Since the angular spacing \(\Delta \theta\) of interference peaks in the two slit case depends on the wavelength of the incident wave, the two slit system can be used as a crude device to distinguish between the wavelengths of different components of a non-sinusoidal wave impingent on the slits. However, if more slits are added, maintaining a uniform spacing d between slits, we obtain a more sophisticated device for distinguishing beam components. This is called a diffraction grating.

Substituting in the above expressions for \(\Delta \theta \text { and } \alpha_{\max }\) and solving for \(\Delta \lambda, \text { we get } \Delta \lambda>\lambda /(2 m n)\), where \(\lambda\) is the average of the two wavelengths and \(n = w ∕ d\) is the number of slits in the diffraction grating. Thus, the fractional difference between wavelengths which can be distinguished by a diffraction grating depends solely on the interference order m and the number of slits n in the grating:

Available in metric or inch sizes, state-of-the-art Thomson universally self-aligning linear slide bearings have been manufactured to the highest quality standards for smooth, accurate motion for the past 75 years. And when used with Thomson 60 Case® LinearRace® shafting, travel life and load capacity are significantly increased compared to conventional models.

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Whereas the angular width of the interference peaks is governed by the single slit equation, their angular positions are governed by the two slit equation. Let us assume for simplicity that \(|\theta|<1\) so that we can make the small angle approximation to the two slit equation, \(\mathrm{m} \lambda=\mathrm{d} \sin \theta \approx \mathrm{d} \theta\), and ask the following question: How different do two wavelengths differing by \(\Delta \lambda\) have to be in order that the interference peaks from the two waves not overlap? In order for the peaks to be distinguishable, they should be separated in \(\theta\) by an angle \(\Delta \theta=m \Delta \lambda / d\), which is greater than the angular width of each peak, αmax:

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From shafting and supports, to round and square rail guides, linear motion systems to pillow blocks, Thomson demonstrates how our products excel as the best solution in a wide array of industrial applications.

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How to choose between the main types of linear technologies, and how to design automation systems that deliver optimal performance using design requirements, rather than cost, as the primary consideration in selecting linear components.

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The width of the peaks is actually related to the overall width of the grating, \(w = nd\), where n is the number of slits. Thinking of this width as the dimension of a large single slit, the single slit equation, \(\mathrm{a}_{\max }=\lambda /(2 \mathrm{w})\), tells us the angular width of the peaks.

The efficiency of your linear ball bushing bearings depends largely on how well it is mounted into your machine or device. Watch this video for tips and accessories to help you properly mount your linear bearings.

After selecting shafting for your linear motion design, linear ball bushing bearings are next. An open or closed bearing will depend on the type of shafting you chose.

Advancements in load capacity, life and ease of manufacture allowed an ever-widening range of applications to benefit from nearly friction free linear guidance. Since the introduction of the square, or profile rail, linear guide in the 1970s, the design engineer has been faced with the pivotal question: round or square?

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For maximum capacity, linear bearings are oriented so the load is distributed between load bearing tracks. Watch this video to learn why this is so important to linear bearing performance, and, in turn, your machine designs.

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For most manufacturers, the financial cost of machine downtime can be significant, resulting in the loss of thousands or even millions of dollars. Small investments in routine and preventive maintenance, however, can pay off many times over.

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Thomson offers the world's largest selection of state-of-the-art linear bearings. Choose from several families of inch or metric linear bearings and accessories to meet your specific design needs, including our Super Smart Ball Bushings, which offer load capacities up to 7760 lb. When used with RoundRail linear guides, the inherent self-aligning-in-all-directions design of these linear bearings allows for ultra-smooth travel when mounted to wider-toleranced prepared surfaces. When used with Thomson 60 Case® shafting, our linear bearings last up to 50% longer than conventional bearings.

When your design requirements call for something outside of the standard Thomson offering, it’s no problem. Our experienced support team can work with you to create the optimal solution for your application. Our custom bearing options include factory installed pillow block configurations, precision balls (corrosion-resistant, stainless steel, nylon and many more), factory lubrication and special finishes.

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For applications in which heavy loads require linear motion with speed, precision and no friction, Linear Ball Bushing® Bearings provide an optimal solution.

How to choose between the main types of linear technologies, and how to design automation systems that deliver optimal performance using design requirements, rather than cost, as the primary consideration in selecting linear components.

Figures 2.17-2.19 show the intensity of the diffraction pattern as a function of position x on the display screen (see Figure \(\PageIndex{16}\):) for gratings with 2, 4, and 16 slits respectively, with the same slit spacing. Notice how the interference peaks remain in the same place but increase in sharpness as the number of slits increases.

Advancements in load capacity, life and ease of manufacture allowed an ever-widening range of applications to benefit from nearly friction free linear guidance. Since the introduction of the square, or profile rail, linear guide in the 1970s, the design engineer has been faced with the pivotal question: round or square?

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