Light. Light Transmission Thin Films & Thin Films Interference Luminosity Polarized Light Planck’s Constant Coherent Light Lasers Holograms Luminous Flux Illuminance Luminous Intensity Luminous Flux vs. Power Luminous vs. Illuminated. Wave Vs. Particles Electromagnetic Waves
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For centuries the nature of light was disputed. In the 17th century, Isaac Newton proposed the “corpuscular theory” stating that light is composed of particles. Other scientists, like Robert Hooke and Christian Huygens, believed light to be a wave. Today we know that light behaves as both a wave and as a particle. Light undergoes interference and diffraction, as all waves do, but whenever light is emitted, it is always done so in discreet of packets called photons. These photons carry momentum, but not mass.
Light is an electromagnetic wave. As light travels through space an electric field and a magnetic field oscillate perpendicular to the wave direction and perpendicular to each other. We’ll learn more about these fields in later units. A light wave is transverse rather than longitudinal, since each field oscillates in a plane perpendicular to the direction of the wave. Unlike a pulse traveling down a length of rope, nothing is physically moving in a light wave. Light requires no medium! It can travel through space that contains matter (such as air, glass, or water) or through a vacuum.
If light did need a medium in order to propagate, the earth would spend its days submerged in darkness and the sun would not be visible.
Electric and magnetic fields affect charges. Light is an electric field coupled with a magnetic field. The two fields oscillate together but in different planes. To visualize an electromagnetic wave, you must think in 3-D. Let’s put a light wave together one piece at a time.
Above is a set of 3-D coordinate axes. The z-axis is vertical, the y-axis is horizontal, and the x-axis is coming out toward you.
The red wave represents an oscillating electric field in they-zplane. (Every point on this curve has an x coordinate of zero.) It is a snapshot in time. At the crests and troughs, the electric field will exert the greatest force on a charge, but in opposite directions. Charges located at the y-intercepts will experience no electric force (at this point in time).
In the top right picture, the blue wave represents an oscillating magnetic field in the x-y plane. (Every point on this curve has an z coordinate of zero.) It is a snapshot in time. Like the electric field, the magnetic field is strongest at the crests and troughs.
Bottom right is shown an electric and a magnetic field oscillating together. This is an electro-magnetic wave (light). The fields travel through space together. They have the same period and wavelength, but they oscillate in two different planes, which are perpendicular to each other. The electric field, the magnetic field, and the wave direction are all mutually perpendicular. For some additional pictures, check out these links below. Remember, what you’re seeing is just a snapshot in time (see animation).
Wave PicLight animation
Propagation in matter
Oscillating charge animation
The frequency of a light wave corresponds to the color we see. The amplitude corresponds to brightness.
The frequency of visible light is extremely high compared to that of audible sound. Red light, for example, is the lowest frequency of visible light, but even red light has a frequency of over 400 trillion Hertz. This means if you’re looking at a red light, over 400 trillion full cycles of red light enter your eye every second! The frequency of violet light is even higher—over 750 trillion Hz. Other types of electromagnetic radiation, like X-rays, have even higher frequencies, and some have lower frequencies, like radio waves. Just as our ears are only capable of hearing certain range of sounds (20 – 20,000 Hz), our eyes can only see a small range of frequencies.
Because visible light waves have such high frequencies, their wave-lengths are very short. Recall the formula v = f (wave speed = wavelength frequency). Since light of any frequency always travels at the same speed in a vacuum, vis a constant. Thus, the biggerf is, the smallermust be. Red light, for example, has a wavelength of only about 700nm. (1nm = 1 nanometer = 10-9m = 1 billionth of a meter.) Violet light has an even smaller wavelength, since its frequency is higher. X-rays have still smaller wavelengths. Radio waves can have very long wavelengths (many meters) since their frequencies are so low.
Because Jupiter is farther from the sun, it moves much slower around the sun (recall Kepler’s third law). During the six-month period depicted above, Earth is moving away from Jupiter. Therefore, the light carrying the information of the eclipse took a little longer to reach Earth, since Earth was “running away” from that light. At the end of the six months, the light from Io had to travel an extra distance about equal to the diameter of Earth’s orbit. Roemer’s observed that Io eclipses were about 8 minutes behind schedule after six months. Knowing approximately Earth’s orbital diameter, Roemer calculated the speed of light at around 125,000 miles per second! Roemer’s speed, as great as it was, was actually an underestimate. The true speed of light is just a half a smidgeon under 3 · 108 m/s, which is about 186,300 miles per second! We call this speedc. c = 2.9979108 m/s 3108 m/s
Albert Michelson is best known for an experiment he did with Edward Morely in 1887. At the time it wasn’t understood that light needed no medium through which to travel. It was proposed that light traveled through an invisible “ether” in space. The Michelson-Morely experiment was an attempt to detect Earth’s motion through the ether. Here’s how it worked: First imagine you’re standing still outside and there is a wind coming from the north. If you run north, you’ll measure a greater wind speed. If you run south, you’ll measure it slower. Whether you run north or south, though, you’ll still feel the wind coming from the north. If you run east or west, however, not only will the wind seem to change speed, so will its direction.
