Propagation of light: rays versus wave fronts; geometrical and physical optics

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2 Propagatio of light: rays versus wave frots; geometrical ad physical optics A ray is a imagiary lie alog the directio of propagatio of the light wave: this lie is perpedicular to the wave frot If descriptio i terms of rays is eough, it is geometrical optics. Physical optics deals with waves; it describes iterferece ad diffractio.

3 Propagatio of light: reflectio ad refractio θ icidet = θ reflected Specular ad diffuse reflectio The icidet, reflected ad refracted rays as well as the ormal to the surface all lie i the same plae! It this plae which is always draw.

4 Propagatio of light: reflectio ad refractio idex of refractio = c/ v = KKmag K

5 The electromagetic wave i the medium c 1 1 = v = εμ εμ = c/ v = KK K v = c/ mag idex of refractio K depeds very strogly o frequecy: idex of refractio of water i visible light is 1.8, while i a steady electric field (i.e., whe f=0) K=80! K mag is usually close to 1, but i ferrites K mag =10000

6 Propagatio of light: reflectio ad refractio; idex of refractio; Sell s law siθ siθ icidet refracted siθ = refracted icidet = siθ icidet icidet refracted refracted Reversibility of the icidet ad refracted rays siθ = siθ icidet icidet refracted refracted

7 Reflectio ad refractio; idex of refractio; Sell s law. Image of a object i a optically more dese medium = = icidet water refracted air water > air siθ = siθ water water air air

8 Refractio; idex of refractio; wave legths of icidet ad refracted waves air = f = c/ λ = v/ λ air material frequecy is the same!!! λ / λ = c/ v = air material material

9 Example 33.2: idex of refractio i the eye f = c/ λ = v/ λ air material frequecy is the same!!! λ / λ = c/ v = air material material air = red lie of helium eo laser λ λ air eye = = m ( m 10 m) = 474m 633 = λ / λ = = eye air eye :

10 Two typical examples of the reflected ad refracted rays

11 Total iteral reflectio (from more optically dese to less dese): icidet > refracted siθ siθ icidet critical = siθ refracted refracted icidet refracted icidet 1 1 siθcritical = = = θ critical = 41 o glass

12 Typical examples of the total iteral reflectio prisms θ = 41 o < 45 critical o Porro prism

13 Applicatios of the total iteral reflectio: fiber optics

14 Aother applicatio of the total iteral reflectio: jewelry

15 Dispersio: the depedece of the refractio idex o wavelegth

16 Polarizatio of light waves How you ca make a balloo stick to the wall? Iductio (for coductors) Polarizatio (for isulators=dielectrics)

17 Polarizatio of light waves Upolarized light; atural light is upolarized Polarizig filter

18 Polarizatio of light waves; filters

19 Polarizatio of light waves; filters; Malus s law (1809) I = I cos 2 φ max Cautio: Malus s law ca be applied oly if the icidet light is already polarized

20 Polarizatio of light waves; filters; Malus s law (1809) I = I cos 2 φ max Example 35.5 After first filter itesity I becomes I/2; after secod filter: Iiit 2 o 3I I = cos 30 = 2 8 iit

21 Polarizatio of light waves by reflectio; Bruster s law (1812); Bruster s agle Icidet ad refracted rays have two polarizatio, while the reflected oe has oly oe polarizatio, which is trasverse to the icidet plae siθ tgθ icidet icidet refracted refracted polar = refracted icidet = siθ o Bruster : θ icidet =90 -θrefracted

22 Polarizatio of light waves by reflectio; Bruster s law (1812); Bruster s agle Example 33.6 Reflectio from a water surface tgθ θ θ polar polar refracted = refracted icidet refracted = arctg = arctg1.33 = 53.1 = 36.9 o icidet o

23 Superpositio of differet polarizatio; circular polarizatio of light waves E ( x; t) = E cos( kx ωt+ ϕ ) y y y E ( x; t) = E cos( kx ωt+ ϕ ) z z z Circular polarizatio: Liear: Elliptical polarizatio: E E = E π ϕ = ϕ m 2 E π ϕ = ϕ m 2 y z y z y z y z Attetio: quarter of a cycle meas ϕ = ϕ E π m 2 E y z y z

24 Huyges s priciple, 1678 a wave frot may be cosidered as a source of secodary wavelets that spread out i all directios with a speed equal to the speed of wave OQ = vat AB = v t siθ siθ b v = = siθ = v a a b b b a siθ a a b b

25 Huyges s priciple, 1678 a wave frot may be cosidered as a source of secodary wavelets that spread out i all directios with a speed equal to the speed of wave Origi of diffractio

26 Fermat s priciple: the priciple of least time

27 Fermat s priciple: the priciple of least time Sell s law mi a ( a h) + l + ( h b) + ( L l) b h

28 Iterferece compare with