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This page titled 4.5: Diffraction Gratings is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.
Since there are 10,000 lines per centimeter, each line is separated by 1/10,000 of a centimeter. Once we know the angles, we an find the distances along the screen by using simple trigonometry.
Jonathan is the Head of Revenue for Life & Annuities at Coherent, responsible for leading the Life US sales team, drive ARR, and account expansion. He is a passionate leader, family man, all about the team, positive culture oriented, and results driven executive with more than 16 years of experience. He brings together insights from insurance clients, sales, customer success, and product development. Prior to Coherent, Jonathan managed the Tier 1 Insurance team for the Americas at FIS. His team was responsible for a 45M annual quota. Additionally, his team sold actuarial software (Prophet), cloud, data management, and a host of Insurance products to US insurers.
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The large distance between the red and violet ends of the rainbow produced from the white light indicates the potential this diffraction grating has as a spectroscopic tool. The more it can spread out the wavelengths (greater dispersion), the more detail can be seen in a spectrum. This depends on the quality of the diffraction grating—it must be very precisely made in addition to having closely spaced lines.
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If the line spacing of a diffraction grating \(d\) is not precisely known, we can use a light source with a well-determined wavelength to measure it. Suppose the first-order constructive fringe of the \(H_{\beta}\) emission line of hydrogen (\(\lambda = 656.3 \, nm\)) is measured at 11.36° using a spectrometer with a diffraction grating. What is the line spacing of this grating?
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Diffraction gratings with 10,000 lines per centimeter are readily available. Suppose you have one, and you send a beam of white light through it to a screen 2.00 m away.
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A convex lens is used as simple magnifying glass. Reason: When the object is kept very close to convex lens, we get magnified and erect image.
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achromatic (comparative more achromatic, superlative most achromatic) (optics) Free from color; transmitting light without color-related distortion.
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The analysis of multi-slit interference in Interference allows us to consider what happens when the number of slits N approaches infinity. Recall that \(N - 2\) secondary maxima appear between the principal maxima. We can see there will be an infinite number of secondary maxima that appear, and an infinite number of dark fringes between them. This makes the spacing between the fringes, and therefore the width of the maxima, infinitesimally small. Furthermore, because the intensity of the secondary maxima is proportional to \(1/N^2\), it approaches zero so that the secondary maxima are no longer seen. What remains are only the principal maxima, now very bright and very narrow (Figure \(\PageIndex{1}\)).
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Where are diffraction gratings used in applications? Diffraction gratings are commonly used for spectroscopic dispersion and analysis of light. What makes them particularly useful is the fact that they form a sharper pattern than double slits do. That is, their bright fringes are narrower and brighter while their dark regions are darker. Diffraction gratings are key components of monochromators used, for example, in optical imaging of particular wavelengths from biological or medical samples. A diffraction grating can be chosen to specifically analyze a wavelength emitted by molecules in diseased cells in a biopsy sample or to help excite strategic molecules in the sample with a selected wavelength of light. Another vital use is in optical fiber technologies where fibers are designed to provide optimum performance at specific wavelengths. A range of diffraction gratings are available for selecting wavelengths for such use.
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Analyzing the interference of light passing through two slits lays out the theoretical framework of interference and gives us a historical insight into Thomas Young’s experiments. However, most modern-day applications of slit interference use not just two slits but many, approaching infinity for practical purposes. The key optical element is called a diffraction grating, an important tool in optical analysis.
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Doug leads the insurance business globally for Coherent. He has been a technology leader for the past 25+ years, and insurance technology for the past 20 (Blue Cross Blue Shield, Marsh & McLennan, Capgemini, and Global Atlantic). He thrives on helping clients deliver strategic value efficiently and effectively to make a significant impact to each client’s bottom line. In June 2021, after seeing how Coherent Spark would have transformed the businesses in his prior roles, Doug joined Coherent. He is now evangelizing Spark's capabilities across the insurance industry and thrives on seeing his clients succeed in using Spark to accelerate their business initiatives.
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In reality, the number of slits is not infinite, but it can be very large—large enough to produce the equivalent effect. A prime example is an optical element called a diffraction grating. A diffraction grating can be manufactured by carving glass with a sharp tool in a large number of precisely positioned parallel lines, with untouched regions acting like slits (Figure \(\PageIndex{2}\)). This type of grating can be photographically mass produced rather cheaply. Because there can be over 1000 lines per millimeter across the grating, when a section as small as a few millimeters is illuminated by an incoming ray, the number of illuminated slits is effectively infinite, providing for very sharp principal maxima.
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Diffraction gratings work both for transmission of light, as in Figure \(\PageIndex{3}\), and for reflection of light, as on butterfly wings and the Australian opal in Figure \(\PageIndex{4a}\). Natural diffraction gratings also occur in the feathers of certain birds such as the hummingbird. Tiny, finger-like structures in regular patterns act as reflection gratings, producing constructive interference that gives the feathers colors not solely due to their pigmentation. This is called iridescence.
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Once a value for the diffraction grating’s slit spacing \(d\) has been determined, the angles for the sharp lines can be found using the equation
Take the same simulation we used for double-slit diffraction and try increasing the number of slits from \(N = 2\) to \(N = 3, 4, 5, ...\). The primary peaks become sharper, and the secondary peaks become less and less pronounced. By the time you reach the maximum number of \(N = 20\), the system is behaving much like a diffraction grating.