a numerical aperture of 0.7 or higher is that they can tolerate a variation of 10 micrometers, whereas lower numerical aperture objectives (0.3 to 0.7) can tolerate a higher level of deviation, usually up to 30 micrometers.

In order to enable two objectives to be compared and to obtain a quantitative handle on resolution, the numerical aperture, or the measure of the solid angle covered by an objective is defined as:

Observers will miss fine nuances in the image if the objective projects details onto the intermediate image plane that are smaller than the resolving power of the human eye (a situation that is typical at low magnifications and high numerical apertures). The phenomenon of empty magnification will occur if an image is enlarged beyond the physical resolving power of the images. For these reasons, the useful magnification to the observer should be optimally above 500 times the numerical aperture of the objective, but not higher than 1,000 times the numerical aperture.

Are the objective and specimen clean? A fingerprint on the front lens of an air objective may be sufficient to affect the high-contrast image reproduction of a specimen as a result of unwanted scattered light. The same caveats apply to immersion objectives that are soiled with residues of resin or emulsions (such as oil and water). In these cases, careful cleaning of the objective front lens element using a soft cloth and lens cleaner or pure ethanol should alleviate problems.

Does working distanceincreasewith highermagnification

1. Suppose that light passes through two Polaroid filters whose polarization axes are parallel to each other. What would be the result?

Polarization also occurs when light is scattered while traveling through a medium. When light strikes the atoms of a material, it will often set the electrons of those atoms into vibration. The vibrating electrons then produce their own electromagnetic wave that is radiated outward in all directions. This newly generated wave strikes neighboring atoms, forcing their electrons into vibrations at the same original frequency. These vibrating electrons produce another electromagnetic wave that is once more radiated outward in all directions. This absorption and reemission of light waves causes the light to be scattered about the medium. (This process of scattering contributes to the blueness of our skies, a topic to be discussed later.) This scattered light is partially polarized. Polarization by scattering is observed as light passes through our atmosphere. The scattered light often produces a glare in the skies. Photographers know that this partial polarization of scattered light leads to photographs characterized by a washed-out sky. The problem can easily be corrected by the use of a Polaroid filter. As the filter is rotated, the partially polarized light is blocked and the glare is reduced. The photographic secret of capturing a vivid blue sky as the backdrop of a beautiful foreground lies in the physics of polarization and Polaroid filters.

The color temperature of the electromagnetic radiation ; To the extent that a hot surface emits thermal radiation ; Many other light sources, such as fluorescent ...

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Are you using the correct immersion oil? All objectives having a numerical aperture greater than 0.95 are designed for use with immersion media (usually oil of refractive index 1.515). Immersion oil is free of polychlorinated biphenyls and exhibits hardly any autofluorescence. The image will be markedly impaired if air bubbles are introduced into the immersion layer, so oil must be carefully applied to avoid bubbles. Air bubbles can be readily visualized by removing the eyepiece and examining the objective rear focal plane through the microscope observation tubes (or using a Bertrand lens). If air bubbles are observed, the objective and specimen slide should be cleaned and the oil carefully re-applied.

Erin E. Wilson and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.

where λ is the wavelength of light, η represents the refractive index of the imaging medium as described above, and the combined term η • sin(α) is known as the objective numerical aperture (NA). Objectives commonly used in microscopy have a numerical aperture that is less than 1.5, restricting the term α in Equations (2) and (3) to less than 70 degrees (although new high-performance objectives closely approach this limit). Therefore, the theoretical resolution limit at the shortest practical wavelength (approximately 400 nanometers) is around 150 nanometers in the lateral dimension and approaching 400 nanometers in the axial dimension when using an objective having a numerical aperture of 1.40. Thus, structures that lie closer than this distance cannot be resolved in the lateral plane using a microscope. Due to the central significance of the interrelationship between the refractive index of the imaging medium and the angular aperture of the objective, Abbe introduced the concept of numerical aperture during the course of explaining microscope resolution.

Modern microscope objectives permit the theoretical resolving power to be realized in practice provided that suitable specimens are being observed. However, there are several hints that can be followed to ensure success. These are listed below.

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Where λ is the imaging wavelength of light, NACon is the condenser numerical aperture, and NAObj equals the objective numerical aperture. The factor 1.22 has been taken from the calculation for the case illustrated in Figure 4 for the close approach of two Airy disks where the intensity profiles have been superimposed. If the two image points are far away from each other, they are easy to recognize as separate objects. However, when the distance between the Airy disks is increasingly reduced, a limit point is reached when the principal maximum of the second Airy disk coincides with the first minimum of the first Airy disk. The superimposed profiles display two brightness maxima that are separated by a valley. The intensity in the valley is reduced by approximately 20 percent compared with the two maxima. This is just sufficient for the human eye to see two separate points, a limit that is referred to as the Rayleigh criterion.