Now imagine a race between two equally fast swimmers. They each go the same distance in a river, but one goes upstream and back while the other goes directly across the river and back. With no current the race would definitely be a tie, since their speeds and distances are the same. With a current, however, the cross-stream swimmer will win. This is not obvious. You should try to prove this. For a hint see the “river crossing--relative velocities” slide from the presentation on vectors. It involves the same principle as Michelson’s interferometer (but without lasers).
Michelson built something called an interferometer to try to measure a change in the speed of light in two different directions. The Earth moving through the ether around the sun is analogous to a wind or current. Instead of racing two swimmers, Michelson raced beams of light. Light was shone onto a mirror that allowed half of it to pass through. Each beam traveled the same distance before being reflected back and allowed to recombine. Based on the interference pattern of the combined waves, Michelson should have been able to detect a winner. But no matter how the experiment was done, the race was always a tie. This eventually forced physicist to abandon the ether theory. Einstein resolved the problem in 1905 with his theory of special relativity. In it he asserts that the speed of light is the same no matter how fast or which way an observer is moving.
It is important to emphasize just how fast light is. Compared to light, sound is a snail. A wise person once said, “Light travels faster than sound, which is why some people appear bright until you hear them speak.” Have you ever watched a baseball game from a distance? You see the batter make contact with the ball, but the sound of the wallop is delayed. This is because, although sound is really fast, light is super-duper fast. For all practical purposes, when you see something is when it happened (at least for events here on Earth). You can determine how far away a lightning strike is by counting seconds from the time you see the lightning until you hear the thunder. It takes sound about 5 s to travel a mile, so if the thunder lags behind the lightning by 2 or 3 s, then the lightning strike occurred about half a mile away.
Problem:You hear a thunder clap 6 s after you see the lightning. Assume the speed of sound to be 343 m/s. How far away is the lightning?
(Solution on next slide)
Answer: Ignoring the small amount of time light needs to travel to you, we have:
d = v t = (343 m/s) (6 s) = 2058 m
Problem: Now let’s do the same problem without ignoring light’s travel time:
Solution on next slide
We can’t always ignore the time light takes to travel. Whenever you look into the night sky, for example, you’re really looking back into time. The stars you see are so far away that the light they emit takes years to reach us. Nearby stars are tens or hundreds light-years away. A light-year is the distance light travels in one year, almost 6 trillion miles. (Our sun is only about 8 light-minutes away).
Problem: Schmedrick is on a space journey heading toward Alpha Centauri, the nearest star excluding the sun, which is about 4.3 light-years away. Schmedrick\'s rocket goes a constant 0.03c (3% of the speed of light). As he passes Alpha Centauri he sends a radio message back to Earth and continues traveling away from Earth. The Earthlings reply immediately. How long must Schmedrick wait for his reply?
Solution on next slide
Answer: Since we know a trip back and forth from Alpha Centauri takes a total of 8.6 years, we can set up our equation in the following way:
d = vt(c = 1 in light years per year)
8.6 + vt = ct
8.6 + 0.03 ct = ct
8.6 + 0.03t = t
8.6 = 0.97t
8.6 / 0.97 = 8.87
Schmedrick will have to wait 8.87 yearsto get a reply back from earth.
Links: Find out more about Alpha Centauri here.
Visible light is a combination of many wavelengths (colors), which give it a white appearance. When light hits an object certain wavelengths are reflected and others are absorbed. The reflected wavelengths are the ones we see and determine the color of an object.
In the first picture the tomato absorbs blue and green wavelengths and reflects the red wavelength. In the second picture red light is shone upon the tomato. The tomato is still reflecting the red wavelength and thus still looks red. But in the 3rd picture blue light is shone upon the tomato, and since the tomato absorbs the blue wavelength the tomato appears to be black.
Links: Prism (light broken down in different wavelengths.
The primary light colors are Red, Blue, and Green (RGB).
The secondary light colors are Yellow, Cyan, and Magenta.
Combining pigments in painting is exactly the opposite:
The primary pigments are Yellow, Cyan, Magenta.
The secondary pigments are Red, Blue and Green.
Primary colors in light are red, green, and blue because when put together in the right intensities they form white light. Televisions use this idea to project pictures on the screen. When lights these colors are combined in pairs they form the secondary colors for light.
