11.S: Interference (Summary)
Key Terms
| coherent waves | waves are in phase or have a definite phase relationship |
| fringes | bright and dark patterns of interference |
| incoherent | waves have random phase relationships |
| interferometer | instrument that uses interference of waves to make measurements |
| monochromatic | light composed of one wavelength only |
| Newton’s rings | circular interference pattern created by interference between the light reflected off two surfaces as a result of a slight gap between them |
| order | integer m used in the equations for constructive and destructive interference for a double slit |
| principal maximum | brightest interference fringes seen with multiple slits |
| secondary maximum | bright interference fringes of intensity lower than the principal maxima |
| thin-film interference | interference between light reflected from different surfaces of a thin film |
Key Equations
| Constructive interference | \(\Delta l = m\lambda\), for m = 0, ±1, ±2, ±3… |
| Destructive interference | \(\Delta l = (m + \frac{1}{2})\lambda\), for m = 0, ±1, ±2, ±3… |
| Path length difference for waves from two slits to a common point on a screen | \(\Delta l = d \, sin \, \theta\) |
| Constructive interference | \(d \, sin \, \theta = m \lambda\), for m = 0, ±1, ±2, ±3… |
| Destructive interference | \(d \, sin \, \theta = (m + \frac{1}{2})\lambda\), for m = 0, ±1, ±2, ±3… |
| Distance from central maximum to the m- th bright fringe | \(y_m = \frac{m\lambda D}{d}\) |
| Displacement measured by a Michelson interferometer | \(\Delta d = m \frac{\lambda_0}{2}\) |
Summary
3.1: Young's Double-Slit Interference
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Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0) .