SPH3UW/SPH4UI Unit 10.2 Single Slit Diffraction Page 1 of 7. Maxima (bright fringes), occur at the centre and at

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1 SPH3UW/SPH4UI Unit 0.2 Single Slit Diffraction Page of 7 Notes Phsics Tool box ight passing through a single slit creates a diffraction pattern. The saller the slit idth, the larger the distance beteen axia (bright) and inia (dark). The longer the avelength, the greater the distance beteen axia. Minia (dark fringes), occur at sin,2,... Maxia (bright fringes), occur at the centre and at sin 2,2,... The separation relationship: of adjacent axia or inia is given b the, and the central axiu idth is 2. Resolution, or the abilit of an instruent to separate to closel spaced iages, is liited b the diffraction of light. ight passing through a single, narro slit is diffracted. This not hat geoetric optics ould predict ith parallel light traveling though the slit. The extent of the diffraction increases as narroer slits are used. But interference also occurs. When a screen is placed behind a narro slit, pattern of bright and dark lines ill appear on the screen. The central axiu (85% of the poer in the transitted bea) is behind the slit and on either side are dark regions of destructive interference then less intense light (secondar axia) and so on.

2 SPH3UW/SPH4UI Unit 0.2 Single Slit Diffraction Page 2 of 7 Even though the patter resebles Young s pattern, the spacing of the bright and dark areas is quite different. Hugens explains that the slit ill act as a ro of point sources reasonabl close to each other vibrating in phase. Each point source ould produce individual circular aves, thus producing interference patterns on the screen. First e ill look at light that passes straight through the slit. Since the light fro the point sources all start in phase and travel approxiatel the sae distance to the screen, the essentiall arrive in phase. Thus producing a bright central axiu. But hat about light diffracted donard. For exaple if e (for siplicit) assue that the Hugens light has 2 point sources. Then aves fro the top source (point ) ill travel farther than aves fro point 2. If the path difference is one avelength then the light fro the iddle point (point 6) ill travel ½ avelength farther than point 2 (thus be out of phase) and producing destructive interference. Siilarl point and point 5 ill cancel. In fact each point in the loer half of the slit ill cancel a point in the upper half of the slit. As a result the aves ill interfere destructivel causing a dark band. The first iniu ill occur hen sin or sin. What about larger angles? If the path difference beteen the top and botto is 3 2, e find that each point in the botto third of the slit interferes destructivel ith a point in the iddle third that is 2 farther fro the screen. These pairs also interfere destructivel (Note that the points fro the upper third of the slit ill arrive alost in phase ield a not so bright spot.

3 SPH3UW/SPH4UI Unit 0.2 Single Slit Diffraction Page 3 of 7 If e have a distance difference of 2, e ill have ¼ regions that ill interfere producing a totall destructive interference patter. Thus putting these together e have And sin 2 ill produce a axiu. n sin n ill produce a inia.

4 SPH3UW/SPH4UI Unit 0.2 Single Slit Diffraction Page 4 of 7 sin tan here As in the double slit, e appl geoetr is the distance fro the centre point in the diffraction pattern, and is the perpendicular distance fro the slit to the screen. Thus sin tan Note: that the idth of the central axiu is 2 and that the separation of the axia and inia is, e can rite avelength as. Resolution is the abilit to separate to closel spaced iages. When light fro to sources pass through the sae sall hole, not onl is light fro each source diffracted, but the diffraction patterns overlap. This overlapping akes the iage fuzz. The saller the hole, the ore difficult it is to separate to closel spaced objects.

5 SPH3UW/SPH4UI Unit 0.2 Single Slit Diffraction Page 5 of 7 Exaple ight fro a laser pointer has a avelength of A screen is placed 20 c aa n, passes through a slit of 9. a) Ho ide is the central axiu in degrees and c? b) What is the separation of adjacent inia excluding the pair in either side of the central axiu? Solution: a) One either side of the central line the central axiu is defined b the first-order dark fringes sin The angular idth of the central axiu is

6 SPH3UW/SPH4UI Unit 0.2 Single Slit Diffraction Page 6 of 7 Since sin sin 0.20sin The idth of the central opening is c b) Deterine location of = Deterine location of = Therefore the difference is The distance beteen an adjacent dark fringes is.4 c. Note: the central axiu is exactl tice the idth of the separation of other adjacent dark fringes.

7 SPH3UW/SPH4UI Unit 0.2 Single Slit Diffraction Page 7 of 7 Extra Notes and Coents