Clifford parallel - Revision history

en>Rgdboer: /* References */ Sommerville

2014-02-12T01:35:45Z

References: Sommerville

← Older revision		Revision as of 03:35, 12 February 2014
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	~~The~~ '''Fresnel–Arago laws''' are three laws which summarise some of the more important properties of [[Interference (wave propagation)\|interference]] between light of different states of [[polarization (waves)\|polarization]]. [[Augustin-Jean Fresnel]] and ~~[[François Arago]]~~, ~~both discovered~~ the ~~laws, which bear their name~~.		I'm Jeremiah and I live with my husband and our 3 children in Ennetmoos, in the south area. My hobbies are Collecting cards, Petal collecting and pressing and Squash.<br><br>Visit my homepage [http://tinyurl.com/ku6vjks http://tinyurl.com/ku6vjks]

	~~The laws~~ are ~~as follows:<ref>World of Physics; http://scienceworld.wolfram.com/physics/Fresnel-AragoLaws.html</ref>~~

	~~1. Two [[orthogonal]]~~, ~~[[Coherence (physics)\|coherent]] linearly [[polarized]] waves cannot interfere~~. <br>
	~~2. Two parallel coherent linearly polarized waves will interfere in the same way as [[Sunlight\|natural light]].~~<br>
	3. The two constituent orthogonal linearly polarized states of natural light cannot interfere to form a readily observable interference pattern, even if rotated into alignment (because they are incoherent).

	One may understand this more clearly when considering two waves, given by the form <math>\mathbf{E_1}(\mathbf{r},t)=\mathbf{E}_{01}\cos(\mathbf{k_1\cdot r}-\omega t + \epsilon_1)</math> and <math>\mathbf{E_2}(\mathbf{r},t)=\mathbf{E}_{02}\cos(\mathbf{k_2\cdot r}-\omega t + \epsilon_2)</math>, where the boldface indicates that the relevant quantity is a [[Euclidean vector\|vector]], interfering. We know that the [[intensity (physics)\|intensity]] of light goes as the electric field squared (in fact, <math>I=\epsilon v < \mathbf{E}^2 >_T)</math>, where the angled brackets denote a time average), and so we just add the fields before squaring them. Extensive algebra <ref>Which can be found in, e.g Optics, Hecht, 4th edition, pp. 386-7</ref> yields a result for the intensity of the resultant wave, namely that:
	<math>I_{12}=\mathbf{E_{01}\cdot E_{02}}\cos\delta</math> where <math>\delta</math> represents the interference term; the [[phase difference]] arising from a combined [[path length]] and initial phase-angle difference; <math>\delta=(\mathbf{k_1\cdot r - k_2 \cdot r}+\epsilon_1-\epsilon_2)</~~math>.~~

	~~At this point, substituting various correct values of <math>\delta<~~/~~math> yields laws 1 & 3 above~~.



	~~With classical wave formulation for law 1 at absorption the polarisation axis are <math>Y = sin\alpha sin(\omega t)<~~/~~math> and <math>X = cos\alpha sin(\omega t + \phi)<~~/~~math> which combine to <math>I = \sqrt{Y^2+X^2}<~~/~~math>~~. Here <math>\alpha </math> is the angle between the incoming polarization and the (orthogonal) axis of the two polarisers and <math>\phi </math> is the phase shift between both waves. According quantum mechanics the probability of absorption is <math>\int_0^{2\pi} \! I^2\,d\omega t = ... = \pi</math>, so independent of <math>\phi</math>.

	~~== References ==~~

	~~<references~~ />

	<!-- It may look as if the above is plagarised directly from the reference. However, the almost exact same text appears in Optics, 4th Edition, by Eugene Hecht (a standard textbook of undergraduate optics) and can be found on page 392, near the bottom. I do not see how to state the laws differently. -->

	~~{{DEFAULTSORT:Fresnel-Arago laws}}~~
	~~[[Category:Interference]]~~
	~~[[Category:Polarization (waves)]~~]