Pigment colors are seen by reflected light. A primary pigment color is one that absorbs only one primary light color and reflects the other two primary colors. Thus yellow, magenta, and cyan are the primary colors for pigments. Yellow reflects red & green, cyan reflects green & blue, and magenta reflects red & blue. Secondary pigments colors then are blue, green, and red because they absorb two primary light colors and reflect their own light color back.
The electromagnetic spectrum covers a wide range of wavelengths and photon energies. Visible light ranges from 400 to 700 nanometers. About 550 nanometers, which is a yellowish green, is the wavelength to which our eyes are most responsive. Only a small portion of the electromagnetic spectrum is visible to us. The smaller the wavelength, the more energy each photons of the light has.
Wavelengths other that visible light serve useful purposes:
Radio waves are very long (a few centimeters to 6 football fields) and can be used to send signals. These signals are transmitted by radio stations. They transmit information and music via amplitude modulation (AM) and frequency modulation (FM).
Microwaves (a few millimeters long) are also used in communications. Microwave ovens are great for heating food since food is primarily water, and microwaves have just the right frequency to get water molecules vibrating.
Infrared (micrometers in length) are used in remote controls to change the channel, and they are also radiated by objects that are warmer than their surrounding (like your body). They make night vision equipment possible.
Ultraviolet light is harmful to our bodies because its wavelength is so small. Short wavelength mean high energy for photons. UV causes our skin to tan and burn. Fortunately, the ozone layer blocks most UV radiation, but prolonged exposure to the sun should be avoided, since UV rays can cause skin cancer. On the positive side UV radiation helps people to produce their own vitamin D.
X-rays are even more energetic, and hence more dangerous, than UV rays, but luckily they cannot penetrate our ozone layer. They are produced in space and of course are used by doctors to get pictures of your bones.
Gamma rays are the most energetic of the light waves and little is known about them other than they are very harmful to living cells and are used by doctors to kill certain cells and for other operations. They are produced in nuclear explosions. Like other high energy rays, our atmosphere protects us from gamma rays.
Astronomers have many different types of telescopes at their disposal to observe the universe in all parts of electromagnetic spectrum. Some telescopes are ground-based; others are space-based:
Parallax is any alteration in the apparent position of an object due to a change in the position of the observer. A simple demonstration of this effect can be seen by extending your thumb at arm’s length. Then close one eye at a time and note how your thumb appears to jump left and right relative to the background. Now move your thumb closer and note how the jump is greater. This technique can be used in astronomy to find a star’s distance from Earth. For distant objects like stars, astronomers must move their “eyes” as far apart as possible. They accomplish this by observing the apparent displacement of a star against the background of more distant stars resulting from the change of the Earth’s position in orbit. The parallax angle is exaggerated in the picture below.
The picture is not to scale. The diameter of Earth’s orbit is very small compared to the distance of the star being measured, which in turn is very small compared to the distance of the background stars. For this reason the angular displacement of points A and B, as seen from Earth at any point in its orbit, is almost exactly the same as the parallax angle.
Problem: Back on Earth Schmedrick attempts to figure out how far away a certain distant star is. He figures out a 2 degree parallax angle from two different observations made during the earth’s period. How far away is the star? (Earth 93 million miles from the sun.)
Solution on next slide.
Answer: Let R be the Earth-sun distance and x the distance to the star in question. Thus,
tan(/2) = R/ x.With = 2 and R = 93 million miles,
x 5.33109 miles
The Star Schmedrick is looking at is approximately 5 billion miles away. So, Schmed must have been imagining this star, because it’s much too close for any real life star (other than the sun).
A luminous object is a body that produces its own light such as the sun or a light bulb.
An illuminated object is a body that reflects light, just like the moon, people, and buildings.
Some objects, like water and glass, transmit light to some extent. In order to be seen, light must come from an object one way or the other.
Luminosity is the rate at which energy of all types, and in all directions, is radiated by an object. The luminosity of a star depends on its size and its temperature: L R 2T 4. The sun is a medium-sized star with a luminosity of 3.8×1026 J/s. The known luminosities of stable stars range from about a millionth that of the sun for a relatively cool white dwarf to about a million times that of the sun for the hottest known super-giant star. Astronomers assign stars magnitudes based on how bright they are. Apparent magnitude measures how bright a star appears to be from Earth. Absolute magnitude measures its true luminosity.
The brighter the star, the lower its luminosity. Every 5 magnitudes corresponds to brightness changing by a factor of 100. For example, a magnitude 1 star is 10,000 times brighter than a magnitude 11 star. Besides the sun, the brightest star as seen from Earth is Sirius with an apparent magnitude of -1.6.
