Single Slit Diffraction Pattern of Light :: Mathematics Math

Missing Figures SINGLE SLIT DIFFRACTION PATTERN OF LIGHT The diffraction pattern observed with light and a small slit comes up in about every high school and first year university general physics class. The intention of this paper is to explain this pattern at the academic level mentioned above. Light is interesting and mysterious because it consists of both a beam of particles, and of waves in motion. WAVE PARTICLE DUALITY: All carriers of energy and momentum, such as light and electrons, propagate like a wave and exchange energy like a particle. It wasn't until the 19th century that convincing evidence was found showing that light behaves like waves. Before reading on, you may wish to review some wave terminology. The key to understanding why light behaves like waves is in INTERFERENCE and DIFFRACTION. Interference and Diffraction are the phenomena that distinguish waves from particles: waves interfere and diffract, particles do not. Light bends around obstacles like waves do, and it is this bending which causes the single slit diffraction pattern. Some assumptions must be made for this description of the single slit diffraction pattern: * The slit size is small, relative to the wavelength of light. * The screen is far away. * Cylindrical waves can be represented in 2D diagrams as cicular waves. * The intensity at any point on the screen is independent of the angle made between the ray to the screen and the normal line between the slit and the screen (this angle is called T below). This is possible because the slit is narrow. point1 Consider a slit of width a, light of wavelength l, and a smaller than l. When the light encounters the slit, the pattern of the resulting wave can be calculated by treating each point in the aperature as a point source from which new waves spread out. pointb Let L represent the distance between the slit and the screen. Let T represent the angle between the wave ray to a point on the screen and the normal line between the slit and the screen. point2 The top part of the figure to the left is an imitation of a single slit diffraction pattern which may be observed on the screen (there would really be more blending between the bright and dark bands, see a real diffraction pattern at the top of this page). Below the pattern is an intensity bar graph showing the intensity of the light in the diffraction pattern as a function of sin T. Single Slit Diffraction Pattern of Light :: Mathematics Math Missing Figures SINGLE SLIT DIFFRACTION PATTERN OF LIGHT The diffraction pattern observed with light and a small slit comes up in about every high school and first year university general physics class. The intention of this paper is to explain this pattern at the academic level mentioned above. Light is interesting and mysterious because it consists of both a beam of particles, and of waves in motion. WAVE PARTICLE DUALITY: All carriers of energy and momentum, such as light and electrons, propagate like a wave and exchange energy like a particle. It wasn't until the 19th century that convincing evidence was found showing that light behaves like waves. Before reading on, you may wish to review some wave terminology. The key to understanding why light behaves like waves is in INTERFERENCE and DIFFRACTION. Interference and Diffraction are the phenomena that distinguish waves from particles: waves interfere and diffract, particles do not. Light bends around obstacles like waves do, and it is this bending which causes the single slit diffraction pattern. Some assumptions must be made for this description of the single slit diffraction pattern: * The slit size is small, relative to the wavelength of light. * The screen is far away. * Cylindrical waves can be represented in 2D diagrams as cicular waves. * The intensity at any point on the screen is independent of the angle made between the ray to the screen and the normal line between the slit and the screen (this angle is called T below). This is possible because the slit is narrow. point1 Consider a slit of width a, light of wavelength l, and a smaller than l. When the light encounters the slit, the pattern of the resulting wave can be calculated by treating each point in the aperature as a point source from which new waves spread out. pointb Let L represent the distance between the slit and the screen. Let T represent the angle between the wave ray to a point on the screen and the normal line between the slit and the screen. point2 The top part of the figure to the left is an imitation of a single slit diffraction pattern which may be observed on the screen (there would really be more blending between the bright and dark bands, see a real diffraction pattern at the top of this page). Below the pattern is an intensity bar graph showing the intensity of the light in the diffraction pattern as a function of sin T.