Interference - Tran Thi Ngoc Dung

Nội dung text: Interference - Tran Thi Ngoc Dung

1. INTERFERENCE Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016
2. Vocabulary Optical path difference OPD Optical path length OPL Constructive Interference Destructive Interference Wavefront Light rays
3. CONTENTS  Optical path length (OPL),  Malus’s theorem  Conditions for Interference, Constructive Interference, Destructive Interference.  Relationship between Phase Difference and Optical Path Difference.  Change of Phase Due to Reflection  Thin-Film Interference
4. Fundamental Notions  Optical Path Length (OPL) between 2 points A and B : L=nd n: refractive index of the medium d: geometrical distance between A and B d B n A
5. Intensity  Intensity is the wave energy per a unit area, which is perpendicular to the propagation ditection, per unit time.  Intensity is propotional to the squared amplitude of the light wave. I= kA2 [W/m2] We choose the proportional coefficient k =1 I=A2
6. Rays – Wave front ___ light rays O - - - - wave fronts Wave front is the locus of all adjacent points at which the phase of the wave is the same A ray is an imaginary line along the direction of travel of the wave. When waves travel in a homogeneous isotropic material, the rays are always straight lines perpendicular to the wave fronts
7. Malus’s theorem Optical path length of light rays between two wave fronts is equal. A 2 L1 n1 A1I n2 IK n2 KB1 L2 n1 A2 H n1HJ n2 JB2 A 1 H n2 IK n2 IJ sin r n i 1 n HJ n IJ sin i i J 1 1 I r n1 sin i n2 sin r n2 K r n2 IK n1HJ B2 L1 L2 B 1
8. INTERFERENCE  Interference is a phenomenon that occurs when there is the superposition of two or more coherent waves, resulting in bright and dark fringes.  Two waves are coherent if they have - The same frequency, - The same oscillation direction - And the constant phase difference
9. Interference of two coherent waves Consider 2 coherent waves arriving at a point M: E A cos(t ) 1 1 1 A E A cos(t )  2 2 2 A2 2 A The resultant wave function is : 1 1 E E1 E2 A1 cos(t 1) A2 cos(t 2) E Acos(t ) 2 2 A A1 A2 2A1A2 cos( 1 2) A sin A sin tan  1 1 2 2 A1 cos 1 A2 cos 2 2 Intensity I A I1 I2 2 I1I2 cos( 1 2 )
10. Constructive Interference Destructive Interference 2 2 A A1 A2 2A1A2 cos 1 2 2 2 I A1 A2 2A1A2 cos I I1 I2 2 I1I2 cos ConstructiveInterference : cos(Δ ) 1 Δ 2mπ : two waves are IN PHASE Amax A1 A2 Destructive Interference : cos(Δ ) 1 Δ (2m 1)π : two waves are OUT OF PHASE Amin |A1 A2 | Amin A Amax |A1 A2 | A A1 A2 2 2 Imin I Imax (A1 A2) I (A1 A2)
11. Relation between Phase difference and Optical Path Difference (OPD) 2 L  ConstructiveInterference : Δ 2mπ ΔL mλ λ Destructive Interference : Δ (2m 1)π ΔL (2m 1) 2
12. Lloyd’s experiment r1 M Experiment’s equipement: O Light source O Plane glass plate r2 Screen I Screen At M, there are two waves that superpose. Ray OM, and ray OIM. These waves are from the same source, they are coherent waves => Interference
13. Lloyd’s experiment (cont.) Optical Path Difference We Experiment’s expect Results L=(OI+IM)-OM =m M Bright M Dark L=(OI+IM)-OM=(m+1/2) M Dark M Bright Optical Path Difference Experiment’s Results L=(OI+/2 + IM) - OM =m +/2 M Dark = (m+1/2)  L=(OI++/2 IM)-OM=(m+1/2) +/2 M Bright = (m+1) 
14. Phase shift during reflection r M O 1 Thí nghiệm Lloyd r2 - Trình bày thí nghiệm Lloyd và Kết quả rút ra từ TN đó +/2 ―Quang lộ của tia phản xạ trên môi trường có chiết suất lớn I hơn môi trường tới dài thêm 1 lượng /2‖. MQS ― An electromagnetic wave undergoes a phase shift of 180° upon reflection from a medium that has a higher refractive index than the one in which the wave is traveling, or the optical path length of the reflected ray is longer by /2‖.
15. Thin – film interference  a phenomenon that occurs when incident light waves reflected by the upper and lower boundaries of a thin film interfere with one another.  thin layers of oil on water or the thin surface of a soap bubble. The varied colors observed when white light is incident on such films result from the interference of waves reflected from the two surfaces of the film
16. Thin film of Constant Thickness – Fringes of Equal Inclination - Extended Light source - Thin film of thickness d, of refractive index n. ΔL (2nAB 0) ( λ/2 AH) AB d / cosr;AK dtanr AH 2AKsini 2dsinrsini/cosr M 2nd 2dsinrsini ΔL λ/2 ; sini nsinr O cosr cosr 2nd 2ndsin 2 r ΔL λ/2 2ndcosr- λ/2 H cosr cosr i i i 2nd 1 sin 2 r λ/2 A K C r n d ΔL 2d n 2 sin 2i λ/2 B Rays with the same inclined angle i will focus at points on the circle in the focal plane of the convex lens. Fringes are rings on the focal plane, and called Fringes of Equal Inclination.
