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source of visible light:

  • movement of an electron from one orbital to another results in a quantum of light given off with frequency related to the potential energy difference
    • sun, stars
    • hot bodies - see heat radiation
    • chemical reactions
    • artificial light sources:
      • thermal - light from incandescent solid contains all visible wavelengths, though in varying intensities
      • gas discharge - light by maintaining electric current in a gas at low pressure has its intensity in one or a few narrow bands
        • eg. low pressure mercury vapour ⇒ blueish + UV
        • fluorescent lamp - UV discharge from mercury, absorbed by fluorescent substances affixed to wall of lamp which re-emit the radiant energy with a shift into the visible range with the color dependent on the fluorescent substance (eg. calcium tungstate - blue; zinc silicate - green; cadmium borate - pink; or mixtures for white)
      • luminescent


  • a process in which a substance absorbs radiant energy & then immediately re-emits an appreciable part of it with its wavelengths longer than those absorbed.


  • in some materials, the molecules disturbed by the absorption of light do not immediately return to their original state, and the emission of light continues after the exciting radiation is removed, resulting in delayed fluorescence.

scattering of light by particles:

  • molecules in the air scatter light especially short wavelengths, and the scattered light is partly plane polarised
  • the Rayleigh effect:
    • the amount of scatter inversely proportional to the 4th power of the wavelength
  • this results in the short wavelengths being scattered most & thus a clear sky appears blue & as light near the horizon passes through more atmosphere, even more short wavelengths are scattered away from the rays & thus sunsets & sunrises are left with longer wavelengths visible resulting in orange sunsets & sunrises.
  • similarly, a projector beam when viewed from the side appears bluish. 


luminous flux (F):

  • the part of the radiant energy per unit time that is effective in producing the sensation of light
  • 1 lumen = luminous flux in a unit solid angle from a point source of 1 candle

luminous intensity:

  • luminous intensity of a point source (I) = luminous flux (F) / solid angle (w)
    • mean spherical luminous intensity = avg. intensity of a source measured in all directions 
    • total flux = 4pi * mean spherical luminous intensity
    • units: 1 candle = 1/60th the luminous intensity of a sq. cm of a black body radiator operated at 2046degK (freezing pt platinum)
  • luminance (B) (luminous intensity of an extended source):
    • luminance = luminous flux / (surface area of source * cos b * solid angle), b = angle from the normal to the source surface area
    • units: candles per of projected area (NB. 1 lambert = (1/pi) candle per sq. cm)
    • examples in candles per sq. metre:
      • surface of sun = 2 x 109; tungsten lamp filament at 2700degK = 107; white paper in sunlight = 25,000;
      • flourescent lamp = 6000; clear sky = 3200; white paper in moonlight = 0.03;


  • illuminance onto a surface (E) = luminous flux / surface area, (unit is lux = lumen per square meter = meter-candle)
    • for a point source, E = (I/s2)cos a
      • where I = luminous intensity, s = distance from source, a = angle of source from the perpendicular of the surface
      • hence, the intensity of sunlight is less in winter than summer as the angle from the zenith is greater, compounded by some atmospheric extinction as there is more atmosphere through which it must pass.
    • examples of lux of surfaces lit by:
      • bright sunlight 32,000 - 100,000 lux
      • daylight (not direct sun) 10,000 - 25,000 lux
      • 50-60W LED light at 1m - 4000-5000 lux
      • Icelight 2 LED light at 1m - 1700 lux
      • overcast day 1000 lux
      • sunrise on a clear day 400 lux
      • office lighting 320-500 lux
      • very dark overcast day 100 lux
      • toilet lighting 80 lux
      • living room lights 50 lux
      • end of civil twilight clear sky 3.4 lux
      • full moon on clear night 0.05-0.36 lux
  • efficiency of a light source:
  • efficiency = luminous flux / power consumption (ie. units are lumens per watt)
  • eg. tungsten lamps 10-16 lumen/watt; fluorescent lamps: 35-50 lumen/watt;



