Optics-Diffraction Lab



The Wave Nature of Light: Interference and DiffractionPre-Lab Question UM Physics Demo Lab 07/2013Light is said to behave as a wave and as a particle. Cite an example of each type of behavior for light.EXPLORATION: DiffractionMaterialsRed Level Laser40 watt “candle” bulb on wooden basePower stripDiffraction grating (white border)Unknown diffraction grating (colored border)4 Medium binder clips (support legs for diffraction gratings)2 Meter sticksCalculatorCaution: The LASERs we will use today are safe for general use, but must be handled with care. NEVER look into the LASER or shine it into someone’s eye. ALWAYS TURN THE LASER OFF WHEN NOT IN USE and ONLY turn it on when it is POINTED SAFELY AT THE WALL.Lab Tip: Diffraction gratings degrade with finger oil and scratches. To maintain top performance, please handle the diffraction gratings by their edges and avoid touching the clear plastic portions of the gratings.Monochromatic Light: The LASERTo demonstrate the wave nature of light and study interference effects, we need a source of monochromatic light—light of a single wavelength. In the early 1960’s physicists developed a new and powerful way to generate monochromatic light using electron transitions between atomic energy levels as a light source. This technique was named Light Amplification through the Stimulated Emission of Radiation—the LASER. Since its invention, the LASER has become an indispensable tool for science and industry. LASERs read the digital data from CDs and DVDs, transmit vast amounts of information over fiber optics, cut industrial parts with amazing precision, replace metal knives in a variety of surgeries (particularly eye surgery) scan the bar codes on your groceries and serve as pointers for public speaking presentations. The first LASERs employed a high-voltage electrical discharge in gases such as Helium mixed with Neon. Subsequently, solid-state LASER diodes have been developed and are currently used for most applications. For our experiments we will use LASER diode that emits monochromatic red light at a wavelength of 650 nm (1 nm = 10-9 meters). Within the bright LASER light spot we can regard the light as plane waves with a 650 nm wavelength. This is a good approximation to true plane waves (which are infinite in spatial extent) since the laser spot size is ~10,000 wavelengths in diameter so that the wave fronts look infinite in all directions for objects ~10 wavelengths in size illuminated by the laser spot.Light has both particle-like and wave-like characteristics. In the previous lab we explored the classical ray tracing behavior of light, which illustrates the particle-like behavior of light. Now we will demonstrate the wave behavior of lightA) Place the standard diffraction grating (plain white border) one meter from the wall on the lab bench. Place the LASER behind it on the table so that it shines through the grating toward the wall. Turn on the LASER and observe the resulting pattern of light on the wall. Sketch the resulting pattern of LASER light below. The splitting of the LASER light into several beams is caused by diffraction. We can use this effect to measure the spacing between the parallel lines etched onto the surface of the diffraction grating. Figure 1: Fraunhoffer Diffraction of a LASER beam. The diffraction grating lines are out of the page.The geometry of the right triangles shown in Figure 1 yields the Fraunhoffer Diffraction Formula: where = wavelength of the LASER light (650 nm) and d = line spacing of the grating. The integer m is called the order of the maximum. We will make our measurements with the first order maximum so m=1.Check that the diffraction grating is one meter from the wall and measure the distance from the central beam to the first maximum of the diffracted beam. Record your measurements (in meters) below: L= 1 m y = ____________(m) ___________(m)B) Solve the diffraction equation for d. Set m = 1 and calculate the spacing between the grating lines d. Show your work below. For the wavelength of the LASER light use λ = 650 nanometers (recall one nanometer = 1 nm = 1 billionth of a meter = 1 x 10-9 meters) and report your answer in nanometers.d = Grating Spacing =________________________(nm)APPLICATIONNow that we have calibrated the spacing of the diffraction grating, we can use it to study the light emitted by different objects. Using diffraction in this way is called spectroscopy, the study of the spectrum of emitted or absorbed light.The larger the wavelength of light compared to the spacing of the diffraction grating, the larger the angle of diffraction. Given that red light has a longer wavelength than blue light, predict which color will be diffracted to a larger angle and therefore appear farthest from the lamp.View the glowing filament of the candle lamp through diffraction grating and label the order of the colors you observe along the schematic spectrum bar below. Which color appears the farthest from the lamp. Was your prediction for the order of red and blue made in (1) correct?Colors: R=Red, O=Orange, Y=Yellow, G=Green, B=Blue, I=Indigo, V=Violet LAMP Now view one of the hydrogen discharge lamps through the diffraction grating provided. The gratings are set ? meter from the lamp.A) Describe how the hydrogen spectrum is different from the spectrum of the glowing filament. What features are present in the Hydrogen spectrum that is not present in the filament spectrum? In the spectrum you should see a bright red line. This spectral line is called the Hα line of the Balmer spectral series of Hydrogen. The line corresponds to a transition of the Hydrogen electron from the third excited state of the Hydrogen atom to the second excited state. Astronomers map the distribution of hydrogen gas in the Galaxy by observing the intensity of this line to determine both the presence and amount of hydrogen in ionized gas clouds. The prominent greenish-blue line is called Hβ. You should also be able to see a faint violet line (Hγ) and you may be able to see a very faint line in the far violet (Hδ). Measure and record the position y of the Hα line on both sides of the discharge tube and average the two values to produce your final measured y value.yLeft (m)yRight (m)yAverage (m)C) Now use the diffraction equation to calculate the wavelength of the Hα spectral line. Use L=1/2 meter and m =1. Show your calculation below.L= 1/2 m y = ____________(m) ___________(m)λH-α = Wavelength of Hα Spectral Line =_____________(nm)Thus far we have used the known spacing of the