Thus the fringes intensity can be approximately described as, If the screen is placed at distance L from the slit, alternating bright and dark fringes at different positions of y (each fringe will run parallel to the slit) are observed, as schematically shown in Figure 1b (left). For small θ, it can be shown that I(θ) is approximately proportional to |sin(πaθ/λ)/(πaθ/λ)|2. The angular variation of the light intensity is denoted as I(θ), where θ represents the angle of the direction (towards +y or –y) away from the “straight through” direction, through y = 0 in Figure 1a). Fundamentally, it arises from the interference between different parts of the light wave after the aperture (in particular, points between the two edges of the aperture will “re-emit” the light wave towards different directions). This alternation, known as the “diffraction pattern” of the light (through a small aperture), is also a characteristic phenomenon for waves. If the light of wavelength (λ) is shone on a narrow slit of width (a) (shown schematically in Figure 1a), the light intensity (which is proportional to the square of the peak amplitude of wave) far away from the slit will alternate between large and small (nearly zero) values, corresponding to “bright” and “dark” regions, along the width direction (“y-axis” in Figure 1a) of the slit. It also underlies the phenomena of single-slit diffraction and double-slit interference of light (which is an electromagnetic wave) to be observed in this experiment. This phenomenon can be generalized to waves in two- and three-dimensional space. Such a spatial alternation of strong and weak wave amplitude represents an “interference pattern”. The oscillations will have zero (thus minimal) amplitude (also known as “nodes”). The oscillations (as functions of time t) will have maximal amplitude (between −2A and +2A). Which is also known as a “standing wave”. When the two waves overlap, their amplitudes add up (which is known as the “superposition principle of the wave”) to give: Where T is the period (in time) of the wave. Where λ is the wavelength (spatial periodicity of the wave). Here, A is the peak amplitude, and k is the “wave number” or “wave vector” defined as, Propagating to the right (+x direction) and left (−x direction), respectively. Consider a simple example of two waves propagating along a one-dimension line (x-axis) and mathematically represented by:
Interference is one of the most characteristic phenomena associated with waves. Waves or different parts of waves can overlap and “interfere” to produce an alternating strong and weak amplitude. Historically, the observation of diffraction and interference of light played important roles in establishing that light is an electromagnetic wave.Ī wave is an oscillation in the amplitude of some physical quantity in space and/or time. The slits are simply cut using razor blades in an aluminum foil and the characteristic diffraction and interference patterns manifest as patterns of alternating light and dark fringes on a screen placed after the foil, when the light is shone through the slit(s) on the foil. This experiment will demonstrate the wave nature of the light by observing diffraction and interference of a laser light passing through a single slit and double slits, respectively. Diffraction refers to the phenomenon of when a wave passes through an aperture or goes around an object, different parts of the wave can interfere and also give rise to a spatial alternation of large and small amplitude. Interference refers to the phenomenon of when two waves of the same kind overlap to give an alternating spatial variation of large and small wave amplitude. Interference and diffraction are characteristic phenomena of waves, ranging from water waves to electromagnetic waves such as light. Chen, PhD, Department of Physics & Astronomy, College of Science, Purdue University, West Lafayette, IN