	~~{{optics-stub}}~~

en>Steelpillow: /* Clifford surfaces */ rm "base line" phrasing

2013-12-21T10:06:04Z

Clifford surfaces: rm "base line" phrasing

← Older revision		Revision as of 12:06, 21 December 2013
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	~~We supply a complete range~~ of ~~all~~ the ~~popular types~~ of ~~paper carrier bags from the luxury boutique style with rope handles~~ and ~~gloss or matt laminates through to~~ the ~~more cost effective twisted paper or paper tape handles~~. ~~These can be custom printed with a range of impressions from hot-foil through to high quality litho printing with minimum quantities~~ as ~~low as 250.~~<br><br>Our 100% Natural Cotton Drawstring Bag offers outstanding value for money. This environmentally friendly drawstring bag is the perfect promotional giveaway to promote your business, school, sports club or event. Dig up new resources on the affiliated encyclopedia - Click here: [http://~~www~~.~~cottonshoppers~~.co.uk/ ~~analysis~~]~~. These 100% cotton drawstring bags are printed FULL COLOUR and are available on an express service - call or email for details. Prices are based on an A6 size print~~, ~~A5 and A4 size prints also available. Further discounts available on larger quantities~~.<br><br>~~Apart from manufacturing & supplying bags~~, ~~we also trade in some othe products such as baby garments,home furnishing products etc~~. ~~You~~ may ~~also communicate with us for such products.~~ more info Cotton Shoulder ToteBag Chocolat more info Cotton Shoulder ToteBag Coral more info Cotton Shoulder ToteBag Cornflou more info Cotton Shoulder ToteBag Cranberr more info Cotton Shoulder ToteBag KellyGre more info Cotton Shoulder ToteBag Kiwi more info Cotton Shoulder ToteBag Lime Promotional Clothing, ~~Sportswear And Leisure Wear~~ (~~2366~~) ~~We provide a vast array of options for mailing bags~~ and courier bags Branded mailing bags are becoming increasingly popular, especially due to the internet retail/online shopping boom. Cotton Jute Mugs Pens Windbreaks Deckchairs Umbrellas Clothing<br><br>~~A business or company who use promotional gifts to attract their customers obviously have more exposure than~~ a ~~company that doesn"t use such tools~~. We ~~found out about~~ [~~http://www.cottonshoppers.co.uk/ consumers~~] ~~by searching~~ the ~~Internet. Whether you want to give your customers a promotional key-ring~~, ~~a promotional pen~~, a ~~personalised fridge magnet or balloon, a message bug or a promotional mug~~, we ~~have~~ the ~~right promotional tool for you! A popular product for schools and http://www~~.~~cottonshoppers~~.co.~~uk colleges and~~ for ~~corporate events~~, the ~~promotional drawstring bags are~~ the ~~perfect alternative to your standard promotional carrier bag~~. ~~Your customer will hold on to~~ this ~~and use it over and over again promoting your company brand wherever they go! Call for price Cotton Shoulder Tote Bag Black A retail outlet & require shopping bags Large Cotton Canvas Bag from~~ &~~pound;2~~.~~14 Bread Bags~~<br><br>~~Our Luxury Gift Bags range boasts rope or ribbon handle Paper Carrier Bags crafted from high quality ivory card. Clicking [http:~~//~~www~~.~~cottonshoppers.co.uk~~/ copyright] probably provides cautions you can use with your friend. Each of these thicker bags are handmade using printing machines and then expertly laminated with a gloss or matte finish. Reinforced card is ~~used to strengthen~~ the ~~top~~ and ~~bottom and Bespoke Bag options are available, allowing you to alter~~ the ~~shape, size~~ and ~~design. Kraft Paper Bags The minimum run quantity for punched handle polythene carrier bags~~ is ~~1000 and lead-time can be from as little as 7 working days from after you place your order~~. ~~Polythene carrier bags are proven great for marketing, even if it~~ is ~~a last minute decision. Laminated canvas bags - 390 x 365 x 165mm Print options Carrier Bag Wholesalers~~, ~~Manufacturers & Suppliers~~.~~cottonshoppers~~.co.uk<br>~~Part~~ of ~~Positive Media Promotions Ltd~~<br>~~www.positivepromotionalproducts.co.uk~~<br>~~Tel: 0800 0842424~~<br><~~br>In~~ the ~~event you loved this information~~ and ~~you wish~~ to ~~receive more details with regards to health insurance exchange (~~[~~http~~:~~//ceaselessprogre54.exteen.com such a good point~~]) ~~please visit the website.~~		The '''Fresnel–Arago laws''' are three laws which summarise some of the more important properties of [[Interference (wave propagation)\|interference]] between light of different states of [[polarization (waves)\|polarization]]. [[Augustin-Jean Fresnel]] and [[François Arago]], both discovered the laws, which bear their name.

			The laws are as follows:<ref>World of Physics; http://scienceworld.wolfram.com/physics/Fresnel-AragoLaws.html</ref>

			1. Two [[orthogonal]], [[Coherence (physics)\|coherent]] linearly [[polarized]] waves cannot interfere. <br>
			2. Two parallel coherent linearly polarized waves will interfere in the same way as [[Sunlight\|natural light]].<br>
			3. The two constituent orthogonal linearly polarized states of natural light cannot interfere to form a readily observable interference pattern, even if rotated into alignment (because they are incoherent).

			One may understand this more clearly when considering two waves, given by the form <math>\mathbf{E_1}(\mathbf{r},t)=\mathbf{E}_{01}\cos(\mathbf{k_1\cdot r}-\omega t + \epsilon_1)</math> and <math>\mathbf{E_2}(\mathbf{r},t)=\mathbf{E}_{02}\cos(\mathbf{k_2\cdot r}-\omega t + \epsilon_2)</math>, where the boldface indicates that the relevant quantity is a [[Euclidean vector\|vector]], interfering. We know that the [[intensity (physics)\|intensity]] of light goes as the electric field squared (in fact, <math>I=\epsilon v < \mathbf{E}^2 >_T)</math>, where the angled brackets denote a time average), and so we just add the fields before squaring them. Extensive algebra <ref>Which can be found in, e.g Optics, Hecht, 4th edition, pp. 386-7</ref> yields a result for the intensity of the resultant wave, namely that:
			<math>I_{12}=\mathbf{E_{01}\cdot E_{02}}\cos\delta</math> where <math>\delta</math> represents the interference term; the [[phase difference]] arising from a combined [[path length]] and initial phase-angle difference; <math>\delta=(\mathbf{k_1\cdot r - k_2 \cdot r}+\epsilon_1-\epsilon_2)</math>.