diffraction grating to measure the wavelength of light. But recall that we measured the grating spacing by using the known wavelength of LASER light to probe the size of the grating lines. This illustrates one of the most powerful applications of diffraction: to probe the structure of objects too small to observe directly—crystals and molecules. To probe small structures with coherent light requires light of a wavelength comparable to the size of the object. For crystals and molecules this means using very small wavelengths which correspond to X-Ray radiation, which we can regard as very short wavelength light. X-Rays are difficult to work with, but we can “scale up” the process by using larger objects and visible LASER light as a surrogate for X-Rays.We have observed that vertical parallel lines on the diffraction grating split the LASER beam horizontally: Figure 2: The relationship between grating lines and the diffracted Laser beam.A) Predict what will happen to the diffraction pattern if you rotate the grating so that the lines are horizontal.B) Test your prediction for part A by rotating the grating. Sketch the patterns of LASER spots for both the vertical and horizontal grating.C) Predict what pattern of laser spots you would observe if you had two gratings, one vertical and one horizontal in front of the LASER beam. Sketch your predicted pattern below.Test your prediction from (C). Ask your instructor to provide you with a second diffraction grating. Was your predicted pattern for the two crossed gratings correct?D) Shine the LASER onto the wall and place the unknown diffraction grating (colored border) in front of the beam. Sketch the resulting diffraction pattern below.E) Based on your observations for (A-C) sketch the pattern of lines that would produce this pattern for the unknown grating.Below is probably the most important diffraction image ever taken. It was made by Rosalind Franklin in 1952 by exposing purified strands of DNA to X-Rays. Figure 3: Early X-ray diffraction pattern from B-DNA made by Rosalind Franklin in 1952.Your instructor will project a diffraction image of a small unknown object for you.A) Sketch the projected diffraction pattern below.B) Compare your sketch of the projected image to the DNA diffraction image. Label two features on your sketch that are similar to ones present in the DNA image. Also label two features present in the DNA image that do not appear in the projected image. Note that the DNA image is a photographic negative where dark regions correspond to bright X-Ray light. C) Your instructor will lead a class discussion where you will attempt to deduce the structure of the unknown object producing the projected diffraction pattern. After this discussion, predict what structure (shape) might produce the projected image.D) Now view the unknown object under the microscope. What shape is producing the projected pattern? What does this imply about the internal structure of the DNA molecule? Everyday Applications of DiffractionBar code scannersLaser pointersLaser levels for carpentryholographyDetermining atomic structure of matter (using X-Rays, or short-wavelength light). The double helix structure of DNA was discovered this way (by Rosalyn Franklin)Spectroscopy (for example, for chemical analysis and Astronomical observations of the composition of stars)Measuring stresses and strains in transparent materialsChallenge Work:One of the fundamental precepts of Quantum Mechanics is that the energy of light is quantized, that is, light carries energy in discreet packets called quanta. This is part of the particle like behavior of light. When light interacts with matter and gives up its energy, it behaves as a particle called a photon with a discreet, exact energy proportional to its frequency. The proportionality constant is call Plank’s constant and is measured experimentally to be h = 4.14 ×10-15 eV-s. The electron-volt (eV) is a unit of energy corresponding to the work done when one electron of charge moves through a potential difference of one volt. Optical light typically carries energies of a few electron volts, making eV a convenient unit.Consider the following two equations: Equation I states the energy E of a photon of light is proportional to the frequency of the light (a wave property!) and that the proportionality constant is Plank’s constant h. Equation II is the relationship between propagation speed, frequency and wavelength for light as a traveling wave. Here we denote the wave speed as the speed of light c = 3.0 ×108 m/s.A) Solve Equation II for the frequency f in terms of the speed of light c and the wavelength λ. Show your calculation below.B) Now substitute your result from (A) into equation I and obtain an expression for the energy of a photon of light in terms of the wavelength, speed of light and Plank’s constant. Show your calculation below. C) Calculate the energy in eV corresponding to your measured value of the wavelength for the Hа spectral line of Hydrogen. Be sure to convert the wavelength in nanometers to meters. Show your calculation below. Hα Photon Energy =____________________(eV)SummaryLight exhibits both wave-like and particle-like behaviors.The principle of linear superposition says that the amplitudes of two or more waves arriving at a point in space add at every instant of time. This gives rise to interference, where two or more arriving waves add up to larger amplitude, smaller amplitude or zero.Waves which encounter structures small compared to their wavelengths undergo diffraction whereby they bend around corners or obstacles.Light waves projected through a slit narrower than the wavelength will interfere to produce a pattern of alternately light and dark fringes.A diffraction grating consists of many narrow parallel slits and disperses light into its component wavelengths (colors). Each wavelength of light will diffract to a specific angle after passing through the grating.A diffraction grating can be used to measure the wavelength of atomic emission lines. This application of diffraction is called spectroscopy.Conversely, the diffraction of a monochromatic (one color—one wavelength) beam of LASER light can be used to measure the spacing of a diffraction grating.Diffraction of monochromatic light from a LASER or X-Ray source can be used to infer the size and structure of small objects, crystals and molecules. Small structures produce large diffraction angles; large structures produce small diffraction angles. ................
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