Question: 6 (a) State the meaning of diffraction and interference.
(b) A diffraction grating has 650 lines per millimetre and light waves (7.06 × 1014 Hz) from a light source S1 are incident on a diffraction grating. Determine the maximum order (n) of fringes formed by the diffraction grating.
(c) State and explain whether more orders of fringes are formed if the light source S1 is replaced by another light source S2 that has a lower frequency (as compared to S1).
Mark scheme:
6 (a) Diffraction: spreading of a wave as it passes through a slit or an edge. [1] Interference: when two or more waves superpose, [1] resultant displacement is the sum of the displacement of the waves. [1]
(b) Using the equation d sin θ = nλ and v = fλ [1]
Determine maximum order (n) by setting θ = 90°
Deduce n = 7.06 × 1014 / (3 × 108 × 650 × 103) [1]
n = 3.6 and hence maximum order of fringes, n = 3 [1]
(c) Longer wavelength implies fewer orders of fringes observed [1]
Possible answers:
6 (a)
A definition of diffraction: “when waves encounter an edge, an obstacle, or an aperture the size of which is comparable to the wavelength of the waves, those waves spread out as they travel and, as a result, undergo interference (Halliday, Resnick, & Walker, 2005, p. 1012).”
A definition of interference: “in a region of overlap, two waves of the same frequency can combine constructively or destructively, depending on their relative phase, to produce a redistribution of energy in that area (Hecht, 2003, p. 922).”
(b) Using the diffraction grating equation, d sin θ = nλ and v = fλ
Putting them together, d sin θ = n(v/f) or n = (f/v) d sin θ
For maximum order n, we may let θ = 90° and thus, sin θ = 1
Substituting into the equation, n = (f/v) d = (7.06 × 1014/3 × 108) (1/650 × 103) = 3.6
Thus, the maximum order of fringes is 3.
(c) By using the diffraction grating equation d sin θ = nλ again,
We have n = d sin θ/λ and lower frequency (or longer wavelength) implies smaller n or fewer orders of fringes tend to be observed.
Feynman’s insights or goofs?:
In Feynman’s 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, there is no “pure diffraction” as a spreading of waves without the phenomenon interference, and there is no “pure interference” as a superposition of waves without the phenomenon, diffraction. In general, if there are only “two sources,” the phenomenon is usually known as interference. On the other hand, if there are a “large number of sources,” the phenomenon is called diffraction instead.
Historically speaking, Young (1802) states a general law of interference as follows: “wherever two portions of the same light arrive at the eye by different routes, either exactly or very nearly in the same direction, the light becomes more intense when the difference of the routes is any multiple of a certain length, and least intense in the intermediate state of the interfering portions; and this length is different for light of different colors (p. 387).” In other words, constructive interference and destructive interference can be observed if the light waves have the same frequency and the path differences between two sources of light waves are integral numbers of wavelengths and an integral number of wavelengths plus half a wavelength respectively.
Despite the difficulty of defining the difference between diffraction and interference as explained by Feynman, the definitions of diffraction and interference can be more comprehensive as follows: 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 this results in bright and dark fringes instead of light rays moving in a straight line. Interference of light is a superposition of light waves from two or more sources that this results in a redistribution of energy such that bright fringes and dark fringes can be observed; bright fringes are observed when the path differences are multiples of wavelengths (∆x = nλ) and dark fringes are observed when the path differences are odd multiples of half-wavelength (∆x = [2n + 1][½λ]) respectively. The resultant displacement of light waves is the sum of individual displacement of each wave.
References:
1. 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.
2. Halliday, D., Resnick, R., & Walker, J. (2005). Fundamentals of Physics (7th ed.). New York: Wiley.
3. Hecht, E. (2003). Physics: Algebra /Trigonometry (3rd ed.). Pacific Grove, California: Brooks/Cole Publishing.
4. Young, T. (1802). An Account of Some Cases of the Production of Colors, not Hitherto Described. Philosophical Transactions, 92, 387–92.
