oph 411 file

Upload: stanley-mwaila

Post on 07-Apr-2018

235 views

Category:

Documents


0 download

TRANSCRIPT

  • 8/6/2019 OPH 411 FILE

    1/17

    Why are clouds white?

    Clouds appear white because the light coming from the sun has to pass through thewater droplets and ice crystals or we can say that the seven colors of visible spectrum

    (red, orange, yellow, green, and blue, indigo, violet) which when combines forms whitelight and this process of combining isdone by water droplets or ice crystals present in

    theclouds. On the whole we can say that light is reflected in many ways which combinesto give white color. Mainlyclouds at a high altitude appear white and at that height water

    vapors are frozen and changed in ice crystals.

    Many times cloud alsoappears dark in color it is mainly because of its altitude andreflection of sunlight. Stormsclouds are thickestclouds. So when sunlight falls on them

    from above they soak the light altogether and very negligible light reaches to our eyes

    which give dark color to theclouds when we look at them from bottom but if we observethe sameclouds from above they will be pure white.

    Greyclouds are caused because of the shadow of higherclouds on the lowerclouds or

    theclouds are sometimes so dense that they cast their own shadow on the base whichgives them grey color. Darkclouds not always cause rain. More the droplets formed intheclouds more is the light absorbed in it. During sunsetclouds are orange or red because

    blue color of sunlight is scattered and light has to pass through thick layer of atmosphere

    and dust particles when sun is lowered in the west. Sometimes a cloudappears blue due tothe scattered blue light which makes the sky look blue.

    The most unusual color is green. When reddish light falls on the cloud having large

    amount of water droplets make them look green.

    CloudsWhat areclouds?

    A cloud is a large collection of very tiny droplets of water or ice crystals.

    The droplets are so small and light that they can float in the air.

    How areclouds formed?

    All air contains water, but near the ground it is usually in the form of aninvisible gas called water vapor. When warm air rises, it expands and cools.

    Cool air can't hold as much water vapor as warm air, so some of the vapor

    condenses onto tiny pieces of dust that are floating in the air and forms a

    tiny droplet around each dust particle. When billions of these droplets come

    together they become a visible cloud.

  • 8/6/2019 OPH 411 FILE

    2/17

    Why areclouds white?Clouds are white because they reflect the light of the sun. Light is made up

    of colors of the rainbow and when you add them all together you get white.

    The sunappears a yellow color because it sends out more yellow light than

    any other color.Clouds reflect all the colors the exact same amount so theylook white.

    Why do clouds turn gray?Clouds are made up of tiny water droplets or ice crystals, usually a mixture

    of both. The water and ice scatter all light, makingclouds appear white. If

    theclouds get thick enough or high enough all the light abovedoes not make it

    through, hence the gray or dark look. Also, if there are lots of otherclouds

    around, their shadow can add to the gray or multicolored gray appearance.

    With extreme weather, emergency preparedness is a necessity for your

    family. By taking special precautions and checking for hazards before a

    disaster strikes, you'll be much more likely to stay safe.

    Why do clouds float?

    A cloud is made up of liquid water droplets. A cloud forms when air is heatedby the sun. As it rises, it slowly cools it reaches the saturation point and

    water condenses, forming a cloud. As long as the cloud and the air that its

    made of is warmer than the outside air around it, it floats!

    Howdo clouds move?Clouds move with the wind. High cirrusclouds are pushed along by the jet

    stream, sometimes traveling at more than 100 miles-per-hour. Whenclouds

    are part of a thunderstorm they usually travel at 30 to 40 mph.

    Why do clouds form at different heights in the atmosphere?The characteristics ofclouds are dictated by the elements available,

    including the amount of water vapor, the temperatures at that height, the

    http://emergency-preparedness.com/http://emergency-preparedness.com/
  • 8/6/2019 OPH 411 FILE

    3/17

    wind, and the interplay of other air masses.

