Lab Report
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Wave Nature of Light
Objective:
The purpose of this lab is to investigate interference, otherwise known as the diffraction of light. A beam of light acts a wave, and we are able to use equations so calculate the wavelength of the light used. The diffraction of a straight edge demonstrates that light waves bend around straight edges, allowing light to enter an area of shadow. When waves are superposed, they reinforce each other when crests are in phase and cancel out when they are not in phase. An image projected by light waves shows this by producing concentric circles of light. When slits are used, the laser superposes itself and creates constructive interference. The resulting spots are measured to give data that allows one to find the wavelength using the equation λm = dsin θ. These diffraction and interference with such slits was successful because of low percent errors in the wavelengths calculated. Additionally, a diffraction gradient creates better-defined spots, and more accurate measurements, yielding the lowest uncertainties.
Diffraction by a Straight Edge
Using the slide marked “straight edge/opaque disks,” a laser is positioned so that it falls on the edge. The light does go into the shadow region, it bends around the edge and spreads out into the shadow region. The picture below shows what happens when the laser beam falls on a straight edge.
Superposition of Waves and Diffraction by a Disk
A 48mm focal length lens and opaque disk slide are used to observe
superposition and the diffraction patterns. Due to symmetry, all waves that arrive from the edge of the disk at the same point on the axis will be in phase, causing a bright spot on the center of the pattern. The first disk used created concentric circles of bright light. The next disk produced a dark circle in the center. The pictures below show the patterns of diffraction.
C. Diffraction by a Narrow Slit
The slide with several narrow slits is placed in the holder, and this causes
diffraction fringes. These fringes are caused by the interference of wavelets from the various areas of the slit. An equation relating the first dark band to the wavelength and angular position is given by asinθ = λ. The width of the slit is marked on the disk, and represents the a value. The value of L is kept at 1m throughout the experiment to maintain consistency, and w is the width between the central peaks. See the diagram below. The angle θ is given by the equation tanθ = w/2L.
The known value of the wavelength is 632.8nm. The experimental value for the wavelength is 559.9nm, which has a percent error of approximately 11.5%. There are however some uncertainties in the experiment that may account for this error. When measuring the value for L, object may move or the edge of the meter stick could yield an inaccurate reading, which accounts for about +/-0.03m of error. Also, the value of w may be slightly off because of a worn ruler, or difficulties in measuring the distance of peaks on the wall without blocking the laser beam. The measurement was also supposed to be horizontal, which is hard to maintain, so this may attribute +/-0.02m of error.
w = 0.014cm
a= 0.08nm= 8E-5m
L = 1.0m
Tan θ = w/2L
λ= (8E-5m)sin(0.401)
Tan-1 (0.014/2) = 0.401= θ
= 559.9nm
Using the known value of the wavelength, one may also calculate the value for a. This value is compared to the given actual value of 8E-5 and has an error of about 13%. Again, this is accounted for by the uncertainties in the values of w and L.
a= λ/sin θ
= 632.8nm/sin(0.401)
= 9.04E Ð-5
Interference: The Double Slit
This part of the experiment uses two slits, and a laser goes through both of
them, allowing them to superpose and interfere with one another. When the two beams are in phase, a bright dot is created on the wall, called constructive interference. The equation used is dsin θ= m λ for all orders of m. Because there are several bands in this section, one must remember that tan θ= (Y/5) x (1/L). The diagram below shows how the constructive interference is created.
The L for this part is 1.0m, and there is about +/-0.03m of uncertainty, as there was in the previous part, due to objects being moved slightly, or a meter stick that is worn at the end. The Y value for this part, the distance between two bright bands, may be off by about +/-0.02cm due to the difficulty in measuring a horizontal distance on the wall without