Polarized sunglasses. Polarization

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2 Polarized sunglasses

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5 : is a propert of the wave of light that can oscillate with certain orientation; the wave ehibits polarization which has onl one possible polarization, namel the direction in which the wave is travelling. 5

6 : Consider the superposition of two plane polarized waves: ψ If εmπ, m being an integer, ψ ψ + ψ + sin ( kz ωt) ( kz ω ε ) ψ sin t + sin ( kz ωt) tanθ If ε(m+)π, m being an integer, ψ ψ + ψ + sin ( kz ωt) tanθ 6

7 Right Circularl Polarized Light: If ε(m-/)π, m being an integer, ψ ψ ψ ψ tan θ ψ + + cosωt sin ωt θ π ωt at z 0 Left Circularl Polarized Light: If ε(m+/)π, m being an integer, ψ ψ ψ + + ψ cosωt tanθ ψ sin ωt θ π + ωt at z 0 Right and left circular light can be written as, R ( z, t) [ isin( kz ωt) jcos( kz ωt) ] ( z, t) [ isin( kz ωt) + jcos( kz ωt) ] L Their superposition becomes ( z t) i sin( kz ωt), A plane polarized wave can be snthesized from two oppositel polarized circular waves. 7

8 llipticall Polarized Light: Suppose and ε(m+/)π, m being an integer. ψ sin ( kz ωt) ψ sin( kz ωt + π ) cos( kz ωt) ψ ψ + State of : P-state R-state and L-state -state Natural Light: Natural light is randoml polarized. We can mathematicall represent natural light in terms of two arbitrar, incoherent, orthogonal, linearl polarized waves of equal amplitude (i.e., waves for which the relative phase difference varies rapidl and randoml). 8

9 ample: A wave ψ has the components ψ cos(kz-ωt) and ψ - cos(kz-ωt). What is its state of polarization? ψ ψ + ψ cos kz ωt ψ tanθ ψ ( ) θ 35! 9

10 Polarizers: a device to generate polarized light out of natural one. It can also be used as an analzer to allow all -vibrations parallel to the transmission ais to pass. Malus Law: I I cos 0 θ θ When a natural light passes though an ideal polarizer, its intensit is reduced b half. 0

11 Dichorism: selective absorption of one of the two orthogonal P-state in incident natural light. wire-grid polarizer dichroic crstal Commercial Polaroid H-Sheet: It s a dichroic sheet polarizer. An ideal H-sheet would transmit 50% of the incident natural light and is designated HN-50. In practice, due to loss, the H-sheet might be labeled HN-46, HN-38, HN-3, and HN- with the number indicating the percentage of natural light transmitted through the H-sheet.

12 ample: Natural light of intensit I i is incident on three HN-46 sheets of Polaroid with their transmission aes parallel. What is the intensit of the emergent light? I I i 46%; I I 46%; I 3 I 46% I i ( 0.46) I i ample: Suppose the third Polaroid in the last question is rotated through 45. What is now the intensit transmitted? I 3 I cos 45! 46% I i ( 0.46) I i

13 Birefringence: A material which displas two different speeds of propagation in fied and orthogonal directions, and therefore displas two refractive indices, is known as birefringent. Distinction: A dichroic material absorbs one of the orthogonal P-states is dichroic while in birefringent material we usuall neglect the absorption. Atomic structure of a CaCO 3 tetrahedron. Rhombohedron of calcite. The optic ais passes smmetricall through a blunt corner where the three face angles equal 0. n e c v // n o v c Δn If If n e n Δn > 0 Δn < 0 o is called birefringence. uniaial positive uniaial negative 3

14 ample: A calcite plate is cut as shown in figure with the optic ais perpendicular to the plane of the paper. A ra of natural light, λ589.3 nm, is incident at 30 to the normal. The plane of the paper is the plane of incidence. Find the angle between the ras inside the plate. n e.4866; nsin i n nsin i n α iʹ iʹ e o e o sin iʹ e sin iʹ o.0! n o i ʹ.6584 e iʹ o 9.65! 7.55! 4

