Double Slit Interference Deriving l = ws/D

2-source interference Interference arises from the superposition of waves. The two sources are coherent sources. Constructive interference Destructive interference Peak Trough Coherent sources result in waves that are: in phase; same wavelength; same frequency. Sunday, 09 December 2018 Leeds City College

Important Points When two crests meet, there is reinforcement. Where a crest and a trough meet, there is cancellation. If there is zero path difference, there is constructive interference (reinforcement). If there is a path difference of a whole number of wavelengths, there is constructive interference (reinforcement). Often we say that a whole number of wavelengths is an even number of half-wavelengths. If there is a path difference of ½, 1 ½ etc. wavelengths, there is destructive interference (cancellation). In other words, path difference of an odd number of half wavelengths leads to cancellation. All types of wave can interfere. Sunday, 09 December 2018 Leeds City College

Young’s Double Slits Lasers give off monochromatic (single colour) coherent light Laser Double slit Screen Bright spots In the Eighteenth Century, Thomas Young did not have a laser, so he had to make do with apparatus like this: An ordinary bulb (or candle in Young’s day) does not give off coherent light. The first slit ensures that the light arriving at the double slit is coherent. Sunday, 09 December 2018 Leeds City College

Equation D w Fringe spacing Wavelength (m) Slit spacing Fringes Distance from slit to the screen Sunday, 09 December 2018 Leeds City College

Explanation Red laser light The path difference is zero, so we get a bright fringe in the middle. s D The path difference is 1 half wavelength, so there is cancellation, leading to a dark fringe The path difference is 1 whole wavelength, or 2 half-wavelengths. This gives another bright fringe Sunday, 09 December 2018 Leeds City College

Derivation P is at the 1st bright fringe. Therefore S1Q = l. We will look at the first bright fringe P is at the 1st bright fringe. Therefore S1Q = l. OP is the fringe spacing = w Simple geometry tells us that triangles QS1S2 and OMP are similar. Therefore: Red laser light S1 Q D O s M S2 Therefore: Consider two rays, one going from S1 to P and one going from S2 to P …and rearranging gives: P Now draw a line perpendicular to S1P at Q. Sunday, 09 December 2018 Leeds City College

Two Slit Interference Double slit Screen Ray-box Single slit Fringes Coloured Filter Sunday, 09 December 2018 Leeds City College