LAB 13 - To analysis and study the characteristics of light waves by it’s interference PDF

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LAB 13 : Interference and Diffraction12/11/Section M9bbBy: Hamzah Sibil and Suraksha KhadkaProfessor FrancoPurposeTo analysis and study the characteristics of light waves by it’s interference and diffraction patterns as passes through single and double slitsPrinciples being ExaminedAs light passes t...

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LAB 13 : Interference and Diffraction 12/11/19 Section M9bb By: Hamzah Sibil and Suraksha Khadka Professor Franco

Purpose

To analysis and study the characteristics of light waves by it’s interference and diffraction patterns as passes through single and double slits

Principles being Examined As light passes through a single or double slit, it creates a diffraction/interference pattern on a screen placed beyond the slits. The pattern formed is because of the superposition of the waves coming from the slits. A position on the screen is where the pattern emerges is characterized by an angle θ formed by the line from the slits to this position, relative to the perpendicular line. The Interference pattern is due to a double slit and will have dark and bright fringes due to destructive and constructive interference of the waves coming from the two slits. When the constructive interference criterion has been met, we can represent it as the equation: d sin θ = n λ where n is an integer, d is the separation of the slits, and and sin θ  tan θ = y/L where is the separation of fringes and L is the distance between the screen and slits. Substituting y/L for sin θ we get the equation d (y/L ) = n λ, We can solve for y, get the equation y = n λL/d Diffraction pattern formed by a single slit and will have a wide and bright pattern at the center with alternating dark and bright fringes with diminishing intensity on both sides A single slit with slit width D will produce dark regions on the screen at positions where the following destructive interference criterion is satisfied and we will get a similar equation to constructive interference D sin θ = n λ where n is a non-zero integer and D is the slit width and sin θ  tan θ = y/L. Substituting y/L for sin θ and rearranging for y we get a similar equation y = n λL/D Equipment Slides with various slits; lasers (to be shared and passed from group to group); mount that holds laser and slide; black wooden target board; paper; tape; meter stick; ruler. Results In Part I we observed wave phenomena when a coherent and monochromatic light is passed through a single slit of different slit width. We determine the distance from the center of the pattern to different order dark from our  values. Since  is the distance between the dark fringes on both sides from the center, we can define y as yn where yn = n/2 as different orders of maxima. Using measured values of L and known slit width D, we calculate the wavelength of

the laser λ. We find that the average value of the wavelength is 564.7 nm. The wavelength that we used was red light and it had a value of 632.8 nm giving us a 10.7% error. This large percent error may be due to human error, specifically measurement error or equipment. We may have not taken proper measurements or the slit we may have been obscured or damaged. In Part II we performed the same experiment as in Part I but with double slits. We determined the distance between two neighboring spots in the double slit interference pattern for each respective pattern. We can calculate the wavelength of the laser light, λ from yn , our measured L, and our known d (the slit separation) to get wavelengths 636.25 nm for pattern A and 333.75 for pattern B. This gives us a respective percent error of 0.36% for pattern A and more 40% for pattern B. This large error is due improper measurements of the fringes or the slit we may have been obscured or damaged. For the single slit aspect of this experiment we determine the distance from the center of the pattern to the order dark fringe to be roughly 13x10-2 m. From this we can determine the slit width from y measured previously, your measured L, and your known laser λ to get an average width of 0.038 m. Compare this to the known width of 0.04 m, we get an acceptable 5% error. In Part III recorded data for the two slit patterns of different colors of light. By taking similar measurements as previously in part II, we determine the wavelength of light for yellow and green and orange to be 556.8 nm, and 528 nm, and 613 nm respectfully. By comparing these values with the wavelength provided we get percent errors less 1% which suggest that our experiment relatively successful. Conclusion In conclusion, we were better able to understand light through its wave phenomenon as it produces interference and diffraction patterns. This experiment was able to illustrate its unexpected behavior when passing through the slits by measuring and determining its wavelength. This lab proved successful as we were able to better grasp the wave optics of light.

1. How would be the pattern on the screen if a thin wire on wide open slide is used instead of the thin opening (slit) in Part I? A narrow slit will produce very tight diffraction fringes along the long axis and wide fringes along the narrow axis as opposed to a thin wire which will produce wide spaced circular fringes and a large circular aperture will produce tight fringes. The diffraction is highly dependent on wavelength. To observe diffraction from the hole produce by wire, the size of it must be of a very small comparable to the size of the wavelength 2. Discuss the possible sources of error that contribute to the percent errors in your experimentally determined values of d and D. Possible sources of error that might contribute may be found at equipment error such as the slits being obscured or damaged, other sources of light interfering with the observed patterns, or human/measure errors of the fringes’s length 3. For a given pair of slits, how does the pattern alter if one switches from a higher-λ laser (say, red) to a lower- λ (say, green) laser?

A change in wavelength will alter the number of lines in the pattern and alter the proximity or closeness of the lines. A shorter wavelength such as green will result in more lines per centimeter and a smaller distance between each consecutive line compare to a longer wavelength such as red which has less lines per centimeter and a greater distance between each consecutive line. 4. What will happen in the two-slit pattern obtained in your experiment, (i) if the slit width (D) is reduced keeping the distance between the slits (d) same? And (ii) if the distance between the slits (d) is reduced keeping the slit width (D) same? Explain with diagrams. 5. In your experiments, the slits are placed vertically. How would be the pattern on the screen with two-slit if another two-slit is overlapped horizontally? 6. What do you think will happen in the interference pattern if you keep adding slits at the same separation d?...