Until now, we assumed that slits act as point sources of light.
Rays 3 and 4 in Figure 27.
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Note that the central bright fringe is twice as wide as the weaker maxima.
Condition for destructive interference in thin films.
The conditions are also valid if different media are above and below the film and if both have n less than or larger than that of the film.
Let us consider a common situation, that of light passing through a narrow opening modeled as a slit and projected onto a screen.
Determine the minimum film thickness that produces the least reflection at a wavelength of 550 nm, which is the center of the visible spectrum.
Both causes must be considered when determining which type of interference occurs.
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In reality, it is another interference pattern.
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The general features of the intensity distribution are shown in Figure 27.
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This camera lens has several coatings (of different thicknesses) that minimize reflection of light waves having wavelengths near the center of the visible spectrum.
The diffraction pattern that appears on a screen when light passes through a narrow vertical slit.
Consider waves 1 and 3, which originate at the bottom and center of the slit, respectively.
Interference in a Soap Film.
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In this section, we shall determine how their finite widths are the basis for understanding the nature of the Fraunhofer diffraction pattern produced by a single slit.
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The sound is then reflected from walls, floor, and ceiling, further distributing the sound throughout the room.
As a result, a wedge of air exists between the slides.
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Sound waves have wavelengths larger than the slit width, so sound is effectively diffracted by the opening and spread throughout the room.
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What happens to the diffraction pattern?
The result is the enhancement of the transmission of light through the lenses.
From the triangle in Figure 27.
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In contrast, from the viewpoint of geometric optics, the center of the pattern would be completely screened by the penny, and so an approach that does not include the wave nature of light would not predict a central bright spot.
If the media above and below the film both have index of refraction larger than that of the film or if both indices are smaller, use Equation 27.
We might expect that the light passing through one such small opening would simply result in a broad region of light on a screen due to the spreading of the light as it passes through the opening.
The analysis of these effects is similar to that of the reflected light.
In a laboratory accident, you spill two liquids onto water, neither of which mixes with the water.
The Fresnel pattern is more difficult to analyze, so we shall restrict our discussion to Fraunhofer diffraction.
An interference pattern results when monochromatic light is incident on the wedge.
Where Are the Dark Fringes?
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Thus, the midpoint is a region of constructive interference and a bright spot appears.
Describe the interference pattern observed for this case.
The pattern consists of a central bright region flanked by much weaker maxima alternating with dark bands.
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Reasoning The space between the slightly open door and the wall is acting as a single slit for waves.
To finalize this problem, note that this value is much greater than the width of the slit.
Glass lenses used in cameras and other optical instruments are usually coated with a transparent thin film, such as magnesium fluoride (MgF2 ), to reduce or eliminate unwanted reflection.
INTERFERENCE IN THIN FILMS.
Finalize Inspect your final results to see if they make sense physically and are of an appropriate size.
If white light is used, bands of different colors are observed at different points, corresponding to the different wavelengths of light.
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We can deduce some important features of this problem by examining waves coming from various portions of the slit as shown in the geometric model of Figure 27.
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Solution The interference pattern is that of a thin film of variable thickness surrounded by air.
Categorize Confirm that you should use the techniques for thin film interference by identifying the thin film causing the interference.
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In reality, the coating is never perfectly.
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Analyze The type of interference that occurs is determined by the phase relationship between the portion of the wave reflected at the upper surface of the film and the portion reflected at the lower surface.
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Light near the ends of the spectrum is reflected from the coating.
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According to Equation 27.
Hence, we find that.
Find the positions of the first dark fringes and the width of the central bright fringe.
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The positive and negative signs correspond to the dark fringes on either side of the central bright fringe.
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The surrounding medium may have a refractive index less than or greater than that of the film.
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Light wavelengths are much smaller than the slit width, so virtually no diffraction for the light occurs.
In this model, the pattern on the screen is called a Fraunhofer diffraction pattern.
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The preceding conditions for constructive and destructive interference are valid when the medium above the top surface of the film is the same as the medium below the bottom surface.
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They both form thin films on the water surface.
This situation can also be achieved experimentally by using a converging lens to focus the parallel rays on a nearby screen.
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From the same choices, what happens to the central bright fringe when the wavelength of the light is made half as great?
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What accounts for the difference?
The positions of two minima on each side of the central maximum are labeled.
Yet you cannot see what is happening in the hallway.
Hence, the pattern is a series of alternating bright and dark parallel bands.
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This situation is shown in the soap film in Figure 27.
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The coating on the lens is designed with a thickness such that light near the center of the visible spectrum experiences little reflection.
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We describe here the diffraction pattern seen on a screen when a single slit is illuminated.
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Keep in mind, however, that Equation 27.
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Each portion of the slit acts as a point source of waves.
Interference in a vertical film of variable thickness.
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Solution The reflected light is a minimum when rays 1 and 2 in Figure 27.
According to Huygens's principle, each portion of the slit acts as a source of waves.
One microscope slide is placed on top of another with their left edges in contact and a human hair under the right edge of the upper slide.
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