    How is fog formed?There are many different types of fog, but fog is mostly formed when

    southerly winds bring warm, moist air into a region, possibly ending a coldoutbreak. As the warm, moist air flows over much colder soil or snow, dense

    fog often forms. Warm, moist air is cooled from below as it flows over a

    colder surface. If the air is near saturation, moisture will condense out of

    the cooled air and form fog. With light winds, the fog near the ground can

    become thick and reduce visibilities to zero.

    (Graphic Credit: USA TODAY.)

    You need warm air!

    Southerly winds bring

    warm, moist air over cold

    ground or snow.

    Fog Forms! Moisture

    condenses into fog as air is

    cooled from below.

    Cloud ChartCloud Group Cloud Height Cloud Types

    HighClouds = Cirrus Above 18,000 feet

    Cirrus

    Cirrostratus

    Cirrocumulus

    MiddleClouds = Alto 6,500 feet to 18,000 feetAltostratus

    Altocumulus

    LowClouds = Stratus Up to 6,500 feet

    Stratus

    StratocumulusNimbostratus

    Clouds with Vertical GrowthCumulus

    Cumulonimbus

    SpecialClouds Mammatus

    Lenticular

  • 8/6/2019 OPH 411 FILE

    4/17

    Fog

    Contrails

    CirrusCloudsCirruscloudsare the most common of the highclouds. They are composed of

    ice and are thin, wispyclouds blown in high winds into long streamers.

    Cirrusclouds are usually white and predict fair to pleasant weather. By

    watching the movement of cirrusclouds you can tell from which direction

    weather is approaching. When you see cirrusclouds, it usually indicates that

    a change in the weather will occur within 24 hours.

    Cirrostratuscloudsare thin, sheetlike highclouds that often cover the entire

    sky. They are so thin that the sun and moon can be seen through them.

    Cirrostratusclouds usually come 12-24 hours before a rain or snow storm.

    Cirrocumuluscloudsappear as small, rounded white puffs that appear in long

    rows. The small ripples in the cirrocumulusclouds sometime resemble the

    scales of a fish. Cirrocumulusclouds are usually seen in the winter and

    indicate fair, but cold weather. In tropical regions, they may indicate an

    approaching hurricane.

    http://start%28%27cirrostratus.jpg%27%29/http://start%28%27cirrus.jpg%27%29/
  • 8/6/2019 OPH 411 FILE

    5/17

    "Alto"CloudsAltostratuscloudsare gray or blue-gray mid levelclouds composed of ice

    crystals and water droplets. Theclouds usually cover the entire sky. In the

    thinner areas of theclouds, the sun may be dimly visible as a round disk.

    Altostratusclouds often form ahead of storms with continuous rain or snow.

    Altocumuluscloudsare mid levelclouds that are made of water droplets and

    appear as gray puffy masses. They usually form in groups. If you see

    altocumulusclouds on a warm, sticky morning, be prepared to see

    thunderstorms late in the afternoon.

    StratusCloudsStratuscloudsare uniform grayishclouds that often cover the entire sky.

    They resemble fog thatdoesn't reach the ground. Light mist or drizzle

    sometimes falls out of theseclouds.

    http://start%28%27altocumulus.jpg%27%29/http://start%28%27altostratus.jpg%27%29/http://start%28%27cirrocumulus.jpg%27%29/
  • 8/6/2019 OPH 411 FILE

    6/17

    Stratocumuluscloudsare low, puffy and gray. Most form in rows with blue sky

    visible in between them. Rain rarely occurs with stratocumulusclouds,

    however, they can turn into nimbostratusclouds.

    Nimbostratusclouds form a dark gray, wet looking cloudy layer associated

    with continuously falling rain or snow. They often produce precipitation that

    is usually light to moderate.

    CumulusCloudsCumuluscloudsare white, puffyclouds that look like pieces of floating cotton.

