Question: Explain the meaning of diffraction of light.
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Textbooks may not provide a comprehensive definition of diffraction. For example, Hewitt (2006) defines diffraction as “[t]he bending of light that passes around an obstacle or through a narrow slit, causing the light to spread (p. 578).” Essentially, this definition refers to a bending or spreading of light waves as a result of a narrow slit or an obstacle. However, we can explain that the diffraction of light is a spreading of light waves passing through a slit or obstacle whose size is comparable to the wavelength of the light waves and it results in bright and dark fringes (instead of light rays moving in a straight line).
How would Feynman answer?
Feynman would answer this question from the perspectives of diffraction through a single slit, diffraction grating (diffraction through multiple slits), and problems of defining diffraction.
1. Diffraction through a single slit:
Firstly, Feynman would explain that, “[a]ccording to the wave theory, there is a spreading out, or diffraction, of the waves after they go through the slit, just as for light. Therefore, there is a certain probability that particles coming out of the slit are not coming exactly straight. The pattern is spread out by the diffraction effect, and the angle of spread, which we can define as the angle of the first minimum, is a measure of the uncertainty in the final angle (Feynman et al., 1963, section 38–2 Measurement of position and momentum).” In short, the word diffraction means a spreading of waves.
In addition, Feynman would elaborate that “[t]o say it is spread means that there is some chance for the particle to be moving up or down, that is, to have a component of momentum up or down (Feynman et al., 1963, section 38–2 Measurement of position and momentum).” That is, Feynman views the spreading of waves from the perspective of particles. Simply phrased, this physical phenomenon can be explained by the uncertainty of particles in moving up or down. In a sense, it means that we can explain the wave theory of diffraction by using the uncertainty principle.
On the other hand, Feynman (1990) also says that “when you try to squeeze light too much to make sure it’s going in only a straight line, it refuses to cooperate and begins to spread out (p. 55).” Essentially, “it ‘smells’ the neighboring paths around it (p. 54)” while moving through a single slit before forming the diffraction pattern. This is based on his formulation of quantum electrodynamics that does not require an uncertainty principle. In other words, Feynman’s sum-over-paths recipe for a particle moving from a location A to another location B means that physicists need to consider all possibilities (or possible paths) between A to B. Thus, it is not simply about travelling in a straight line path, but one needs to include paths that include twists and turns.
2. Diffraction grating:
Feynman would discuss diffraction of waves through multiple slits or diffraction grating. According to Feynman, “a diffraction grating consists of nothing but a plane glass sheet, transparent and colorless, with scratches on it. There are often several hundred scratches to the millimeter, very carefully arranged so as to be equally spaced. The effect of such a grating can be seen by arranging a projector so as to throw a narrow, vertical line of light (the image of a slit) onto a screen. When we put the grating into the beam, with its scratches vertical, we see that the line is still there but, in addition, on each side we have another strong patch of light which is colored (Feynman et al., 1963, section 30–2 The diffraction grating).” This can be explained by the diffraction grating equation d sin θ = λ because the angle (θ) of spreading depends on lights of different colors or wavelengths.
Interestingly, a block of graphite may also function like a diffraction grating. More important, it is the slowest neutrons that pass through the long block of graphite. Thus, Feynman explains that “[i]f we take these neutrons and let them into a long block of graphite, the neutrons diffuse and work their way along. They diffuse because they are bounced by the atoms, but strictly, in the wave theory, they are bounced by the atoms because of diffraction from the crystal planes (Feynman et al., 1963, section 38–3 Crystal diffraction).” That is, these neutrons have longer wavelengths and behave more like waves. Note that neutrons having higher energy behave more like particles, whereas neutrons having lower energy behave more like waves.
3. Problems of defining diffraction:
It is possible that Feynman would discuss problems of defining diffraction. For example, in his own words, “[n]o one has ever been able to define the difference between interference and diffraction satisfactorily. It is just a question of usage, and there is no specific, important physical difference between them. The best we can do, roughly speaking, is to say that when there are only a few sources, say two, interfering, then the result is usually called interference, but if there is a large number of them, it seems that the word diffraction is more often used (Feynman et al., 1963, p. 30-1).” In essence, diffraction refers to a spreading of waves that includes the phenomenon interference, whereas interference refers to a superposition of waves that includes the phenomenon diffraction.
Feynman also clarifies that if there are only “two sources” of light, the phenomenon is commonly called interference; on the other hand, if there are a “large number of sources” of light, the phenomenon is known as diffraction. Importantly, we should include the nature of waves when we define the concept of diffraction. For example, we may speak of diffraction and interference of light waves and water waves. However, there is a spreading of elastic waves from a drum that has two-dimensional cylindrical symmetry instead of diffraction of one-dimensional string waves.
References:
1. Feynman, R. P. (1990). QED: The Strange Theory of Light and Matter. London: Penguin.
2. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.
3. Hewitt, P. (2006). Conceptual Physics (10th ed.). San Francisco: Addison-Wesley.