17. Thin film of Varied Thickness – Fringes of Equal Thickness - Extended Light source - Thin film of varying thickness, of refractive index n. O The optical path difference of the mắt two waves reflected at the lower H and upper surfaces of the thin i’ i film is : A K M 2 2 n ΔL 2d n sin i  / 2 B OPD depends on incident angles i and thickness d . Angles i and i’ are almost the same. OPD depends on thickness d. Points of equal thichness have the same intensity. Interference fringes are called Fringes of Equal Thickness .
18. Air Wedge Consists of two plane glass plates, making a small angle . (10-4 rad) The light reflected from the upper and lower air wedge boundaries interfere with one another OPD ΔL 2d λ/2 Bright Fringes : ΔL 2d λ/2 mλ λ d (m 1/2) m 1,2 bright 2 Dark Fringes : ΔL 2d λ/2 (m 1/2)λ ddark m / 2 m 0,1,2 Fringes are straight lines, parallel to the edge of the wedge. The edge of the wedge is dark fringe.
19. Air Wedge The distance between any two consecutive bright fringes or two consecutive dark fringes is called fringe spacing d d  m=2 sin m 1 m m=1 i 2i i m=0 x  i 2 Dark fringe positions O Bright fringe position xd mi m 0,1,2 i x mi m 0,1,2 b 2
20. GLASS WEDGE the wedge of glass with the small angle 10^-4rad ) The waves reflected from the upper and lower surfaces of the wedge interfere. OPD ΔL 2nd λ/2 Bright fringes : ΔL 2nd λ/2 mλ λ d (m 1/2) m 0,1,2 b 2n Dark fringes : ΔL 2nd λ/2 (m 1/2)λ d,n λ d m m 0,1,2 d 2n Fringe spacing i is the distance between any two consecutive bright fringes or two consecutive dark fringes dm 1 dm   sin i i 2ni 2n
21. Glass wedge ( Cont.)  i 2n m=2 n m=1 x m=0 i Bright Fringe Position Dark Fringe Position O x t mi m 0,1,2 i x mi m 0,1,2 s 2
22. Newton’s Rings Experiment’s equipements: A plane glase plate O’ A convex lens of a spherical surface and a plane surface R OPD ΔL 2d λ/2 Bright fringes : ΔL 2d λ/2 mλ r λ d db (m 1/2) m 1,2 +/2 O 2 Dark Fringes : ΔL 2d λ/2 (m 1/2)λ dd m / 2 m 0,1,2 Locus of points of equal thickness are on the circle of the axis OO’. Fringes are rings. The central fringe is dark. The larger is the order m, the closer are fringes.
23. Newton’s rings O’ Fringe radius Ro R r R2 (R d)2 2Rd d2 2Rd 1 r 2Rd R m m 1,2,3 Bright Bright 2 r rDark 2RdDark R m m 0,1,2,3 d +/2 O R: curvature radius of the spherical surface of the convex lens.
24. Newton fringes O’ Fringe Radius 1 s R r R m m 1,2,3 bright 2 Ro rdark R m m 0,1,2,3 r How many fringes are there: d +/2 O 1 r R m R bright 2 o R 2 m o 1/ 2 m 1,2,3 R rdark R m Ro R 2 m o m 0,1,2,3 R R: curvature of the spherical surface of the lens Ro: the radius of the plane of the convex lens.
25. Example 35.4 0.02 10 3 2 10 4(rad) 10 10 2  0.5 10 6 i 1.25mm 2 2 2 10 4 Example 35.5  0.5 10 6 i 0.94mm 2n 2 1.33 2 10 4
26. 1 OPD 2nd (m ) 2  0.550m d 99.64nm min 4n 4 1.38
27. Example 37.4 Nonreflective Coatings for Solar Cells Solar cells—devices that generate electricity when exposed to sunlight—are often coated with a transparent, thin film ofsilicon monoxide (SiO, n = 1.45) to minimize reflective losses from the surface. Suppose that a silicon solar cell (n = 3.5) is coated with a thin film of silicon monoxide for this purpose (Fig. 37.20). Determine the minimum film thickness that produces the least reflection at a wavelength of 550 nm, near the center of the visible spectrum.  550nm d 94.8nm min 4n' 4 1.45 To finalize the problem, we can investigate the losses in typical solar cells. A typical uncoated solar cell has reflective losses as high as 30%; a SiO coating can reduce this value to about 10%. This significant decrease in reflective losses increases the cell’s efficiency because less reflection means that more sunlight enters the silicon to create charge carriers in the cell. No coating can ever be made perfectly nonreflecting because the required thickness is wavelength dependent and the incident light covers a wide range of wavelengths.
28. The reflected light from a coated camera lens often has a reddish-violet appearance. Glass lenses used in cameras and other optical instruments are usually coated with a transparent thin film to reduce or eliminate unwanted reflection and enhance the transmission of light through the lenses. The camera lens has several coatings (of different thicknesses) to minimize reflection of light waves having wavelengths near the center of the visible spectrum. As a result, the little light that is reflected by the lens has a greater proportion of the far ends of the spectrum and often appears reddish-violet.