    Cumulusclouds are often called "fair-weatherclouds". The base of each cloudis flat and the top of each cloud has rounded towers. When the top of the

    cumulusclouds resemble the head of a cauliflower, it is called cumulus

    congestus or towering cumulus. Theseclouds grow upward and they can

    develop into giant cumulonimbusclouds, which are thunderstormclouds.

    http://start%28%27nimbostratus.jpg%27%29/http://start%28%27stratocumulus.jpg%27%29/http://start%28%27stratus.jpg%27%29/
  • 8/6/2019 OPH 411 FILE

    7/17

    Cumulonimbuscloudsare thunderstormclouds. High winds can flatten the top

    of the cloud into an anvil-like shape. Cumulonimbusclouds are associated with

    heavy rain, snow, hail, lightning and even tornadoes. The anvil usually points in

    the direction the storm is moving.

    SpecialCloudsMammatuscloudsare low hanging bulges that droop from cumulonimbusclouds.

    Mammatusclouds are usually associated with severe weather.

    Lenticularclouds are caused by a wave wind pattern created by the

    mountains. They look like discs or flying saucers that form near mountains.

    http://start%28%27mammatus3a.jpg%27%29/http://start%28%27cumulonimbus.jpg%27%29/http://start%28%27cumulus.jpg%27%29/
  • 8/6/2019 OPH 411 FILE

    8/17

    Fog is a cloud on the ground. It is composed of billions of tiny water droplets

    floating in the air. Fog exists if the atmospheric visibility near the Earth's

    surface is reduced to 1 kilometer or less.

    Contrails are condensation trails left behind jet aircrafts. Contrails form

    when hot humid air from jet exhaust mixes with environmental air of low

    vapor pressure and low temperature. The mixing is a result of turbulence

    generated by the engine exhaust.

    GreenCloudsare often associated with severe weather. The green color is

    not completely understood, but it is thought to have something todo with

    having a high amount of liquid water drops and hail inside theclouds. In theGreat Plains region of the U.S. greenclouds are associated with storms likely

    http://start%28%27contrails.jpg%27%29/http://start%28%27fog.jpg%27%29/http://start%28%27lenticular1.jpg%27%29/
  • 8/6/2019 OPH 411 FILE

    9/17

    to produce hail and tornadoes.

    Radiation

    Laws

    The average or bulk properties of electromagnetic radiation interacting with matter

    are systematized in a simple set of rules called radiation laws. These laws apply when

    the radiating body is what physicists call a blackbody radiator. Generally, blackbody

    conditions apply when the radiator has very weak interaction with the surrounding

    environment and can be considered to be in a state of equilibrium. Although stars

    do not satisfy perfectly the conditions to be blackbody radiators, they do to a

    sufficiently good approximation that it is useful to view stars as approximate

    blackbody radiators.

    Planck Radiation Law

    The primary law governing blackbody radiation is thePlanck Radiation Law, which

    governs the intensity of radiation emitted by unit surface area into a fixed direction

    (solid angle) from the blackbody as a function of wavelength for a fixed

    temperature. The Planck Law can be expressed through the following equation.

    The behavior is illustrated in the figure shown above. The Planck Law gives a

    distribution that peaks at a certain wavelength, the peak shifts to shorter

  • 8/6/2019 OPH 411 FILE

    10/17

    wavelengths for higher temperatures, and the area under the curve grows rapidly

    with increasing temperature.

    The Wien and Stefan-Boltzmann Laws

    The behavior of blackbody radiation is described by the Planck Law, but we can

    derive from the Planck Law two other radiation laws that are very useful. The WienDisplacement Law, and the Stefan-Boltzmann Law are illustrated in the following

    equations.

    The Wien Law gives the wavelength of the peak of the radiation distribution, while

    the Stefan-Boltzmann Law gives the total energy being emitted at all wavelengths by

    the blackbody (which is the area under the Planck Law curve). Thus, the Wien Law

    explains the shift of the peak to shorter wavelengths as the temperature increases,

    while the Stefan-Boltzmann Law explains the growth in the height of the curve as

    the temperature increases. Notice that this growth is very abrupt, since it varies as

    the fourth power of the temperature.

    The following figure illustrates the Wien law in action for three different stars of

    quite different surface temperature. The strong shift of the spectrum to shorter

    wavelengths with increasing temperatures is apparent in this illustration.

