Interference of Light via Double Slit Lab Online EDITED 7.17.23(1)

Interference of Light Via Double Slit Lab Online Purpose The purpose of this activity is to examine the diffraction and interference patterns that occur when monochromatic laser light passes through difference combinations of apertures. Theory/Background In 1801, Thomas Young obtained convincing evidence of the wave nature of light. Light from a single source falls on a slide containing two closely spaced slits. If light consists of tiny particles (or ‘corpuscles’ as described by Isaac Newton) then on a viewing screen placed behind those two slits we would observe two bright lines directly in line with the two slits. However, Young observed a series of bright lines. Young was able to explain this result as a wave interference phenomenon, because of diffraction, the waves leaving the two small slits spread out from the edges of the slits. This is equivalent to the interference pattern of ripples from two wave sources, to the top for a body of water crossing each other’s paths, and interference with each other when they do. In general, the distance between the slits is very small compared to the distance from the slits to the viewing screen where the interference pattern is observed. The rays from the edges of the slits are essentially parallel to each other. Constructive interference will occur on the screen when the distance that the rays from each of the slits travels to the screen is different by a whole number multiple of the wavelength of the light itself. Those spots are where the bright spots in the observed interference pattern form. While destructive interference will occur on the screen when the different distances that the rays from each of the slits travels to the viewing screen is related to half a wavelength of the light itself. 1

When the monochromatic (single wavelength) light is passed through two slits, the bright spots (maxima) of the interference pattern that forms is symmetric around a central bright spot. Each of the maxima are evenly spaced, and of the same width. They will get slightly dimmer as they get further away from the central maxima. Equations for Double Slits If we draw a diagram for the double slit configuration, we can use simple trigonometry to determine where the bright spots will form on the viewing screen. Here d is the distance between the two slits. L is the distance from the two slits and the viewing screen. y is the displacement from the center point of the viewing screen to the point P where the bright spot forms. θ is the angular location of the bright spot. Finally, S is the difference in the distance traveled by the two light rays r 1 and r 2 . From the properties of the right triangle, it is clear that S = d sin θ . Since we know that the bright spots will form where S is to equal integer multiples of the wavelength (λ) of the light that means; d sin θ = nλ ? is an integer ? = . . . −2, −1, 0, 1, 2, . .. where 0 corresponds to the central maxima located at location C in our diagram. As previously stated, L is going to be much larger than d, which is going to result in L also being much larger than y. This means that θ, the angular position of the bright spots, is always going to be very small. So we can invoke the small angle approximation of sin θ . (sin θ ≅ tan θ , when θ is small) Which makes our equation; d tan θ = nλ Finally, since tan θ = !"" we have tan ? = & in this case. Substituting that in gives us: Solving for y: #$% ' ? ? ( = ?? ? ? ( = ? ?? ? Our equation tells us that for the two slit configuration, the various maxima will be located integer multiples of the wavelength of the light multiplied by the distance from the slits to the viewing screen,

3. Please note the following in the simulation: a. The two blue dots separated by a distance d on the lef side of the simulation represent our two light sources. b. The two sets of blue concentric circles represent the wave fronts of the light being emitted from our two light sources. c. The grey dashed lines represent the location of the local maxima of the interference pattern, and local maxima correspond to the locations where the two wave fronts overlap with each other. Procedure 1. In the purple box on the lef side of your screen make the following settings, then record then in the Table 1: a. Slit distance, d = 3 µm. b. Wavelength, λ = 400 nm 2. At the bottom of the simulation window, it is listed that the distance from the two light sources, and the viewing screen on the right side of the simulation window is, L = 10 µm. Record this in the Table 1. 3. Using the scale on the right side of the screen, measure and then record the location of all the maxima locations (y) that are visible on the screen in Table 2. There should be 5 of them. a. Remember that the center maxima correspond to n = 0.

Analysis Table 1 (2 points) d (µm) λ (nm) L (µm) Table 2 Peak (n) 2 1 0 -1 -2 ? Δ ? (µm) 1. According to the theory, the distances (Δy) between consecutive peaks for two slit interference patterns should all be the same. Calculate the distances between consecutive peaks, record them in the chart. Show work. (4 points) 2. Calculate the experimental location ? ( for each of the peaks. Show work. (2 points) 3. Calculate the % error between the theoretical value and your measured value for the peak ? = 2 . Show work. (4 points) 4. Calculate the angular location ? ( for each of your measured maxima. Show work. (2 points)