6.2 Thin Film, Michelson Interferometer, X-Ray Diffraction

6.2 Thin Film, Michelson Interferometer, X-Ray Diffraction...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

Ask a homework question - tutors are online