15 Various Tpes of Plane Polarizers: Glan-Air prism Nicol prism 5

16 ample: A 50 calcite prism is cut with its optic ais as shown in the figure. Sodium light is used in a spectrometer eperiment to find n o and n e. Two images of the slit are seen and minimum deviation is measured for each. Find n o and n e if the angles of minimum deviation are 7.83 and plain how ou would decide which image was formed b the o-ras and which was formed b the e-ras. When d min sin n sin When d 7.83!! ( a + d ) sin ( ) min sin n sin a min 38.99! sin! ( 50 )!! ( a + d ) sin ( ) a min! sin! ( 50 ) Since calcite is uniaial negative, therefore n e.4864 and n o

17 Scattering: The displacement of an electron oscillating harmonicall under an eternal field is q m sin ωt ω where ω 0 is the natural frequenc (resonant frequenc) of the oscillation of the bound electron. At resonant frequenc, strong absorption occurs. At non-resonant frequencies the absorption of the wave packet and its subsequent emission is known as scattering. Raleigh Scattering: 0 ω Scattering centers have dimensions smaller than the wavelength. The radiated power is inversel proportional to the fourth power of the wavelength of the incident radiation. due to scattering: 7

18 Brewster s angle Brewster's angle (also known as the polarization angle) is an angle of incidence at which light with a particular polarization is perfectl transmitted through a transparent dielectric surface, with no reflection. When unpolarized light is incident at this angle, the light that is reflected from the surface is therefore perfectl polarized. This special angle of incidence is named after the Scottish phsicist Sir David Brewster (78 868) 8

19 Brewster's angle n 90 o n With simple geometr, this condition can be epressed as i + i' 90 o where i is the angle of reflection (or incidence) and i is the angle of refraction. Using Snell s law: n sini n sini' one can calculate the incident angle i i p at which no light is reflected: Solving for i p gives n sini p n sin(90 o i p ) n cosi p " i p tan n % $ ' # & n 9

20 b Reflection: At Brewster s angle i p, r // tan ( i p i" ) tan( i p + i" ) 0 polarized perpendicular to the plane of incidence. the reflected light becomes plane pile-of-plates polarizer Brewster window Degree of polarization: P I p I p + I u ( I p + Iu ) Iu I ma I min ( I p + Iu ) + Iu I ma + I min 0

21 ample: Calculate the Brewster s angle of natural light is incident on (i) a plane air/water boundar, (ii) a plane air/glass. ample: Natural light is incident on a plane air/glass boundar. Suppose the angle of incidence is about 55 and the refractive inde of glass is.5. Calculate the degree of polarization. n R R air // sin i n I I I I r // i // r i g sin iʹ r // i // r i r r // " θ B tan $ # " θ B tan $ # iʹ 33. tan tan sin sin! ( i iʹ ) ( i + iʹ ) ( i iʹ ) ( i + iʹ ) n water n air n glass n air % " ' tan.33% $ ' 53 o & # & % " ' tan.5% $ ' 56 o & # & 4 P I p R R I p + I + u R R // // 0.997

22 Retarders: Retarders are devices that cause one orthogonal P-state component to lag behind the other on emerging from the retarders. The path difference is OPD ( n n )t e o Full wave plate: OPD Quart-wave plate: ( n n ) t mλ,,,3... m e Half-wave plate: OPD e o m o ( n n ) t m + λ,,,3... OPD e o m 4 ( n n ) t m + λ,,,3... The component // and that travels faster defines the fast ais of the plate.

23 Compensator: A device that allows a continuous adjustment of the relative phase shift, the retardance. Soleil-Babinet compensator. (Left) Zero retardation. (Right) Maimum retardation. A circular light can be changed into P- state with a quarter-wave plate. The handiness of circular light can be checked b this method. 3