![]() ![]() Then you must include on every physical page the following attribution: ![]() If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission. To obtain constructive interference for a double slit, the path length difference must be an integral multiple of the wavelength, or The difference between the paths is shown in the figure simple trigonometry shows it to be d sin θ d sin θ, where d d is the distance between the slits. If the screen is a large distance away compared with the distance between the slits, then the angle θ θ between the path and a line from the slits to the screen (see the figure) is nearly the same for each path. The waves start out and arrive in phase.įigure 27.14 shows how to determine the path length difference for waves traveling from two slits to a common point on a screen. (b) Constructive interference occurs here because one path is a whole wavelength longer than the other. The waves start in phase but arrive out of phase. (a) Destructive interference occurs here, because one path is a half wavelength longer than the other. Similarly, if the paths taken by the two waves differ by any integral number of wavelengths ( λ λ, 2 λ 2 λ, 3 λ 3 λ, etc.), then constructive interference occurs.įigure 27.13 Waves follow different paths from the slits to a common point on a screen. More generally, if the paths taken by the two waves differ by any half-integral number of wavelengths, then destructive interference occurs. If the paths differ by a whole wavelength, then the waves arrive in phase (crest to crest) at the screen, interfering constructively as shown in Figure 27.13(b). Waves start out from the slits in phase (crest to crest), but they may end up out of phase (crest to trough) at the screen if the paths differ in length by half a wavelength, interfering destructively as shown in Figure 27.13(a). Thus different numbers of wavelengths fit into each path. Each slit is a different distance from a given point on the screen. To understand the double slit interference pattern, we consider how two waves travel from the slits to the screen, as illustrated in Figure 27.13. (c) When light that has passed through double slits falls on a screen, we see a pattern such as this. Wave action is greatest in regions of constructive interference and least in regions of destructive interference. (b) Double slit interference pattern for water waves are nearly identical to that for light. We can only see this if the light falls onto a screen and is scattered into our eyes. These waves overlap and interfere constructively (bright lines) and destructively (dark regions). (a) Light spreads out (diffracts) from each slit, because the slits are narrow. Figure 27.11 shows the pure constructive and destructive interference of two waves having the same wavelength and amplitude.įigure 27.12 Double slits produce two coherent sources of waves that interfere. ![]() We illustrate the double slit experiment with monochromatic (single λ λ) light to clarify the effect. Young used sunlight, where each wavelength forms its own pattern, making the effect more difficult to see. Why did Young then pass the light through a double slit? The answer to this question is that two slits provide two coherent light sources that then interfere constructively or destructively. Incoherent means the waves have random phase relationships. By coherent, we mean waves are in phase or have a definite phase relationship. ![]() Furthermore, Young first passed light from a single source (the Sun) through a single slit to make the light somewhat coherent. Why do we not ordinarily observe wave behavior for light, such as observed in Young’s double slit experiment? First, light must interact with something small, such as the closely spaced slits used by Young, to show pronounced wave effects. Without diffraction and interference, the light would simply make two lines on the screen. Here pure-wavelength light sent through a pair of vertical slits is diffracted into a pattern on the screen of numerous vertical lines spread out horizontally. This is not a standard abbreviation.Figure 27.10 Young’s double slit experiment. Geometric Optics Definitions, Quantities įor conveinece in the table below, " r-surface" refers to reflecting/refracting surface. ![]()
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