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Transcription

1 Lecture Notes (When Light Waves Interfere) Intro: - Newton believed that light was composed of fast-moving, tiny particles which he called corpuscles - Grimaldi, an Italian scientist, discovered in the 17th century, that shadows were not perfectly sharp; ; Newton believed that this was due to the corpuscless interacting with the vibrating particles on the edges of the opening - Newton didd not believe that this was actually a diffraction effect due to the wavelength nature of light Diffraction: - from our earlier studies of waves, we know that a wave can go around a corner; for example, you can hear a voice coming from the other side of a tree or thee other side of a hill even though there is nothing around to reflect the sound to you - we are so used to this effect that we don't even notice it - the phenomenon of energy waves spreading into what we would expect to be "shadow" regions is called diffraction - one way to visualize this effect is with ripple tanks - if the slit is less than one wavelength wide, the wave will emerge and spread in all directions

2 Wave Theory of Light: - a Dutch scientist named Christiaan Huygens ( ) proposed a wave model to explain diffraction

3 - although the wave model of diffraction was easy to see for water waves, it was not at all intuitive ass an explanation for the nature of light - light does not seem to bend around corners as water does around a barrier; furthermore, it was argued that if light was a wave, then we should also be able to see around corners just as we hear around corners - we now know that light does indeed bend around corners, but it is not easy to observe because the wavelength of light is so small - an English physician/physicist named Thomas Young ( ) also believed that many properties of light could be explained in terms of wave theory - Young devised a "double-slit" experiment, which is considered one of the most important experiments ever performed

4 Young's Double-Slit Experiment: - Young cut a hole in a windoww shutter, covered it with a thick piece of paper punctured with a tiny pinhole and used a mirror to divert the thin beam thatt came shining through (the pinhole was used to allow only a small portion of light into the experiment; this ensured that all the light waves were in phase; this is called coherent light) - then he took "a slip of a card, about one-thirtieth of an inch in breadth" and held it edgewise in the path of the beam, dividing it in two (Young split thee coherentt light beam in two in orderr to let the light waves interact with one another)

5 - the result was a shadow of alternating light and dark bands, a phenomenon that could be explained if the two beams were interacting like waves - bright bands appeared wheree two crests overlapped (constructive interference), reinforcing each other; dark bands marked where a crest lined up with a trough (destructive interference), neutralizing each other; he called the series of alternating light and dark bands interference fringes

6 - the demonstration was often repeated over the years using a card with two holes to divide the beam; these so-called double-slit experiments became the standard for determining wavelike motion, a fact that was to become especially important a century later when quantum theory began - Young used monochromatic light in this experiment; light of only one color or wavelength, instead of white light; Young used monochrom matic light becausee it produced a diffraction effect of light and dark bands whereas white light would produce the effect of colored bands - Young used the double-slit experimen nt to make the first precise measurement of the wavelength off light - the diagram below illustrates s the analysis of the angles formed by double-slit interferencee of light S 2 x S 1 L - areas of constructive interference willl show up on the screen as bright bands; the areas of destructive interference will appear as dark regions between the brightt bands - constructive interference occurs at thee red points on the screen, starting with the central band (n = 0) - the first bright band on either side of the central band is called the first-order line and falls at points (n = 1) and (n = -1)

7 - the distance from the point (n = 0) to the point (n = 1) is given the symbol x - the distance between the slits and the screen is given the symbol L - the distance between the centers of the two slits, S 1 and S 2, is given the symbol d - due to geometrically similar triangles, Young devised the following mathematical relationship: λ xd L - this allows an accurate measurement of the wavelength of light Single-Slit Diffraction: - this effect occurs when light passes through a single, small opening and a series of light and dark bands appear - instead of the equally spaced, bright bands seen in double-slit diffraction, however, a bright central band with dimmer bands on either side is seen in single-slit diffraction - single-slit diffraction can be explained by the Huygens Principle which states that all points of a wave front are taken as point sources for new wavelets which propagate in the forward direction - here each portion of the slit can act as a source of waves, therefore, light from one portion of the slit can interfere with light from another portion - as stated earlier, this will result in a central bright band with alternating dark and bright fringes on each side of the central bright fringe; these non-central bands will be dimmer than the central band

8 - this diffraction pattern closely resembles the interference fringe pattern formed by Young's experiment - in the case of Young's experiment, thee slits behave as point sourcess of light; for single-slit diffraction the wavelets interfere with one another: the width of the slit is important - to help understand what is happening,, we will occurring at the opening of the single-slit simplify what is 1) Light in the form of a plane wave enters the slit; where the width of the slit is given the symbol w 2) Each point within the slit is a source of Huygens's wavelets; only a few points are drawn as a simplification 3) As in Young's experiment, the screen is far away enough from the slit thatt the rays emergingg from the slit are considered to be parallel 4) Each of the wavelets can interfere with one another constructively or destructively 5) At the screen's midpoint a bright line will appear; this occurs due to constructi ive interference 6) Destructive interference will occur at intervals of ½ λ 7) If you narrow the slit or increase the λ of monochromatic light used, then the light bands on the screen will spread out and the dark bands will decrease in width Light Diffracted by an Obstacle: - light diffracted by an obstacle can also produce a pattern - light diffracts around the edges of all objects

9 - remember, the famous diffraction effect on the penny hypothesized by Fresnel