  • light from ordinary sources is unpolarised - its waves run in all planes perpendicular to the direction of the light
  • a polarising filter can be imagined as a grid of vertical lines which only allows through the waves that run in a plane parallel to the grid lines & blocking all other planes
  • when unpolarised light is reflected or refracted through glass, the reflected or refracted rays are partly plane-polarised
  • the angle of incidence, p, called the polarising angle, for which the polarisation of the reflected beam is complete is related to the index of refraction of the medium
    • Brewster's law:  tan p =  index of refraction
    • at the polarising angle (57deg for glass), none of the vibrations that lie in the plane of incidence is reflected, thus the reflected beam is plane polarised, but of relatively low intensity since only ~8% of the incident beam is reflected at the polarising angle.
    • the transmitted beam is not completely plane polarised at the polarising angle, unless many plates of glass are used, which also increases the intensity of the reflected polarised beam.
  • intensity of polarised beam:
    • Malus' law: intensity of polarised beam = intensity of incident beam * cos2 (angle of incidence)
  • double refraction:
    • when text is viewed through a crystal of calcite, two images of the text are visible, this is double refraction, 1st observed by Bartholinus in 1669.
    • Huygen's in 1690, observed that the rays which produced the two images were plane-polarised, in mutually perpendicular planes
    • unlike most optical materials we have experience with which are isotropic, calcite's crystal structure is a rhombohedron and thus when light falls obliquely on its surface, the light is split into two parts & both are refracted, with one ray having a constant index of refraction (the ordinary ray), whilst the 2nd ray is regarded as being an extraordinary ray as its index of refraction changes with the angle of incidence.
    • Nicol in 1832, used an artifice to separate these rays to give a single beam of plane-polarised light - the Nicol prism.
  • dichroic:
    • certain crystals (eg. tourmaline), known as dichroic, produce two internal beams polarised at right angles to each other & in addition, strongly absorb one beam while transmitting the other, although the transmitted light is colored.
    • Herapth in 1852, discovered that dichroic crystals of quinine iodosulphate (herapathite) transmit a beam as plane-polarised light with transmission close to the ideal 50% for all wavelengths of visible light
    • Land in 1929 invented a practical method for embedding the tiny synthetic crystals of herapathite (~1011 per in a transparent cellulosic film 0.001-0.004“ thick in uniform alignment which acted like a single huge crystal - the Polaroid sheet, with its ability to be bonded to glass, had the advantage of large size, low cost & polarising effectiveness approaching that of the Nicol prism except at the extremities of the spectrum.
    • more recently, Polaroid materials have been prepared by aligning molecules (eg. polymeric iodine in polyvinyl alcohol or polyvinylene) rather than tiny crystals, which have greater stability & freedom from scattered light.
    • when two Polaroid light polarisers are held in the line of vision in the crossed position, no light gets through & the field of view is dark. If a crystal of quartz or a tube of sugar solution is placed between these polarisers, the light reappears as these are optically active substances and rotate the plane of polarisation.
  • polarisation by scattering:
    • when a strong beam of light is passed through a region containing no fine particles, it is not visible from the side. If, however, the beam is intercepted by fine particles such as smoke, dust, colloidal suspensions, the beam is partly scattered, and becomes visible.
    • in this Tyndall effect, the color & intensity of the scattered light depend on the size of the particles.
    • very small particles scatter chiefly blue light, as the particles are made larger, the longer wavelengths are also scattered until the scattered light appears white.
    • scattered light is partly plane-polarised (hence the effectiveness of a photographic polarising filter in making the blue sky darker, which is maximal at 90deg. from the sun)
  • optically active substances:
    • materials that have the property of rotating the plane of polarisation while transmitting polarised light are called optically active substances.
    • polarimeters are instruments for measuring optical rotation.
  • photoelasticity:
    • certain materials such as glass become doubly refractive under mechanical strain. & when the material is placed between a crossed polariser & analyser, patterns of interference fringes can be observed & can be used for detecting strains in glassware, plastics, etc.
photo/light.txt · Last modified: 2017/08/08 12:43 by gary1