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Unformatted text preview: Interference effects 6.1 Interference and Diffraction II. rec ombi ned Thin film interference Michelson Interferometer Xray D iffraction Coherent li ght Interference effec ts phas e shifted Thin film interference Phase shift due to reflection phas e shift p phas e shift 0 n 1 n 2 n1 n > n 1 2 n 2 • In thin film interference the phase differenc e is due to refl ection at either side of a thin film of transparent m aterial. • The phase difference is due to two factors: – Path difference through the film (corrected for the change in speed of light in the m ateri al) – Phase shift at the interface n < n 1 2 • When a wave is reflected in going from a medium with a lower refractive index to a higher refractive index the phase is shifted by p. • When a wave is reflected in going from a medium with a higher refractive index to a lower refractive index, the phase is not shifted. Interference due to thin film reflection (e.g. film in air) Beams 1 a nd 2 ref lec ted of f the front and bac k surfac es of a thi n fi lm combi ne to sho w i nterference effec ts. • A net phas e shift dif ference of p due to reflec tion • Beam 2 has a phas e shift due to pat h difference Conditions for constructive and destructive interference (film in air) Constructive interference 1 l 2d = ( m + ) 2 n
Destructive interference l /n is the speed of li ght i n the me dia with ref rac tive index n. The conditio n invo lves the ha lf inte ger wa vele ngth bec ause of the phas e shift due to reflec tion 2d = m n l The conditio n invo lves i nte ger wa ve lengths bec ause of the phas e shift of p As d> 0 , there is des tructive interference due to the phas e shift Phas e shift p Phas e shift 0 1 Soap film Exam ple 37.4 A rec tangular loo p of wire 20 c m square is dippe d i nto a soap solution an then he ld vertica lly, producing a soap film whos e thicknes s varies li nearly from es sentially zero at the to p to 1.0 μm a t the bot to m. If the fi lm is i llumi nated with 650 nm light ho w ma ny bright bands wi ll a ppear? Soap film interference pattern Blac k film Antireflective Coating no coating Antiref lec tive coatings are used to reduce reflec tions at the airglas s interfac e. Antireflective Coating Antiref lec tive coatings consists of a thi n layer of material wi th a refrac tive index in bet wee n that of air and glas s. Des tructive interf erence bet wee n light ref lec ted a t the two surfac es reduces the intensity of ref lec ted light. The phas e shift is p at bot h s urfac es. Theref ore no phas e shift difference Condition for des tructive i nterference. d antiref lec tive coating 1 l 2d = ( m + ) 2 n 2 n =1.00 1 < n < n 3 2 Question An antireflective coating of MgF (n=1.38) is used on a glass surface to 2 reduce reflections. Find the minimum thickness of the coating that can be used for green light (l=550 nm). Compact discs Digita l i nformatio n stored on pits i n trac ks. Spac ing bet ween trac ks 1.6m m 2 optical compact discs CD hi gh reflec tance lo w ref lec tance Question A cd is m ade out of a plastic with a refractive index of 1.55. If the cd is scanned with a laser with a wavel ength of 780 nm how high should the pits on the surface be for destructive interference. d ref lec ted li ght Coding of i nformatio n read o ut by a las er bea m. Ref lec tion from trac ks is modula ted by des tructi ve i nterference. Michelson Interferometer . Question A Michelson interferom et er uses a hydrogen em ission line at 486.1 nm. As you m ove one m irror, 530 bright fringes pass a fi xed point in the viewer. How far did the m irror m ove? d mov ing the mirror by a distance d produces fringe shifts, from bri ght to dark to bri ght. The no. of fringe shifts, m is rela ted to the c hange i n the path le ngth. 2d = m l Interference pattern Xray diffraction • Xray diffraction uses xrays to scatter from atom s in a crystal. • The crystal acts as a 3dim ensi onal grating. • The pattern of spots in the diffracted beam contains inform ation about the 3dim ensional structure of at om s in the crystal. NaCl Crystal – an ordered array of atom s 0.56 n 3 Diffraction of xrays from a crystal. Each atom acts as a wave source. Xray diffraction pattern of NaCl Fig. 2711, p.883 Bragg condition Question An xray sourc e with a wavel ength of 0.154 nm passes through a NaCl crystal and is shows a first order diffraction peak at an angle of 15o away from the central m axim um . W hat is the spacing of the cryst al plane responsibl e for the diffraction? Xrays are scattered from planes of ato ms in a crystal lattice spac ed a distance d a part. The conditio n for ref lec tion is the conditio n for constructive i nterference of x rays scattered from different pla nes ( pat hlength diffference =ml ) 2d sin = ml q
Note the difference in the def ini tion of θ DNA structure determ ined by xray diffraction Xray diffraction pattern from a crystalline fiber of DNA. W atson And Crick used this data to deduce the structure of the DNA molecule 4 ...
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