Lecture physics a2 interference

INTERFERENCE Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016 Vocabulary Optical path difference OPD Optical path length OPL Constructive Interference Destructive Interference Wavefront L[.]

INTERFERENCE Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016 Vocabulary Optical path difference OPD Optical path length OPL Constructive Interference Destructive Interference Wavefront Light rays 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 Fundamental Notions  Optical Path Length (OPL) between points A and B : L=nd n: refractive index of the medium d: geometrical distance between A and B B d n A 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 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 Malus’s theorem Optical path length of light rays between two wave fronts is equal L1  n1 A1 I  n2 IK  n2 KB1 A2 A1 n1 n2 L2  n1 A2 H  n1 HJ  n2 JB2 H n2 IK  n2 IJ sin r i i I K r B1 r n1 HJ  n1 IJ sin i J n1 sin i  n2 sin r B2  n2 IK  n1 HJ  L1  L2 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  Interference of two coherent waves Consider coherent waves arriving at a point M: E1  A1 cos(t  1 ) E  A cos(t  2 ) The resultant wave function is : A A2  A1 E  E1  E  A1 cos(t  1 )  A cos(t  2 ) E  A cos(t   ) A  A12  A 22  2A1A cos(1  2 ) tan   A1 sin 1  A2 sin  A1 cos1  A2 cos Intensity I  A  I1  I  I1I cos(1  2 )  1 Constructive Interference Destructive Interference   1  2 A  A12  A 22  2A1A cos  I A1  A2  2A1A cos  I  I1  I  I1I cos  Constructive Interference : cos(Δ)  1  Δ  2mπ : two waves are IN PHASE  A max  A1 A Destructive Interference : cos(Δ)  1  Δ  (2m  1)π : two waves are OUT OF PHASE  A |A1 A | A  A  A max I  I  I max |A1 A | A  A1 A (A1 A )  I  (A1 A ) ... sin 1  A2 sin  A1 cos1  A2 cos Intensity I  A  I1  I  I1I cos(1  2 )  1 Constructive Interference Destructive Interference   1  2 A  A12  A 22  2A1A cos  I A1  A2  2A1A... n2 IK  n2 KB1 A2 A1 n1 n2 L2  n1 A2 H  n1 HJ  n2 JB2 H n2 IK  n2 IJ sin r i i I K r B1 r n1 HJ  n1 IJ sin i J n1 sin i  n2 sin r B2  n2 IK  n1 HJ  L1  L2 INTERFERENCE Interference... Constructive Interference Destructive Interference Wavefront Light rays CONTENTS       Optical path length (OPL), Malus’s theorem Conditions for Interference, Constructive Interference,