DISPERSION & SCATTERING OF LIGHTlecture by PROF. ARDAMAN SIDHU : DISPERSION & SCATTERING OF LIGHTlecture by PROF. ARDAMAN SIDHU DISPERSION SCATTERING
DISPERSION & SCATTERING OF LIGHTL10/AS 30th,JULY,09 7.00 P.M. : DISPERSION & SCATTERING OF LIGHTL10/AS 30th,JULY,09 7.00 P.M. REFRACTION THROUGH PRISM.
DISPERSION OF LIGHT.
ANGULAR DISPERSION.
SCATTERING OF LIGHT.
NATURAL PHENOMENON DUE TO SUNLIGHT.
PRISM : PRISM A prism is a portion of a transparent medium bounded by two plane faces inclined to each other at a suitable angle.
REFRACTION THROUGH A PRISM : REFRACTION THROUGH A PRISM ABC is principal section of a prism with angle of prism = A.
A ray of light KL is incident on the face AB of the prism at . It bends towards the normal N1 O and is refracted along LM at .
The refracted ray LM is incident at on face AC of the prism. ,
which is the angle of deviation.
REFRACTION THROUGH A PRISM : REFRACTION THROUGH A PRISM ( sum of four angles of a quad. = 360°)
Using eqn. (2).
REFRACTION THROUGH A PRISM : REFRACTION THROUGH A PRISM It ? is refractive index of the material of the prism, then according to Snell’s law,
(when angles are small)
Derivation of Prism Formula : Derivation of Prism Formula The Fig. Shows the variation of angle of deviation ( with angle of incidence (i). When I is increased, decreases, reaches a minimum and increases again. For one value of there are two angles of incidence i1 and i2.
Derivation of Prism Formula : Derivation of Prism Formula However, at minimum deviation i.e.
the incident ray and the emergent ray are symmetrical with respect to the refracting faces. The refracted ray in the prism, in that case will be parallel to the base,
Result mathematically: From(4),
Derivation of Prism Formula : Derivation of Prism Formula Thus in the minimum deviation position
…(6)
This relation is called Prism formula. It is used for accurate determination of refractive index of a transparent medium.
DISPERSION OF LIGHT : DISPERSION OF LIGHT Dispersion of light is the phenomenon of splitting of a beam of white light into its constituent colours on passing through a prism. The band of seven colours so obtained is called the (visible) spectrum. The order of colours from the lower end of the spectrum is Violet (V), Indigo (I).
DISPERSION OF LIGHT : DISPERSION OF LIGHT Cause of dispersion. Each colour has its own characteristic wavelength (?).
According to Cauchy’s formula, refractive index (?) of a material depends on wavelength (?) of light as
…(7)
where A, B, C are constants.
DISPERSION OF LIGHT : DISPERSION OF LIGHT of material of prism is different for different colours.
For prisms of small refracting angle, we have shown that angle of deviation is
As of prism is different for different colours, therefore, different colours deviate through different angles on passing through the prism.
ANGULAR DISPERSION : ANGULAR DISPERSION Angular dispersion produced by a prism for white light is the difference in the angles of deviation of two extreme colours i.e., violet and red colours.
ANGULAR DISPERSION : ANGULAR DISPERSION If = deviation of violet colour
= deviation of red colour,
Then,
Angular dispersion = -
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ANGULAR DISPERSION : ANGULAR DISPERSION Now, the deviation through a thin prism of refracting angle A is
Angular dispersion,
Obviously, angular dispersion produced by a prism depends upon (i) angle of prism (ii) nature of material of the prism.
DISPERSIVE POWER : DISPERSIVE POWER The dispersive power of a prism is defined as the ratio of angular dispersion to the mean deviation produced by the prism. It is represented by
The mean deviation produced by the prism is
As dispersive power =
DISPERSIVE POWER : DISPERSIVE POWER Clearly, ? depends only on nature of material of the prism.
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SCATTERING OF LIGHT : SCATTERING OF LIGHT Most of the beautiful phenomena like Blue colour of sky, white colour of clouds, have been explained in terms of scattering of light.
SCATTERING OF LIGHT : SCATTERING OF LIGHT As sunlight travels through the earth’s atmosphere, it gets scattered by the large number of molecules present in the atmosphere. Scattering represents basically change in the direction of light.
SCATTERING : SCATTERING Scattering is different from reflection, where radiation is deflected in one direction, some particles and molecules found in the atmosphere have the ability to scatter solar radiation in all directions. The particles/molecules which scatter light are called scatterers and can also include particulates made by human industry.
SCATTERING : SCATTERING Scattering of light occurs when a beam of light is broken into several smaller, less intense beams of light by gases, aerosols, or particulates in the atmosphere.
TYPES OF SCATTERING : TYPES OF SCATTERING LORD RAYLEIGH was the first to deal with scattering of light from air molecules.
As intensity of scattered light (Is) varies directly as square of amplitude of scattered light (a2), therefore, i.e. intensity of scattered light varies inversely as the fourth power of the wavelength of incident light.
