index of refraction
(noun)
For a material, the ratio of the speed of light in vacuum to that in the material.
Examples of index of refraction in the following topics:
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Refraction and Magnification
- Refraction occurs when light travels through an area of space that has a changing index of refraction.
- The simplest case of refraction occurs when there is an interface between a uniform medium with an index of refraction and another medium with an index of refraction.
- Some media have an index of refraction that varies gradually with position.
- This effect is what is responsible for mirages seen on hot days where the changing index of refraction of the air causes the light rays to bend creating the appearance of specular reflections in the distance (as if on the surface of a pool of water) .
- As the light is reflected off the pencil we see that, due to the different refraction indexes of water and air, the pencil appears to bend in the water.
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Dispersion: Rainbows and Prisims
- The angle of refraction depends on the index of refraction, as we saw in the Law of Refraction.
- We know that the index of refraction n depends on the medium.
- Since the index of refraction of water varies with wavelength, the light is dispersed, and a rainbow is observed.
- Since the index of refraction varies with wavelength, the angles of refraction vary with wavelength.
- A sequence of red to violet is produced, because the index of refraction increases steadily with decreasing wavelength.
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Dispersion of the Visible Spectrum
- The index of refraction is different for every medium that light travels through, as we learned in previous atoms.
- When a light ray enters a medium with a different index of refraction, the light is dispersed, as shown in with a prism.
- Since the index of refraction varies with wavelength, the light refracts at different angles as it exits, causing the exiting light rays to appear as a rainbow, or as a sequence of decreasing wavelengths, from red to violet.
- Since the index of refraction varies with wavelength, the angles of refraction vary with wavelength.
- A sequence of red to violet is produced, because the index of refraction increases steadily with decreasing wavelength.
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Polarization By Scattering and Reflecting
- First, lets remember the index of refraction of air and water:nair - 1.00nwater- 1.33 Now, we can apply Brewster's Equation and solve for θb: $tan heta_b= rac{n_water}{n_air}\tan heta_b= rac{1.33}{1.00}\tan heta_b=1.33\ heta_b=tan^{-1}1.33\ heta b=53.1^{ rc}$
- When light hits a reflective surface, the vertically polarized aspects of that light are refracted at that surface.
- Since the light is split into two, and part of it is refracted, the amount of polarization to the reflected light depends on the index of refraction of the reflective surface.
- where: θb = angle of reflection of complete polarization (also known as Brewster's angle); n1 = index of refraction of medium in which reflected light will travel; and n2 = index of refraction of medium by which light is reflected.
- Calculate angle of reflection of complete polarization from indices of refraction
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The Law of Refraction: Snell's Law and the Index of Refraction
- The change in the speed of light is related to the indices of refraction of the media involved.
- In mediums that have a greater index of refraction the speed of light is less.
- Snell's experiments showed that the law of refraction was obeyed and that a characteristic index of refraction n could be assigned to a given medium.
- This video introduces refraction with Snell's Law and the index of refraction.The second video discusses total internal reflection (TIR) in detail. http://www.youtube.com/watch?
- Formulate the relationship between the index of refraction and the speed of light
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Aberrations
- This happens because lenses have a different index of refraction for different wavelengths of light.
- The refractive index decreases with increasing wavelength.
- Since the index of refraction of lenses depends on color or wavelength, images are produced at different places and with different magnifications for different colors. shows chromatic aberration for a single convex lens.
- Since violet rays have a higher refractive index than red, they are bent more and focused closed to the lens. shows a two-lens system using a diverging lens to partially correct for this, but it is nearly impossible to do so completely.
- Different parts of a lens of a mirror do not refract or reflect the image to the same point, as shown in .
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The Speed of Light
- The speed at which light propagates through transparent materials (air, glass, etc.,) is dependent on the refractive index of that material, n:
- where v = actual velocity of light moving through the medium, c = speed of light in a vacuum, and n = refractive index of medium.
- The refractive index of air is about 1.0003, and from this equation we can find that the speed of visible light in air is about 90 km/s slower than c.
- Below is an example of an application of the constant c.
- Relate speed of light with the index of refraction of the medium
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The Lensmaker's Equation
- The lensmaker's formula is used to relate the radii of curvature, the thickness, the refractive index, and the focal length of a thick lens.
- In this case, we can not simply assume that a light ray is only refracted once while traveling through the lens.
- Instead the extent of the refraction must be dependent on the thickness of the lens.
- The lensmaker's formula relates the radii of curvature, the index of refraction of the lens, the thickness of the lens, and the focal length.
- The lensmaker's formula relates the radii of curvature, the index of refraction of the lens, the thickness of the lens, and the focal length.
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Phase-Contrast Microscopy
- Phase-contrast microscopy visualizes differences in the refractive indexes of different parts of a specimen relative to unaltered light.
- In phase-contrast microscopy, parallel beams of light are passed through objects of different densities.
- Light that is slightly altered by passing through a different refractive index is allowed to pass through.
- Light passing through cellular structures, such as chromosomes or mitochondria is retarded because they have a higher refractive index than the surrounding medium.
- Elements of lower refractive index advance the wave.
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Refraction
- Refraction is described by Snell's law, which states that for a given pair of media and a wave with a single frequency, the ratio of the sines of the angle of incidence θ1 and angle of refraction θ2 is equivalent to the ratio of phase velocities (v1/v2) in the two media, or equivalently, to the opposite ratio of the indices of refraction (n2/n1):
- In optics, refraction is a phenomenon that often occurs when waves travel from a medium with a given refractive index to a medium with another at an oblique angle.
- For example, a light ray will refract as it enters and leaves glass, assuming there is a change in refractive index.
- Understanding of refraction led to the invention of lenses and the refracting telescope.
- Air has a refractive index of about 1.0003, and water has a refractive index of about 1.33.