  • 8/6/2019 OPH 411 FILE

    11/17

    For convenience in plotting these distributions have been normalized to unity at therespective peaks; by the Stefan-Boltzmann Law, the area under the peak for the hot

    star Spica is in reality 2094 times the area under the peak for the cool star Antares.

    Temperatures and Characteristic Wavelengths

    By the Planck Law, all heated objects emit a characteristic spectrum of

    electromagnetic radiation, and this spectrum is concentrated in higher wavelengths

    for cooler bodies. The following table summarizes the blackbody temperatures

    necessary to give a peak for emitted radiation in various regions of the spectrum.

    Some Blackbody Temperatures

    Region Wavelength

    (centimeters)

    Energy

    (eV)

    Blackbody Temperature

    (K)

    Radio > 10 < 10-5 < 0.03

    Microwave 10 - 0.01 10-5 - 0.01 0.03 - 30

    Infrared 0.01 - 7 x 10-5 0.01 - 2 30 - 4100

    Visible 7 x 10-5 - 4 x 10-5 2 - 3 4100 - 7300

    Ultraviolet 4 x 10-5 - 10-7 3 - 103 7300 - 3 x 106

    X-Rays 10-7 - 10-9 103 - 105 3 x 106 - 3 x 108

    Gamma Rays < 10-9 > 105 > 3 x 108

  • 8/6/2019 OPH 411 FILE

    12/17

    Blackbody radiation corresponds to radiation from bodies in thermal equilibrium.

    We will consider later the emission of non-thermal radiation, which doesn't follow a

    blackbody law. Such radiation is often produced by violent collisions rather than

    equilibrium heating. For example, in astrophysical environments radiation at the

    long and short wavelength ends of the above table is more likely to be produced by

    non-thermal processes.

    Java Virtual Experiments: Blackbody Radiation

    Here are three Java applets illustrating some important properties of blackbody

    radiation.

    The Planck Law

    Wien's Law, Stefan-Boltzmann Law, and Color Indices

    BlackBody: The Game!

    RADIATION

    Radiation is energy that comes from a source and travels through some material or throughspace. Light, heat and sound are types of radiation. The kind of radiation discussed in thispresentation is called ionizing radiation because it can produce charged particles (ions) in matter.

    Ionizing radiation is produced by unstable atoms. Unstable atoms differ from stable atomsbecause they have an excess of energy or mass or both.

    Unstable atoms are said to be radioactive. In order to reach stability, these atoms give off, oremit, the excess energy or mass. These emissions are called radiation. The kinds of radiation areelectromagnetic (like light) and particulate (i.e., mass given off with the energy of motion).Gamma radiation and X-rays are examples of electromagnetic radiation. Betaandalpha radiationare examples of particulate radiation. Ionizing radiation can also be produced by devices such asX-ray machines.

    A scale heightis a term often used in scientific contexts for a distance over which a

    quantity decreases by a factor ofe (the base ofnatural logarithms). It is usually denoted

    by the capital letterH.

    For planetary atmospheres, it is the vertical distance upwards, over which thepressure oftheatmosphere decreases by a factor ofe.The scale height remains constant for a

    particular temperature. It can be calculated by:-

    where:

    http://csep10.phys.utk.edu/astr162/lect/light/planck.htmlhttp://csep10.phys.utk.edu/astr162/lect/light/wien.htmlhttp://csep10.phys.utk.edu/astr162/lect/light/blackbody.htmlhttp://orise.orau.gov/reacts/guide/gamma.htmhttp://orise.orau.gov/reacts/guide/beta.htmhttp://orise.orau.gov/reacts/guide/beta.htmhttp://orise.orau.gov/reacts/guide/alpha.htmhttp://orise.orau.gov/reacts/guide/alpha.htmhttp://www.answers.com/topic/e-mathematical-constanthttp://www.answers.com/topic/e-mathematical-constanthttp://www.answers.com/topic/natural-logarithmhttp://www.answers.com/topic/pressurehttp://csep10.phys.utk.edu/astr162/lect/light/planck.htmlhttp://csep10.phys.utk.edu/astr162/lect/light/wien.htmlhttp://csep10.phys.utk.edu/astr162/lect/light/blackbody.htmlhttp://orise.orau.gov/reacts/guide/gamma.htmhttp://orise.orau.gov/reacts/guide/beta.htmhttp://orise.orau.gov/reacts/guide/alpha.htmhttp://www.answers.com/topic/e-mathematical-constanthttp://www.answers.com/topic/natural-logarithmhttp://www.answers.com/topic/pressure
  • 8/6/2019 OPH 411 FILE