Unpolarized light can also undergo polarization by reflection off of nonmetallic surfaces. The extent to which polarization occurs is dependent upon the angle at which the light approaches the surface and upon the material that the surface is made of. Metallic surfaces reflect light with a variety of vibrational directions; such reflected light is unpolarized. However, nonmetallic surfaces such as asphalt roadways, snowfields and water reflect light such that there is a large concentration of vibrations in a plane parallel to the reflecting surface. A person viewing objects by means of light reflected off of nonmetallic surfaces will often perceive a glare if the extent of polarization is large. Fishermen are familiar with this glare since it prevents them from seeing fish that lie below the water. Light reflected off a lake is partially polarized in a direction parallel to the water's surface. Fishermen know that the use of glare-reducing sunglasses with the proper polarization axis allows for the blocking of this partially polarized light. By blocking the plane-polarized light, the glare is reduced and the fisherman can more easily see fish located under the water.

The diffraction rings in the Airy disk are caused by the limiting function of the objective aperture such that the objective acts as a hole, behind which diffraction rings are found. The higher the aperture of the objective and of the condenser, the smaller d0 will be. Thus, the higher the numerical aperture of the total system, the better the resolution. One of the several equations related to the original Abbe formula that have been derived to express the relationship between numerical aperture, wavelength, and resolution is:

Polarization is also used in the entertainment industry to produce and show 3-D movies. Three-dimensional movies are actually two movies being shown at the same time through two projectors. The two movies are filmed from two slightly different camera locations. Each individual movie is then projected from different sides of the audience onto a metal screen. The movies are projected through a polarizing filter. The polarizing filter used for the projector on the left may have its polarization axis aligned horizontally while the polarizing filter used for the projector on the right would have its polarization axis aligned vertically. Consequently, there are two slightly different movies being projected onto a screen. Each movie is cast by light that is polarized with an orientation perpendicular to the other movie. The audience then wears glasses that have two Polaroid filters. Each filter has a different polarization axis - one is horizontal and the other is vertical. The result of this arrangement of projectors and filters is that the left eye sees the movie that is projected from the right projector while the right eye sees the movie that is projected from the left projector. This gives the viewer a perception of depth.

A comparison may help to make this easier to understand. It is most unlikely that a telephone cable would be used for the electronic transfer of the delicate sound of a violin, since the bandwidth of this medium is very restricted. Much better results are obtained if high-quality microphones and amplifiers are used, the frequency range of which is identical to the human range of hearing. In music, information is contained in the medium sound frequencies; however, the fine nuances of sound are contained in the high overtones. In the microscope, the subtleties of a structure are coded into the diffracted light. If you want to see them in the imaging space behind the objective, you must make sure that they are first gathered by the objective. This becomes easier with a higher aperture angle and thus an increased numerical aperture.

The most common method of polarization involves the use of a Polaroid filter. Polaroid filters are made of a special material that is capable of blocking one of the two planes of vibration of an electromagnetic wave. (Remember, the notion of two planes or directions of vibration is merely a simplification that helps us to visualize the wavelike nature of the electromagnetic wave.) In this sense, a Polaroid serves as a device that filters out one-half of the vibrations upon transmission of the light through the filter. When unpolarized light is transmitted through a Polaroid filter, it emerges with one-half the intensity and with vibrations in a single plane; it emerges as polarized light.

The relationship betweenmagnificationand brightnessis

3. Consider the three pairs of sunglasses below. Identify the pair of glasses is capable of eliminating the glare resulting from sunlight reflecting off the calm waters of a lake? _________ Explain. (The polarization axes are shown by the straight lines.)

Opaque specimens are typically illuminated from above (with reflected light), using orientations ranging from on-axis (parallel to the microscope optics) to ...

It is important, first of all, to know that the objective and tube lens do not image a point in the object (for example, a minute hole in a metal foil) as a bright disk with sharply defined edges, but as a slightly blurred spot surrounded by diffraction rings, called Airy disks (see Figure 3(a)). Three-dimensional representations of the diffraction pattern near the intermediate image plane are known as the point-spread function (Figure 3(b)). An Airy disk is the region enclosed by the first minimum of the airy pattern and contains approximately 84 percent of the luminous energy, as depicted in Figure 3(c). The point-spread function is a three-dimensional representation of the Airy disk.

Referring to the above question, the glare is the result of a large concentration of light aligned parallel to the water surface. To block such plane-polarized light, a filter with a vertically aligned polarization axis must be used.

The useful numerical aperture of the objective and therefore the resolving power would be reduced by the reflection described above. The numerical aperture of an objective is also dependent, to a certain degree, upon the amount of correction for optical aberration. Highly corrected objectives tend to have much larger numerical apertures for the respective magnification as illustrated in Table 1.

A picket-fence analogy is often used to explain how this dual-filter demonstration works. A picket fence can act as a polarizer by transforming an unpolarized wave in a rope into a wave that vibrates in a single plane. The spaces between the pickets of the fence will allow vibrations that are parallel to the spacings to pass through while blocking any vibrations that are perpendicular to the spacings. Obviously, a vertical vibration would not have the room to make it through a horizontal spacing. If two picket fences are oriented such that the pickets are both aligned vertically, then vertical vibrations will pass through both fences. On the other hand, if the pickets of the second fence are aligned horizontally, then the vertical vibrations that pass through the first fence will be blocked by the second fence. This is depicted in the diagram below.