Basic Waves and Optics

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Lasers ad appliatios APPENDIX Basi Waves ad Optis. Eletromageti Waves The eletromageti wave osists of osillatig eletri ( E ) ad mageti ( B ) fields.

A eletromageti wave has a eletri field E ad a mageti field B travellig alog the positive x-axis ad depeds o x ad t: E E si( kx ω ) ad B B si( kx ω ).

Eergy flow The so-alled Poytig s vetor, the rate at whih eergy is trasported is give by S E B µ The itesity (I) of a wave [W/m ] is writte by E E I E RMS, where E

1 Lasers ad appliatios APPENDIX Basi Waves ad Optis. Eletromageti Waves The eletromageti wave osists of osillatig eletri ( E ) ad mageti ( B ) fields. The eletromageti spetrum is formed by the various possible frequeies (ωπf) of the eletromageti waves. A eletromageti wave has a eletri field E ad a mageti field B travellig alog the positive x-axis ad depeds o x ad t: E E si( kx ω ) ad B B si( kx ω ). t t The speed of a eletromageti wave i vauum a be writte as E B fλ µ ε. Eergy flow The so-alled Poytig s vetor, the rate at whih eergy is trasported is give by S E B µ The itesity (I) of a wave [W/m ] is writte by E E I E RMS, where E RMS µ µ The itesity of a wave at distae r from a poit soure is give by P I 4π r 3. Radiatio pressure A eletromageti wave that hits a surfae (area A), exerts a fore (F) ad a pressure o the surfae aordig to IA F (Total absorptio) If the radiatio is totally refleted we have IA F (Total refletio bakwards) The orrespodig radiatio pressures will the be

I p ad I p respetively 4. Polarizatio The eletromageti waves are polarized if their filed vetors are all i a sigle plae.

A polarizatio sheet, a Polaroid, a make upolarized light beome polarized, with the itesity I I Malu s law: If the origial light is polarized liearly, the

Polarizatio by refletio, Brewster agle p ta p A refleted wave will be fully polarized with its E-vetors perpediular to the plae of iidee if it hits the

2 I p ad I p respetively 4. Polarizatio The eletromageti waves are polarized if their filed vetors are all i a sigle plae. Light waves from ordiary soures are ot polarized; that is, they are upolarized or radomly polarized. A polarizatio sheet, a Polaroid, a make upolarized light beome polarized, with the itesity I I Malu s law: If the origial light is polarized liearly, the trasmitted light through a Polaroid tilted a agle betwee the polarizatio diretio of the iomig beam ad the polarizatio diretio of the Polaroid, we have I I os Polarizatio by refletio, Brewster agle p ta p A refleted wave will be fully polarized with its E-vetors perpediular to the plae of iidee if it hits the boudary at the Brewster agle, p. 5. Geometrial Optis Sell s law: The refrative idex,, for a material, is defied as the fator with υ whih the speed of light i vauum is redued, whe eterig the material. This auses the light to hage diretio aordig to Sell s law. si si

Total iteral refletio, ritial agle : si Example. Let the agle of iidee be withi the fiber at refletio agaist the matle. Determie the ruial agle for total refletio. Let,53 ad,8.

3 Total iteral refletio, ritial agle : si Example. Let the agle of iidee be withi the fiber at refletio agaist the matle. Determie the ruial agle for total refletio. Let,53 ad,8. Solutio Sells law with the agle of refratio β 9 o gives:,53 si,8 si 9 o si, ,9 o 6. Fresel formulae for refletio ad trasmissio Here we have split the eletromageti field ito two ompoets, E ad E Ι Ι. The oeffiiets desribig the refleted ad trasmitted parts a be see i the piture to the right. R r // gives the oeffiiet of refletio. Example ta(5 3) At a agle of iidee i 5 o ad refrative agle of p 3 o we have R // ta(5 + 3) si(5 3) The ormal ompoet has the oeffiiet R %. The rest of the light is the si(5 + 3) trasmitted; T T // + T 87,6%. 7. Les equatios Gaussia les equatio,4% + a b f

Newto les equatio xy f, where x f - a ad y f -

reprodutio of a objet via light ad if the image

If the image requires the visual system of a

Spherial mirror equatio + a b f r, where r is

4 Newto les equatio xy f, where x f - a ad y f - b Real ad virtual images A image a be see as a reprodutio of a objet via light ad if the image a be formed o a surfae, it is a real image. If the image requires the visual system of a observer, it is a virtual image. 8. Spherial mirror equatio + a b f r, where r is the radius of a spherial mirror 9. Spherial refratig surfaes + a b R

. Thi leses + a b f r r. Magifiatio The lateral magifiatio by a thi les or spherial mirror is m b a The magitude of m is give by m H h, where H is the height of the image ad h of the objet.

5 . Thi leses + a b f r r. Magifiatio The lateral magifiatio by a thi les or spherial mirror is m b a The magitude of m is give by m H h, where H is the height of the image ad h of the objet.. Optial istrumets A simple magifyig les produes a agular magifiatio give by 5m m γ f f γ 5 m is the distae for lear seeig A ompoud mirosope produes a total magifiatio M give by s γ M mm f obj f eye, where s is the tube legth, ad f obj ad f eye are the foal widths of the objetive ad eyepiee. A refratig telesope produes a agular magifiatio m of m f f obj eye

6 3. Huyges priiple All poits of a wavefrot serve as a poit soures for seodary wavelets. 4. Wavelegth ad refrative idex The wavelegth λ of a wave i a medium with refrative idex is related to the wavelegth i vauum λ by λ λ 5. Iterferee Youg s double slit experimet d si mλ Maxima for m,,, 3, Coheree It two waves at a poit will iterfere, they have to be oheret, i.e. their phase differee has to be ostat i time. The double slit itesity φ π d I 4I os, where φ si λ Iterferee i thi films

Diffratio Sigle-slit diffratio Diffratio Miima ours whe a si mλ, m,, 3, Sigle slit itesity si α π a I I where

7 Optial path differee + phase differee Coditio for maximum ( λ / ) mλ d os β + If ormal iidee ( ), we have: d (m-/)λ, m,,, 6. Diffratio Sigle-slit diffratio Diffratio Miima ours whe a si mλ, m,, 3, Sigle slit itesity si α π a I I where α si ad I is the itesity at the patter etre α λ Rayleigh s riterio First maximum for irular apertures with diameter D λ. D Diffratio gratigs Maxima our whe λ d si ad,, 3,.. is the order, d is the slit width

8 λ Resolvig power R λ d Dispersio dλ d os N, where N is the total umber of grooves Liks:

Physics 3 (PHYF144) Chap 8: The Nature of Light and the Laws of Geometric Optics - 1

Physics 3 (PHYF144) Chap 8: The Nature of Light and the Laws of Geometric Optics - 1 Physis 3 (PHYF44) Chap 8: The Nature of Light ad the Laws of Geometri Optis - 8. The ature of light Before 0 th etury, there were two theories light was osidered to be a stream of partiles emitted by a