    13/17

    k= Boltzmann constant = 1.38 x 1023 JK1

    T= mean planetary surface temperatureinkelvins

    M= mean molecular mass of dry air (units kg)

    g= acceleration due togravity on planetary surface (m/s)

    The pressure at the Earth's surface (or at higher levels) is a result of the weight of theoverlyingatmosphere [force per unit area]. If at a height ofztheatmosphere hasdensity

    and pressureP, then moving upwards at aninfinitesimally small height dzwill decreasethe pressure by amount dP, equal to the weight of a layer ofatmosphere of thickness dz.

    Thus:

    wheregis used to denote the acceleration due to gravity. For small dzit is possible to

    assumegto be constant; the minus signindicates that as the heightincreases the pressuredecreases. Therefore using the equation of statefor anideal gas of mean molecular massMat temperature T, the density can be expressed as such:

    Therefore combining the equations gives

    which can then beincorporated with the equation forHgiven above to give:

    which will not change unless the temperature does.Integrating the above and assumingwhereP0 is the pressure at heightz= 0 (pressure atsea level) the pressure at heightzcan

    be written as:

    This translates as the pressure decreasing exponentially with height.[3]

    In the Earth'satmosphere, the pressure at sea levelP0 averages about 1.01105Pa, the

    mean molecular mass of dry air is 28.964u and hence 28.964 1.6601027 =4.8081026 kg, andg= 9.81 m/s. As a function of temperature the scale height of the

    http://www.answers.com/topic/boltzmann-constanthttp://www.answers.com/topic/temperaturehttp://www.answers.com/topic/kelvinhttp://www.answers.com/topic/kelvinhttp://www.answers.com/topic/molecular-masshttp://www.answers.com/topic/accelerationhttp://www.answers.com/topic/gravityhttp://www.answers.com/topic/gravityhttp://www.answers.com/topic/densityhttp://www.answers.com/topic/densityhttp://www.answers.com/topic/g-1http://www.answers.com/topic/g-1http://www.answers.com/topic/equation-of-statehttp://www.answers.com/topic/equation-of-statehttp://www.answers.com/topic/ideal-gashttp://www.answers.com/topic/ideal-gashttp://www.answers.com/topic/sea-levelhttp://www.answers.com/topic/sea-levelhttp://www.answers.com/topic/exponential-decayhttp://www.answers.com/topic/scale-height#cite_note-iapetus_1-2http://www.answers.com/topic/upper-atmospherehttp://www.answers.com/topic/atomic-mass-unithttp://www.answers.com/topic/atomic-mass-unithttp://www.answers.com/topic/boltzmann-constanthttp://www.answers.com/topic/temperaturehttp://www.answers.com/topic/kelvinhttp://www.answers.com/topic/molecular-masshttp://www.answers.com/topic/accelerationhttp://www.answers.com/topic/gravityhttp://www.answers.com/topic/densityhttp://www.answers.com/topic/g-1http://www.answers.com/topic/equation-of-statehttp://www.answers.com/topic/ideal-gashttp://www.answers.com/topic/sea-levelhttp://www.answers.com/topic/exponential-decayhttp://www.answers.com/topic/scale-height#cite_note-iapetus_1-2http://www.answers.com/topic/upper-atmospherehttp://www.answers.com/topic/atomic-mass-unit
  • 8/6/2019 OPH 411 FILE

    14/17

    Earth'satmosphere is therefore 1.38/(4.8089.81)103= 29.26 m/deg. This yields the

    following scale heights for representative air temperatures.

