Wave Optics Lecture Note

Wave Optics Optics Ray Optics -> reflection -> refraction etc. Wave-optics -> Interference -> polarization Quantum Optics -> Photoelectric effect -> Lasers etc. Interference Effect of interference:- (a) coloured appearance of soap bubbles. (b) Anti-reflection & anti-transmission coatings. (c) Used to inspect preciseness of the optical devices. Interference is the modification in the intensity when two or more waves are super-imposed. -> Occurs only when waves overlap -> As the waves surpass the point, they travel independently. -> Principle of superposition => y = y1 + y2 resultant. = Instantaneous displacement of wave 1 & 2. Huygens wave theory: each point on wavefront acts as secondary source of light. Types of interference Constructive Destructive I = 4a² amplitude Fringe with enhanced intensity. ① Constructive Interference (Maxima) Superposition of two light waves are in phase. Thus resultant intensity is greater. Path difference => Δ=nλ Phase diff. " " => ϕ=kΔ ; k= λ2π ​ ② Destructive Interference (Minima) -> I = 0 They are out of phase thus resultant intensity decreases. Path diff. " " => Δ=(n+21​ ) 2λ ​ Phase diff. " " => ϕ=kΔ Note: Here in Maxima & Minima, neither the energy is created nor destroyed, it's just redistributed. i.e the energy which has to go at minima it goes to maxima, thus interference is also defined as redistribution of energy due to superposition of the waves. Condition for stable interference pattern. Both wave coherent & phase diff. between them at any point should be constant w.r.t time. Both wave must be monochromatic & have same amplitude. If not satisfied the intensity won't be max at maxima & not zero at minima. There should be path difference & vary only with the position & not with time. Both propagated along same direction. Systematic a gradual variation of path diffs. For 0th, 1st, 2nd maxima => Delta = 0, lambda, 2lambda For 1st, 2nd, 3rd minima => Delta = lambda/2, 3lambda/2, 5*lambda/2 Methods for coherent waves of same amplitude Division of wave fronts: Source :)) S1)) (i) Source is monochromatic (ii) Light from S1 & S2 is coherent & have same amplitude. S2)) Exp: Double Slit. Division of Amplitude: R1 R0 (45 degrees angle shown) R2 (i) R0 is incident ray (ii) Silvered plate is inclined So we get 2 Ray R1 & R2 with intensity I/2. Exp: Thin film interference. The arrangement which takes care of all these conditions and which generates a steady state "Sharp interference pattern" is called "Interferometer". Stack law Light reflected from denser to rarer medium . Delta_phi = pi & Delta = lambda/2 for reflected light. . No changes for transmitted light. No changes when rarer to denser medium. Thin film interference It's a transparent film having thickness slightly above the average wavelength of light. Effects: Oil on road, soap bubbles. Antireflection coating on camera lenses & solar cell. Anti-transmission coating on invisible glasses. Thickness = t ~ lambda (wavelength of monochromatic) Refractive Index = mu Reflected rays I II (diagram with rays showing reflection and transmission) mu is less than the inner mu'. Transmitted rays I' II' Ray I & II are coherent & point A will appear bright if constructive interference takes place & will appear dark for destructive interferen. Delta = 2mut*cos(r) Delta = 2mut*cos(r) +/- lambda/2 (phase change). Reflected System Condition for maxima 2mut*cos(r) = (n + 1/2)*lambda Condition for minima 2mutcos(r) = nlambda Transmitted System Maxima 2mutcos(r) = nlambda minima 2mut*cos(r) = (n + 1/2)*lambda Note: Interference for very thin film (t << lambda) => Delta = +/- lambda/2 Constructive => 2mutcos(r) = nlambda Destructive => 2mut*cos(r) = (n + 1/2)*lambda Inter in wedge shaped film (Diagram showing a wedge film with rays, angles, and distances) inclined at alpha t -> 0 to max Delta = 2mut*cos(r + alpha) +/- lambda/2 Condition for maxima (Constructive) 2mut*cos(r + alpha) = (n + 1/2)*lambda minima (destructive) 2mutcos(r + alpha) = nlambda Fringe width & Distn between two constructive bright or dark rings. (Diagram showing fringe widths and distances) (R_n+1 - R_n) = lambda / (Fringe width) * 2mualpha