RAYLIEGH SCATTERING : RAYLIEGH SCATTERING Another important factor in scattering is relative size of the wavelength of light (?) and the size of scatterer ( of typical size, say, x). For x < < ?, Rayleigh scattering is valid, i.e.,when size of scatterer is much less than wavelength of light, .
BLUE SKIES : BLUE SKIES Selective scattering (or Rayleigh scattering) occurs when certain particles are more effective at scattering a particular wavelength of light. Air molecules, like oxygen and nitrogen for example, are small in size and thus more effective at scattering shorter wavelengths of light (blue and violet). The selective scattering by air molecules is responsible for producing our blue skies on a clear sunny day.
Blue colour of sky : Blue colour of sky is due to scattering of sunlight. Light from the sun, while traveling through earth’s atmosphere, gets scattered by large number of molecules in the earth’s atmosphere. The intensity of scattered light varies inversely as the fourth power of wavelength of light. As blue colour has a shorter wavelength than red, therefore, blue colour is scattered much more strongly.
Slide 26 : The blue color of the sky is caused by the scattering of sunlight off the molecules of the atmosphere. This scattering, called Rayleigh scattering, is more effective at short wavelengths (the blue end of the visible spectrum). Therefore the light scattered down to the earth at a large angle with respect to the direction of the sun's light is predominantly in the blue end of the spectrum.
SCATTERING : SCATTERING RAYLIEGH SCATTERING Rayleigh scattering can be considered to be elastic scattering since the photon energies of the scattered photons is not changed. RAMAN SCATTERING Scattering in which the scattered photons have either a higher or lower photon energy is called Raman scattering. Usually this kind of scattering involves exciting some vibrational mode of the molecules, giving a lower scattered photon energy, or scattering off an excited vibrational state of a molecule which adds its vibrational energy to the incident photon.
RED COLOUR OF SKY AT TIME OF SUNSET AND SUNRISE : RED COLOUR OF SKY AT TIME OF SUNSET AND SUNRISE
RED COLOUR OF SKY : RED COLOUR OF SKY During a sunset, light travels through more atmosphere (See the diagram at right).
Thus, as it travels through more atmosphere, the light is subjected to more and more gas molecules in the air.
Which scatter blue light, . So Blue is "scattered out" and the part of light that is left over is red, orange and yellow.
When the blue has been scattered out, even the clouds which scatter all colors, look reddish. The only color the clouds can reflect, is the color that shines on it. If blue is scattered out, only red will be reflected and scattered off of the clouds and in to your eyes.
BLACK SPACE : BLACK SPACE In space, the sky appears black, because space has no atmosphere to scatter the blue. Further, all of the colors of the sun reach your eye, and the sun appears white.
MIE SCATTERING : MIE SCATTERING But for x >> ?, Rayleigh scattering is not valid and all wavelengths are scattered nearly equally. Mie Scattering
The scattering from molecules and very tiny particles (< 1 /10 wavelength) is predominantly Rayleigh scattering. For particle sizes larger than a wavelength, Mie scattering predominates. This scattering produces a pattern like an antenna lobe, with a sharper and more intense forward lobe for larger particles.
Mie scattering is not strongly wavelength dependent and produces the almost white glare around the sun when a lot of particulate material is present in the air. It also gives us the the white light from mist and fog.
Slide 32 :
White colour of clouds : White colour of clouds Clouds contains large dust particles, water droplets, ice particles etc. In this case, size of scatterer x >> ?. Therefore, all wavelengths are scattered nearly equally. All colours scattered equally merge to give us the sensation of white. Hence clouds generally appears white.
Why Are Storm Clouds Gray? : Why Are Storm Clouds Gray? Clouds usually look gray when we are directly underneath them. This is because sunlight does not shine directly on the bottom of clouds, but rather shines through the tops of clouds.
Sunlight gets blocked more when the cloud is thicker. So the bottom of the cloud looks dark. If the cloud is thin, it may appear more white because there is less cloud matter to block sunlight.
If you are under a tall dark cloud, wait until it passes, and look at it's side. The side of the cloud will be illuminated by sunlight, and thus all white. So, the brightness of the cloud (white versus gray or black) has a lot to do with where you are standing and the thickness of the cloud.
SUMMARY – CLOUD COLOR : SUMMARY – CLOUD COLOR Sunlight reflects equally off of the water and ice particles that make up a cloud. This is called Mie Scattering, and it means that all wavelengths of sunlight reach your eyes, thus clouds are white.
1) Cloud color is due to Mie Scattering-This means that clouds scatter all wavelengths of light equally. All wavelengths of light = white color
2) Cloud brightness is due in part to where you are standing relative to the cloud.-If underneath a tall thick cloud, it looks gray, but from a side view it looks white
3) Cloud brightness also depends on the type of cloud -Thin clouds versus thick clouds
4) Cloud color also depends on the color of the light being reflected from the clouds-If a red light shines off the clouds, the clouds will look red
Slide 36 : For all your Physics Problems
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