    T= 290 K,H= 8500 mT= 273 K,H= 8000 m

    T= 260 K,H= 7610 mT= 210 K,H= 6000 m

    These figures should be compared with the temperature and density of theEarth'satmosphere plotted atNRLMSISE-00, which shows the air density dropping from

    1200 g/m3 at sea level to 0.53 = .125 g/m3at 70 km, a factor of 9600,indicating an average

    scale height of 70/ln(9600) = 7.64 km, consistent with theindicated average air

    temperature over that range of close to 260 K.

    Note:

    1. Density is related to pressure by the ideal gaslaws. Therefore with somedepartures caused by varying temperaturedensity will also decrease

    exponentially with height from a sea level value of0 roughly equal to 1.2 kg m3

    2. At heights over 100 km, moleculardiffusion means that each molecular atomic

    species has its own scale height.

    inertial forceAn apparent force that appears to affect bodies within a non-inertial

    frame, but is absent from the point of view of an inertial frame.

    Centrifugal forces and Coriolis forces, both observed in rotatingsystems, are inertial forces. Inertial forces are proportional to the

    body's mass.

    Homogeneneous and heterogeneous nucleation

    The main difference between the treatment of homogeneous andheterogeneous nucleation is the geometry of the system. The classicaltheory of homogeneous nucleation treats the forming droplet as aspherical object. In the heterogeneous case the forming embryo isconsidered to be part of a sphere attached to the substrate surface. As

    in the homogeneous case, the cluster is thought to consist ofincompressible, uniform liquid.

    The shape of the cluster is a part of a sphere with the base attachedto the insoluble surface. The angle between the embryo surface andthe substrate surface is called the contact angle. The critical radius inheterogeneous nucleation is the same as in homogeneous nucleation,as it only depends on the vapor super saturation.

    http://www.answers.com/topic/nrlmsise-00http://www.answers.com/topic/ideal-gashttp://www.answers.com/topic/diffusion-5http://www.answers.com/topic/nrlmsise-00http://www.answers.com/topic/ideal-gashttp://www.answers.com/topic/diffusion-5
  • 8/6/2019 OPH 411 FILE

    15/17

    Diamond and Graphite

    Graphite and diamond are two of the most interesting minerals. They are identicalchemicallyboth are composed of carbon (C), but physically, they are very different.

    Minerals which have the same chemistry but different crystal structures are calledpolymorphs.

    When you look at graphite and diamond, it is hard to imagine that they are identicalchemically, for they are so different physically. Graphite is opaque and metallic- to

    earthy-looking, while diamonds are transparent and brilliant. (See examples on display.)

    Another important physical difference is their hardness. The hardness of minerals is

    compared using the Mohs Hardness Scale, a relative scale numbered 1 (softest) to 10(hardest). Graphite is very soft and has a hardness of 1 to 2 on this scale. Diamonds are

    the hardest known natural substance and have a hardness of 10. No other naturally

    occurring substance has a hardness of 10. The crystal structure of graphite yields physicalproperties that permit the use of graphite as a lubricant and as pencil lead. The gem and

    industrial properties of diamond, physical properties that we cherish and exploit, are also

    a result of diamond's crystal structure.

    The reason for the differences in hardness and other physical properties can be explainedwith the molecular models below. In graphite, the individual carbon atoms link up to

    form sheets of carbon atoms. Each sheet of carbon atoms is translated (offset) by one-half

    of a unit such that alternate sheets are in the same position. Within each sheet every

    carbon atom is bonded to three adjacent carbon atoms that lie at the apices of equilateraltriangles. This produces hexagonal rings of carbon atoms. Each carbon atom has four

    valence electrons available to participate in the formation of chemical bonds. Three ofthese electrons are used in forming strong covalent bonds with the adjacent atoms in thesheet. Covalent bonds are a type of chemical bond in which electrons are shared between

    atoms. The fourth electron is free to wander over the surface of the sheet making graphite

    an electrical conductor. The spacing between the sheets of carbon atoms is greater thanthe diameter of the individual atoms. Weak bonding forces called van der Waals forces

    hold the sheets together. Because these forces are weak, the sheets can easily slide past

    each other. The sliding of these sheets gives graphite its softness for writing and itslubricating properties.

