FresnelLens price

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:

Fresnel lenses, characterized by their concentric grooves, find applications in computer-controlled systems, traffic lights, and scenarios requiring light beam manipulation. These lenses play a crucial role in light-gathering applications, including condenser systems, emitter/detector setups, magnifiers, and projection lenses.

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While Fresnel lenses share the curvature of traditional lenses, their engraved grooves result in a trade-off between reduced thickness, mass, and imaging quality. The ability to focus light becomes challenging, and curvature accuracy may vary. However, for applications where precise imaging is not paramount, the thin profile and lightweight construction of Fresnel lenses make them a suitable choice.

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.

FresnelLens Sheet

In conclusion, Fresnel lenses showcase notable efficiency in specific applications, such as traffic lights and computer-controlled systems, due to their innovative design and optical capabilities. While trade-offs exist in imaging quality, their unique construction allows for versatility in various optical applications.

The design advantage of Fresnel lenses lies in their division into concentric annular sections. This allows for the creation of lenses with large apertures and short focal lengths, minimizing material usage compared to conventional lenses. Whether made of plastic or glass, some Fresnel lenses can even take the form of a flat sheet, especially in the case of plastic construction.

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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.

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:

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This page titled 2.6: Diffraction Gratings is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by David J. Raymond (The New Mexico Tech Press) via source content that was edited to the style and standards of the LibreTexts platform.

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.

Fresnel lenses, crafted from plastic or glass, offer distinct advantages, including thin and lightweight construction, availability in various sizes, and excellent light-gathering ability. Their ability to focus light similar to traditional optical lenses makes them beneficial in smaller-scale applications compared to many conventional lenses.

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Fresnel lenses, named after physicist Augustin Jean Fresnel, are unique optical devices consisting of concentric grooves etched into plastic or glass. Despite trade-offs in imaging quality, their thin and lightweight design, along with versatile applications, makes them noteworthy in various fields.

At Shanghai Optics, we specialize in creating custom optics, including plastic and glass Fresnel lenses, for clients in fields ranging from medicine and defense to research and industry. Do not hesitate to contact Shanghai Optics today. We’d be more than happy to discuss your projects and how best they can become a success.

Alpha Industrial Park, Tu Thon Village, Ly Thuong Kiet Commune, Yen My District, Hung Yen Province Vietnam 17721 +84 221-730-8668 rfqvn@shanghai-optics.com