University of South Carolina

PHYSICS AND THE VISUAL ARTS
Notes on LESSON 7


Things to remember from Lesson 7 and readings from chapter 6.

"White" light can be characterized by a color temperature corresponding to a black body radiator. Such a radiant source has a characteristic wavelength at which the intensity is a maximum. Call this wavelength λmax. The relationship between the wavelength of maximum intensity (λmax) and the absolute (thermodynamic) temperature T (in units of kelvins) is

(λmax)(T) = constant.

This relationship is known as Wien's law. Notice that increasing the temperature of a source results in a shorter lambda max, i.e. a bluer light. In addition a light source such as the sun, a lamp, or even the blue sky can be characterized by a temperature that we call the color temperature.

The overall radiated power of a black body radiator increases with the fourth power of the temperature T. That is,

Total radiated power = σeAT4,

where σ (sigma) is the Stefan-Boltzmann constant, e is the emissivity, a number between 0 and 1, and A is the surface area. This relationship is the Stefan-Boltzmann law. The Stefan-Boltzmann constant = 5.67 x 10-8 W/m2K4.

As the temperature of an object increases, eventually it becomes hot enough to begin to radiate in the visible. Here is an approximate color scale of temperatures. [Remember that the temperature in kelvins is equal to the temperature in degrees Celsius + 273.

Color of ObjectApprox. Temp (deg. C)
Incipient red500-550
Dark red650-750
Bright red850-950
Yellowish red1050-1150
Incipient white 1250-1350
White1450-1550



Remember the demonstration of the incandescent lamp that we did in the lecture. As the power to the lamp increased, the lamp grew hotter and brighter (Steffan-Boltzmann law) and as it grew hotter (brighter) more and more blue light could be seen in the spectrum. Consequently, the light grew whiter as the filament became hotter.

Approximate color temperature of common light sources

Light sourceColor Temperature (K)
Mercury arc6000
Daylight5500
Carbon arc5500
Cool white flourescent4200
Incandescent tungsten (3400 photoflood) 3400
Incandescent tungsten (3200 photoflood) 3200
Warm white fluorescent 3000
Incandescent tungsten (100 W) 2900
Incandescent tungsten (40 W) 2650
High pressure sodium arc2200


We discussed light measurement. The main points are:
  • Lumens is the measure of the light power emitted from a source. (The radiometric unit would be watts.) The number of lumens per watt depends on the sensitivity of the eye and is maximum of 683 lm at 555 nm.

  • The light power per solid angle is the luminous intensity. It is measured in units of lumens/steradian or candelas. The candela was chosen to give essentially the same luminous intensity as a candle. The candela is defined as the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 Hz and that has a radiant intensity of 1/683 watt/steradian. (The frequency of 540 x 1012 Hz corresponds to a wavelength of 555 nm.)

  • Illuminance is the density of light upon a surface. Illuminance has units of lumens/m2 = lux . An older unit for illuminance is the footcandle. One footcandle is more that 10 lux. In fact, the relationship is
    1 footcandle = 10.76 lux.

  • Efficacy of a light source is the ratio of the light emitted (flux in lumens) to the electrical power input (in watts). Thus the efficacy of a 60 W incandescent lamp that emits 870 lumens is
    efficacy = 870 lm/60 W = 14.5 lm/W.

  • Efficiency is the ratio of the light emitted as measured in watts to the input power. An approximation of the power out is given by dividing the output in lumens by 683 lm/W. The efficiency of a 60 W incandescent lamp is poor as it emits only about 870 lm which corresponds to 1.27 W. Thus only 2% of the electric energy used by the lamp is radiated as visible light!

    Some materials glow when exposed to visible light of short wavelengths or to ultraviolet radiation. This behavior is called fluorescence. In this process, light is absorbed and immediately reradiated, usually at a longer wavelength. The related behavior, phosphorescence, is a delayed fluorescence that persists after the illuminating UV is turned off.

    Experiments at the beginning of the twentieth century established that light behaves as a particle as well as a wave. The "particles" of light are called photons. Each photon carries an amount of energy given by
    E = hf,
    where h is Planck's constant = 4.136 x 10-15 eV-s and f is the frequency of the light.

    In the photoelectric effect, electrons are kicked out of a metal when the incident light energy (per photon) exceeds the binding energy, or work function, of the metal. Thus there is a threshhold wavelength for photoelectric emission. For longer wavelengths (and thus smaller energies) there is no effect. For wavelengths corresponding to the threshhold energy or shorter we do get photoeffect.

    When light is emitted by an atom the photon emerges with an energy corresponding to the difference in energy of the energy states of the atom before the photon is emitted and after the photon is emitted. Similarly, absorption takes place when a photon of just the right energy excites an atom from one energy state to another and the photon disappears. In the lecture you saw the emission lines from the mercury gas in a street light. There was a strong green line, a yellow line and a blue line visible. Then with the aid of fluorescent paper, you were able to see the presence of two invisible ultraviolet lines. These lines are the wavelengths of the discrete emissions of light by the mercury atoms as the atoms undergo an energy shift from an excited state to an unexcited (or at least less excited) energy state. The difference in energy between the states is the energy given to the photo when it emerges.

    The wavelength of the photon is obtained from the equation relating the energy to the frequency when we factor in the relationship between frequency and wavelength. The result is

    E = hc/wavelength.

    If the numbers are substituted for h and c and expressed in the proper units,the equation becomes

    E(eV) = 1240/wavelength(nm).

    Thus, if the wavelength in units of nanometers is divided into 1240, the resulting number is the energy in units of electron volts (eV).

    Lasers The word laser stands for light amplification by stimulated emission of radiation. Do you remember what stimulated emission is? Can you tell the requirements to have a laser? You need three things: an active medium, a pumping mechanism, and a resonant cavity. The pumping mechanism is the method to create an inverted population in the active medium. Can you tell what an inverted population is?
    How is stimulated emission different from spontaneous emission?

    One characteristic of laser light is that it is monochromatic. We say that the laser light is coherent. The light waves are not only of the same wavelength (monochromatic) but they all move in phase with each other. One observable effect is the "laser speckle" that was seen in the last lesson.

    Light emitting diodes (LEDs) are semiconductor diodes that have been specially prepared to emit light when a current is passed through them. The early LEDs were long wavelength (infrared or red) and emitted little luminous flux. In recent years the colors of LEDs have been extended to include orange, yellow, green, blue, and violet. Moreover, the luminous flux radiated has increased from a few lumens to 1000s of lumens. They are being used in outdoor signs, traffic signals, and as taillights on cars and trucks.

    Recently (in the May 2008 Photonics Spectra) there was a note on the development of LEDs for lighting with brightness on 900 lm at 10 W. These diodes have an efficacy of 90 lm/W which is much greater that that of a 60 W incandescent that emits 660 lm (11 lm/W) and 50% more than a compact fluorescent lamp (CFL) that emits 924 lm at 15 W for 61.6 lm/W.

    LEDs can be manufactured so that the semiconductor material becomes the resonant cavity needed to turn a simple light emitting diode into a laser diode. Laser diodes are used in laser pointers. If the pointers did not have a collimating lens, the beam would spread out rather than travel as a narrow beam. You can tell that the light from the pointers is laser light because of the "laser speckle."

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    Last Modified: 08/18/08