Interference and Wave Optics Lesson 36 by Owen Borville 1.14.2026
Wave optics describes the interaction of light with small objects or the wave characteristics of light. Wave characteristics are associated with the phenomena of interference and diffraction. Visible light is the type of electromagnetic wave to which our eyes respond and has a wavelength in the range of 380 to 760 nm.
For all electromagnetic waves in a vacuum: c = f λ where c = 3 x 10^8 m/s is the speed of light, f is the frequency of the electromagnetic wave, and λ is the wavelength in a vacuum.
The wavelength λn of light in a medium with index of refraction n is λn = λ/n. Its frequency is the same as in a vacuum.
Thomas Young's double slit experiment (1801) gave definite proof of the wave character of light. An interference pattern is obtained by the superposition of light from two slits. In double-slit diffraction, there is constructive interference when dsin θ = mλ (for m = 0, 1, -1, 2, -2, ...), where d is the distance between the slits, θ is the angle relative to the incident direction, and m is the order of the interference. There is destructive interference occurring when d sin θ = (m + 1/2) λ (for m = 0, 1, -1, 2, -2, ...).
Multiple-slit interference (N>2) produces principal and secondary maxima. When the number of slits is increased, the intensity of the principle maxima increases and the width decreases.
Thin film interference occurs between the light reflected from the top and bottom surfaces of a film. In addition to the path length difference, there can be a phase change. When light reflects from a medium having an index of refraction greater than that of the medium in which it is traveling, a 180 degree phase change (or a λ/2 shift) occurs.
The Michelson interferometer is an optical instrument that splits a beam of light into two paths, reflects them off mirrors, and recombines them to create interference patterns, allowing for extremely precise measurements of distance, wavelength, or refractive index changes by detecting shifts in these fringes. When the mirror in one arm of the interferometer moves a distance of λ/2 each fringe in the interference pattern moves to the position previously occupied by the adjacent fringe. The displacement measured by a Michelson interferometer is Δd = mλ0/2.
The distance from the central maximum to the mth bright fringe is ym = mλD/d
To improve microscope images, various techniques utilizing the wave characteristics of light have been developed and many of these enhance contrast with interference effects.
Wave optics describes the interaction of light with small objects or the wave characteristics of light. Wave characteristics are associated with the phenomena of interference and diffraction. Visible light is the type of electromagnetic wave to which our eyes respond and has a wavelength in the range of 380 to 760 nm.
For all electromagnetic waves in a vacuum: c = f λ where c = 3 x 10^8 m/s is the speed of light, f is the frequency of the electromagnetic wave, and λ is the wavelength in a vacuum.
The wavelength λn of light in a medium with index of refraction n is λn = λ/n. Its frequency is the same as in a vacuum.
Thomas Young's double slit experiment (1801) gave definite proof of the wave character of light. An interference pattern is obtained by the superposition of light from two slits. In double-slit diffraction, there is constructive interference when dsin θ = mλ (for m = 0, 1, -1, 2, -2, ...), where d is the distance between the slits, θ is the angle relative to the incident direction, and m is the order of the interference. There is destructive interference occurring when d sin θ = (m + 1/2) λ (for m = 0, 1, -1, 2, -2, ...).
Multiple-slit interference (N>2) produces principal and secondary maxima. When the number of slits is increased, the intensity of the principle maxima increases and the width decreases.
Thin film interference occurs between the light reflected from the top and bottom surfaces of a film. In addition to the path length difference, there can be a phase change. When light reflects from a medium having an index of refraction greater than that of the medium in which it is traveling, a 180 degree phase change (or a λ/2 shift) occurs.
The Michelson interferometer is an optical instrument that splits a beam of light into two paths, reflects them off mirrors, and recombines them to create interference patterns, allowing for extremely precise measurements of distance, wavelength, or refractive index changes by detecting shifts in these fringes. When the mirror in one arm of the interferometer moves a distance of λ/2 each fringe in the interference pattern moves to the position previously occupied by the adjacent fringe. The displacement measured by a Michelson interferometer is Δd = mλ0/2.
The distance from the central maximum to the mth bright fringe is ym = mλD/d
To improve microscope images, various techniques utilizing the wave characteristics of light have been developed and many of these enhance contrast with interference effects.