    In diamonds, each carbon atom is strongly bonded to four adjacent carbon atoms located

    at the apices of a tetrahedron (a three-sided pyramid). The four valence electrons of each

    carbon atom participate in the formation of very strong covalent bonds. These bonds havethe same strength in all directions. This gives diamonds their great hardness. Since there

    are no free electrons to wander through the structure, diamonds are excellent insulators.

    The brilliance and "fire" of cut diamonds is due to a very high index of refraction (2.42)

    and the strong dispersion of light; properties which are related to the structure ofdiamonds.

  • 8/6/2019 OPH 411 FILE

    16/17

    Derivation of Lamkberts law for the attenuation of solarradiation by the atmosphere.

    The derivation is quite simple in concept. There are many details, so think of this firstparagraph as a conceptual overview. Divide the absorbing sample into thin slices that are

    perpendicular to the beam of light. The light that emerges from a slice is slightly lessintense than the light that entered because some of the photons have run into molecules inthe sample and did not make it to the other side. For most cases where measurements of

    absorption are needed, a vast majority of the light entering the slice leaves without being

    absorbed. Because the physical description of the problem is in terms of differences---

    intensity before and after light passes through the slice---we can easily write an ordinarydifferential equation model for absorption. The difference in intensity due to the slice of

    absorbing material dIis reduced; leaving the slice, it is a fraction of the light enteringthe sliceI. The thickness of the slice is dz, which scales the amount of absorption (thin

    slice does not absorb much light but a thick slice absorbs a lot). In symbols, dI= Idz,

    ordI/ dz= I. This conceptual overview uses to describe how much light isabsorbed. All we can say about the value of this constant is that it will be different foreach material. Also, its values should be constrained between -1 and 0. The following

    paragraphs cover the meaning of this constant and the whole derivation in much greater

    detail.

    Assume that particles may be described as having an absorption cross section (i.e. area),, perpendicular to the path of light through a solution, such that a photon of light is

    absorbed if it strikes the particle, and is transmitted if it does not.

    Definezas an axis parallel to the direction that photons of light are moving, andA and dz

    as the area and thickness (along thezaxis) of a 3-dimensional slab of space throughwhich light is passing. We assume that dzis sufficiently small that one particle in the slab

    cannot obscure another particle in the slab when viewed along thezdirection. The

    concentration of particles in the slab is represented byN.

    It follows that the fraction of photons absorbed when passing through this slab is equal tothe total opaque area of the particles in the slab, AN dz, divided by the area of the slabA,

    which yields N dz. Expressing the number of photons absorbed by the slab as dIz, and

    the total number of photons incident on the slab asIz, the fraction of photons absorbed bythe slab is given by

    Note that because there are fewer photons which pass through the slab than are incident

    on it, dIz is actually negative (It is proportional in magnitude to the number of photonsabsorbed).

    The solution to this simple differential equation is obtained by integrating both sides to

    obtainIz as a function ofz

  • 8/6/2019 OPH 411 FILE

    17/17

    The difference of intensity for a slab of real thickness isI0 atz= 0, andIl atz=. Using

    the previous equation, the difference in intensity can be written as,

    rearranging and exponentiating yields,

    This implies that

    and

    The derivation assumes that every absorbing particle behaves independently with respect

    to the light and is not affected by other particles. Error is introduced when particles arelying along the same optical path such that some particles are in theshadow of others.

    This occurs in highly concentrated solutions. In practice, when large absorption values

    are measured, dilution is required to achieve accurate results. Measurements of

    absorption in the range ofI1 /I0 = 0.1 to 1 are less affected by shadowing than othersources of random error. In this range, the ODE model developed above is a good

    approximation; measurements of absorption in this range are linearly related toconcentration. At higher absorbances, concentrations will be underestimated due to this

    shadow effect unless one employs a more sophisticated model that describes the non-

    linear relationship between absorption and concentration