PHY 1033C Lab #4 September 21, 2010 Measurement of Wavelengths of Light Goal: Measure the wavelength of light with a diffraction grating. Introduction: A transmission diffraction grating consists of a thin piece of clear plastic which contains many closely-spaced scratched parallel lines, from which light scatters as if from many parallel slits. When a beam of light is incident on a diffraction grating, part of the light passes straight through the grating (in the direction of the incident light) and part of the light is diffracted by the grating into different propagation directions. The scratches are very narrow (less than a wavelength) and each re-radiates the light incident on it in all directions; the fraction of the incident light propagating in a given direction is the sum of the light emitted in that direction by the many line slits, like a sum of a number of 2-slit interference patterns. Just like the 2-slit case, the rays emitted by the individual slits at the angle θ (see Fig. 1) will all be focused by the lens at its focal point F. But if the light arriving at the grating from the left is in phase, then the light reaching F will in general not be in phase, since each ray travels a different distance from Figure 1 the particular scratch to the focal point of the lens. The rays will interfere constructively or destructively and the actual intensity of the light striking F depends upon the path differences. If the difference in path length traveled by adjacent rays is a whole number of wavelengths all of the rays will be in phase and will add constructively to produce a bright spot of light at F. The difference between two adjacent paths is the segment AB in Fig. 1, whose size is related to the scratch spacing d and the deflection angle θ by AB = d sinθ Maximum light intensity will be produced at F if AB is an integral number of wavelengths: d sinθ = mλ The value of m is called the order of the diffracted beam. In general, the intensity of the diffracted beam decreases as the order increases. Since sinθ cannot exceed unity the order m cannot exceed d/λ. If the beam of light incident upon the grating contains a number of wavelengths (i.e. colors), each wavelength will have its own angle of deviation in each order. This results in a complete spectrum of the source for each diffraction order. Procedure: In this experiment the grating is placed close to your eye and the eye lens serves to collect the light. Make the distance L between the diffraction grating and the source S 1 meter and place a small piece of masking tape to mark the spot. Place the meterstick at the base of the source S (the light) so that the 50 cm mark is located at S. Looking through the diffraction grating located 1 m from S you will see diffracted images (bands) of color on both sides of the undiffracted image. A different set of images will be present for each color in the incident light. For a given color (red, green, or blue) there will be two images on opposite sides and at equal distances D from the filament in the light (see Fig. 2). While one person looks through the grating he/she should direct a second person to move a finger along the meterstick until his/her finger reaches the middle of each band of color. Measure the distance D for the middle of each band of color (Red, Blue, Green) on both sides of the source, and average to get he best value. Measurements of D and L will give tanθ from which sinθ and λ may be computed. Although both first and second order images may be visible, we will not study the second order ones. Note: your grating is scratched 13,400/inch and 1 inch = 2.54 cm. Draw a picture of the set-up (Fig. 2) in your lab notebook. Construct a table of Figure 2 your measurements and calculate the average wavelength for each color as a result. Show your calculations. Make a “ruler” of color vs. wavelength (color with smallest wavelength first). Compare your results to the table below: Table of Wavelengths for Light emitted from “Hot” Atoms Mercury Color Wavelength (x10-10 m) Yellow 5791 Yellow 5770 Green 5461 Blue-Green(Weak) 4916 Blue-Violet 4358 Violet(Weak) 4078 Violet 4047 Color Red Red Yellow Green Blue-Green Blue Blue-Violet Helium Wavelength (x10-10 m) 7065 6678 5876 5047 4922 4713 4471

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# Measurement of Wavelengths of Light PHY 1033C Lab #4