Wave Model of Light: Note 3

Young’s Double Slit Experiment It was well known that when water waves interact from two point sources, they create an interference pattern that is only characteristic for waves. Thomas Young decided to complete the same experiment with light instead of water. He used the following setup to ensure accurate results: Monochromatic Single Double Interference Pattern Light Slit Slit On Screen 1. A monochromatic (mono: one, chromatic: colour) light was used so that light of one frequency could be produced in phase, and be able to interfere later in the apparatus. 2. The single slit was placed in the apparatus to act as a single point source of light. When light would pass through it, diffraction would occur and it produced a pattern like a rock in a puddle. This way, the waves would reach each double slit at the same time. 3. The double slit allowed for diffraction from two sources, this was so each pattern could interfere with each other. 4. An interference pattern was produced on the screen with a central maximum (called a fringe), bordered by two dark spots (nodes), and then repeated. Basically, two experimental conditions need to be met when light creates an interference pattern. 1. Light needs to be monochromatic (all the same frequency or colour). 2. The waves coming through the double slits need to be in-phase with each other.

Wave Model of Light: Note 3 What Actually Happens S1 d S2





xn

θ

L

Here: s - S1 and S2 are the two sources of light - d is the distance between the two slits in metres - L is the distance between the double slit and the screen in metres - θ is the angle we are observing the light being diffracted at *Note: The “s” line in the middle of the diagram denotes a large distance. The two light rays do, in fact, meet at the same point on the screen (which technically means they are not parallel), but the angle they are on is so similar, that they are approximately equal. But, on closer inspection of the double slits: S1 θ d θ S2 Path Difference (PD) There is a path difference (PD) between the two rays. The bottom ray must travel a little bit further than the top ray to get to the screen. As the angle θ changes, so does the PD. As you can imagine, if θ = 0o, then there is no path difference. This means that crests from S1 meet crests from S2 (and troughs with troughs) and constructive interference occurs, thus producing a fringe. As pictured above, if θ is a certain value and the PD is equal to ½λ, crests from S1 will meet with troughs from S2 and destructive interference occurs, thus producing a node. As the angle increases, if the PD = λ, then constructive interference occurs again. This cycle repeats for different PD’s.

Wave Model of Light: Note 3 In Summary: -When the PD = λ, we get constructive interference (a fringe). In fact, when PD = nλ (any multiple of a wavelength), constructive interference will occur. -When the PD = ½λ, we get destructive interference (a node). In fact, when PD = (n-½)λ (any half multiple of a wavelength), we get destructive interference. Double Slit Formula: From the diagram, and using trigonometry, we can relate the PD with the slit separation and the chosen angle, PD = dsinθ. We can use this to derive some equations: Constructive Interference For Fringes: PD = nλ, and PD = dsinθ, therefore: nλ = d sin θ where: -n is integer number of wavelengths in PD -λ is the wavelength of the light in metres -d is the distance between the slits in metres -θ angle between the source ray and diffracted ray € Destructive Interference For Nodes: PD = (n-½)λ, and PD = dsinθ, therefore: (n − 1 2) λ = d sin θ where: -n is integer number of wavelengths in PD -λ is the wavelength of the light in metres -d is the distance between the slits in metres -θ angle between the source ray and diffracted ray € In real life, it is very difficult to measure θ or the tiny PD. Instead, we can measure the distance between the central bright fringe and some selected fringe (xn) and the distance between the double slits and the screen (L). Using trigonometry, we can find θ using: x tan θ = n L Eg. 1. Determine the wavelength and colour of light used in a double slit experiment if the slit separation is 0.30 mm, the distance between the slits and the screen is 1.00 m € and the distance from the central fringe to the second fringe is 4.00 mm.