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Categories: Physics. Leave a Reply Cancel reply. What's on your mind? Related Posts. Physics What is Entropy? How does a Diffraction grating work? June 25, Fabulous, what a website it is! Thiss website gives valuable daga to us, keep it up. Leave a Reply Cancel reply Your email address will not be published. Check Also. Best Telescopes for kids reviews January 18, When crest of one wave falls on the trough of other wave, the resultant amplitude will be minimum. The case in which resultant amplitude is minimum is called Destructive Interference.
Consider the figure given below. Here the first wave is up and the second wave is down. So when they add together the resultant one becomes zero. Thus in destructive interference, the sum of the wave can either be less than the original waves and or it can be zero. Here the two waves will be out of phase. Destructive Interference.
Constructive Interference results in bright bands and destructive interference results in dark bands. These are called Fringes. This formation of bright and dark bands on the screen results in forming an interference pattern. Consider the picture shown below.
The two slits present in it act as two coherent sources of light. We can see the pattern of light and dark bands here. Interference pattern.
We know that intensity of any light wave is directly proportional to the square of its amplitude. Thus the intensity for the wave is considered as KA 2. Now the resultant intensity at this point can be written as. Here the resultant intensity is maximum. When this is the case, note that they can be elongated parallel to their slow vibration direction or parallel to their fast vibration direction.
Crystals elongated parallel to the slow direction have a positive sign of elongation or are said to be length slow.
Crystals that are elongated parallel to their fast direction have a negative sign of elongation or are said to be length fast. If, one the other hand, the 1 o gray area turns yellow, it tells that subtraction has occurred, and the fast direction in the crystal is aligned with the slow direction in the compensator. The crystal is then said to be length fast. Recall that in isotropic substances preferential absorption of different wavelengths of light may occur upon passage through the crystal.
This results in light of wavelengths that are not absorbed being transmitted and combining to produce a certain color known as the absorption color observed with the analyzer not inserted. Some uniaxial crystals have more than one absorption color because the different wavelengths are absorbed to different extents depending on the direction of vibration of the light as it passes through the crystal.
When a crystal exhibits more than one absorption color it is said to have pleochroism. The relationship between the color of the crystal and the vibration direction for light is called the pleochroic formula. A uniaxial crystal that exhibits pleochroism will show this property best if the C-axis, or optic axis is parallel to the microscope stage, so that both of its principle vibration directions can be observed.
At intermediate positions the crystal will show a combination of the two colors, in this case green. This gives us another method for finding a grain oriented with its optic axis perpendicular to the microscope stage. If the mineral is pleochroic, a grain that shows no change in color on rotation of the stage is one with the optic axis oriented perpendicular to the stage. Such a grain should also give us a centered optic axis interference figure in conoscope mode.
Abnormal Anomalous Interference Colors. If a mineral has strong absorption of certain wavelengths of light, these same wavelengths will be absorbed by the crystal with the analyzer inserted, and thus the crystal may produce an abnormal or anomalous interference color, one that is not shown in the interference color chart.
For example, imagine a crystal that shows strong absorption of all wavelengths of light except green. Thus, all other wavelengths are absorbed in the crystal and the only wavelengths present that can reach the analyzer are green. The crystal will thus show a green interference color that is not affected by the other wavelengths of light, and thus this green color will not appear in the interference color chart.
Examples of questions on this material that could be asked on an exam. Tulane University. Interference Phenomena, Compensation, and Optic Sign. As you have probably noticed by now, viewing an anisotropic crystal under crossed polars analyzer inserted the crystal is extinct when either of the two privileged directions in the crystal are lined up parallel to the polarizing direction of the microscope. This is because when the privileged directions are parallel to the polarizer, the crystal does not change the polarization direction and the light will thus be vibrating perpendicular to the analyzer.
When the privileged directions are not parallel to the polarizer some light is transmitted by the analyzer and this light shows a color, called the interference color.
In this lecture we will discover what causes this interference color and how it can be used to determine some of the optical properties of the crystal. The Interference of Light Waves Polarized in the Same Plane As we discussed in the lecture on X-rays, when electromagnetic waves emerge from a substance, they can interfere with each other and either become enhanced, partially destroyed, or completely destroyed.
Waves Polarized in Perpendicular Planes If the waves are traveling on the same path, but are polarized at 90 o to each other, again the resultant wave becomes the vector sum of the two waves. Polarization of the Resultant Wave As discussed above, when the waves emerge from the crystal they will be polarized at 90 o to each other. Waves are in phase on exit at the top of the crystal. Diagram A, above In this case, the crystal is viewed at some angle off extinction.
Monochromatic light polarized in the E-W direction enters the crystal from below and is broken into two waves, each vibrating parallel to the crystals privileged directions. While in the crystal, the slow wave passes through two wavelength and the fast wave passes through 1 wavelength. After emergence from the crystal the two waves are recombined to produce a resultant wave that vibrates in the same direction as the polarized light entering from below.
This light will be extinguished by the analyzer, since it is vibrating at 90 o to the polarization direction of the analyzer. Waves are exactly out of phase upon emergence from the crystal. Diagram B, above Again, the crystal is viewed at some angle off extinction, with E-W polarized monochromatic light entering from below. With this path difference, the resultant wave that results from recombination of the two waves will be vibrating at an angle of 90 o to the direction of the entering polarized light.
Since this resultant wave is now vibrating parallel to the polarizing direction of the analyzer, it will pass through the analyzer.
This time, the resultant wave produced by recombination of the two polarized waves after leaving the crystal will have a resultant wave vibrating perpendicular to the polarizer parallel to the analyzer , and thus this light will pass the analyzer.
The color will be that of the monochromatic light that entered the crystal from below. For monochromatic light, the color transmitted will be the same as the color of the monochromatic light used to illuminate the crystal. To make things simpler, we have ignored these complications, and will assume all light leaving the crystal becomes plane polarized. Transmission by the Analyzer Monochromatic Light First we will consider only the case of a single wavelength of light monochromatic light as being incident on the crystal from below.
Imagine that the crystal is illuminated with light having a wavelength corresponding to yellow. Interference Colors Produced by Polychromatic Light Next, we consider the case that we will encounter in our studies, that is illumination with white light polychromatic light. This is plotted in the solid curve in the graph shown here. Note that violet and some blue, as well as some red wavelengths are transmitted, while less of the green yellow and orange wavelengths will not be transmitted by the analyzer.
Thus the crystal will show an interference color that is reddish violet. We call this color first order, or 1 o red. If the crystal produces a retardation of nm, the dashed curve would be obtained. This curve shows little transmission of the violet and red wavelengths, and partial to full transmission of the green, yellow, and orange wavelengths.
Thus the crystal will have a greenish interference color. The Interference Color Chart If this is done for all possible retardations and all wavelengths of light, it produces what is called an interference color chart, shown below. For crystals that produce a very high retardation, like nm, the transmission curve is the solid curve in the diagram. Again, all wavelengths are represented, but there are small gaps of wavelength where wavelengths are not transmitted.
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