			At this point, substituting various correct values of <math>\delta</math> yields laws 1 & 3 above.



			With classical wave formulation for law 1 at absorption the polarisation axis are <math>Y = sin\alpha sin(\omega t)</math> and <math>X = cos\alpha sin(\omega t + \phi)</math> which combine to <math>I = \sqrt{Y^2+X^2}</math>. Here <math>\alpha </math> is the angle between the incoming polarization and the (orthogonal) axis of the two polarisers and <math>\phi </math> is the phase shift between both waves. According quantum mechanics the probability of absorption is <math>\int_0^{2\pi} \! I^2\,d\omega t = ... = \pi</math>, so independent of <math>\phi</math>.

			== References ==

			<references />

			<!-- It may look as if the above is plagarised directly from the reference. However, the almost exact same text appears in Optics, 4th Edition, by Eugene Hecht (a standard textbook of undergraduate optics) and can be found on page 392, near the bottom. I do not see how to state the laws differently. -->

			{{DEFAULTSORT:Fresnel-Arago laws}}
			[[Category:Interference]]
			[[Category:Polarization (waves)]]


			{{optics-stub}}

en>Helpful Pixie Bot: ISBNs (Build KC)

2012-05-05T22:58:59Z

ISBNs (Build KC)

New page

We supply a complete range of all the popular types of paper carrier bags from the luxury boutique style with rope handles and gloss or matt laminates through to the more cost effective twisted paper or paper tape handles. These can be custom printed with a range of impressions from hot-foil through to high quality litho printing with minimum quantities as low as 250. Our 100% Natural Cotton Drawstring Bag offers outstanding value for money. This environmentally friendly drawstring bag is the perfect promotional giveaway to promote your business, school, sports club or event. Dig up new resources on the affiliated encyclopedia - Click here: [http://www.cottonshoppers.co.uk/ analysis]. These 100% cotton drawstring bags are printed FULL COLOUR and are available on an express service - call or email for details. Prices are based on an A6 size print, A5 and A4 size prints also available. Further discounts available on larger quantities. Apart from manufacturing & supplying bags, we also trade in some othe products such as baby garments,home furnishing products etc. You may also communicate with us for such products. more info Cotton Shoulder ToteBag Chocolat more info Cotton Shoulder ToteBag Coral more info Cotton Shoulder ToteBag Cornflou more info Cotton Shoulder ToteBag Cranberr more info Cotton Shoulder ToteBag KellyGre more info Cotton Shoulder ToteBag Kiwi more info Cotton Shoulder ToteBag Lime Promotional Clothing, Sportswear And Leisure Wear (2366) We provide a vast array of options for mailing bags and courier bags Branded mailing bags are becoming increasingly popular, especially due to the internet retail/online shopping boom. Cotton Jute Mugs Pens Windbreaks Deckchairs Umbrellas Clothing A business or company who use promotional gifts to attract their customers obviously have more exposure than a company that doesn"t use such tools. We found out about [http://www.cottonshoppers.co.uk/ consumers] by searching the Internet. Whether you want to give your customers a promotional key-ring, a promotional pen, a personalised fridge magnet or balloon, a message bug or a promotional mug, we have the right promotional tool for you! A popular product for schools and http://www.cottonshoppers.co.uk colleges and for corporate events, the promotional drawstring bags are the perfect alternative to your standard promotional carrier bag. Your customer will hold on to this and use it over and over again promoting your company brand wherever they go! Call for price Cotton Shoulder Tote Bag Black A retail outlet & require shopping bags Large Cotton Canvas Bag from £2.14 Bread Bags Our Luxury Gift Bags range boasts rope or ribbon handle Paper Carrier Bags crafted from high quality ivory card. Clicking [http://www.cottonshoppers.co.uk/ copyright] probably provides cautions you can use with your friend. Each of these thicker bags are handmade using printing machines and then expertly laminated with a gloss or matte finish. Reinforced card is used to strengthen the top and bottom and Bespoke Bag options are available, allowing you to alter the shape, size and design. Kraft Paper Bags The minimum run quantity for punched handle polythene carrier bags is 1000 and lead-time can be from as little as 7 working days from after you place your order. Polythene carrier bags are proven great for marketing, even if it is a last minute decision. Laminated canvas bags - 390 x 365 x 165mm Print options Carrier Bag Wholesalers, Manufacturers & Suppliers.cottonshoppers.co.uk Part of Positive Media Promotions Ltd www.positivepromotionalproducts.co.uk Tel: 0800 0842424 In the event you loved this information and you wish to receive more details with regards to health insurance exchange ([http://ceaselessprogre54.exteen.com such a good point]) please visit the website.