Transparent: Materials, such as window glass, through which light can travel easily and through which other objects can clearly be seen.
Translucent: Materials, such as glass blocks, through which light can pass through but no clear image can be seen.
Opaque: Materials which absorb and reflect light. Objects cannot be seen through the material. Most objects are opaque.
The thin film effect refers to colors seen in such things as soap bubbles and oil spills. It occurs as a result of the constructive and destructive interference of light waves, not because of refraction as in a prism. When light hits a bubble, some of it is reflected by the outer (air-soap) interface (ray #1), while some penetrates the bubble wall and is reflected by the inner (soap-air) interface (ray #2). The two reflected rays interfere with one another. Typically, most wavelengths will be out of phase since #2 has to travel a greater
Guinness Soap Bubble Records
distance than #1. However, one wavelength will be in phase and this corresponds to the color produced. The color depends on how great the difference in distance is that the two rays travel, and this distance depends on bubble thickness. The variations in thickness (thinner at the top, thicker at the bottom) are responsible for the different colors.
Continued on Next Slide
Soap Bubble Wall
When light moving through the air encounters the denser film the reflected ray is inverted, just like a pulse traveling down a slinky is inverted when it reflects at the connection point with a heavier spring. The transmitted ray is not inverted, which is also the situation with slinky and spring. When the transmitted ray encounters the soap-air interface at the inside of the bubble, again some of it is reflected back. This time, however, the wave is not inverted (just as a pulse traveling on a heavy spring is not inverted when it reflects at the connection point with a slinky). The two reflected rays may or may not be in phase; it depends on how thick the film is.Since white light is comprised of many wavelengths, those that are nearly in phase after reflecting off the bubble surfaces will be reinforced (constructive interference). This is the color that will appear on the bubble. The other wavelengths are out of phase (destructive interference) and are, at least partially, cancelled out.
Since gravity causes the bubble to be thicker near the bottom, different wavelengths are reinforced at different heights, producing bands of colors. Interestingly, a bubble on the space shuttle will not produce bands of different colors. This is because the shuttle is in free fall around Earth, which means bubbles behavior as if they’re in a gravity-free environment. Thus, bubbles are of uniform thickness.
Continued on Next Slide
So how do we determine which color will be produced at a particular point on a bubble or other thin film? Well, if the thickness of the film is /4, then light of wavelength will be reinforced. Here’s why: The then the round trip in the film will be /2. This means the two waves will be in phase, since one was inverted and one wasn’t.
Bubble Wall /4
Transmitted wave superimposed with upright wave from 2nd reflection
Invertedwave from 1st reflection superimposed with upright wave from 2nd reflection
air outside bubble
air inside bubble
Electric Field Orientations
Light coming directly from the sun or other sources is unpolarized, meaning the electric and magnetic fields oscillate
Beam o’ Light
in many different planes. Polarized light refers to light in which all waves have electric fields oscillating in the same plane. Imagine trying to pass a large piece of sheet metal through the bars of a jail cell. To do this you would have to orient the sheet vertically (or nearly so), otherwise the bars would block the sheet. Here, the bars are analogous to a polarizing filter, and the sheet is analogous to the plane in which the electric field is oscillating.
A polarizing filter is made of a material with long molecules that allow electromagnetic waves of one orientation through. If a wave has an electric field with any other orientation, the filter will only allow a component to pass through, absorbing the rest. Note that only transverse waves such as light can be polarized. Much of the light we see is at least partially polarized. For example, when light reflects off of surfaces it is partially polarized. Some sunglasses contain polarizing filters which helps to block glare (such as the glare that is noticeable when looking out over a lake on a sunny day).
Polarized LightGlareMolecular View
Unpolarized light propagates in all orientations. No particular orientation is preferred. When it passes through a filter that only allows vertical components of electric fields to pass, its intensity is cut in half. This is because, on average, the light is “half horizontal and half vertical” in terms of electric field components. All horizontal components are blocked, making the resulting polarized light half as bright.
Now, imagine that you place another filter that is perpendicular to the direction of the first one, i.e., a filter that only allows the horizontal components of electric fields to pass through. This would completely block the remaining light. Thus, any two perpendicular filters will block all incoming light.
Suppose now that the two filters are offset by some angle . Regardless of the angle, the first filter blocks half the light. If = 0, the second filter has no effect. If = 90, the second filter blocks the other half of the light. In gen-eral, when polarized light with an electric field of amplitude E passes through the second filter, the amplitude will drop to Ecos. Furthermore, since the energy a wave carries is proportional to the square of its ampli-tude, the intensity of the light will be the original intensity multiplied by cos2.
Continued on Next Slide
We know that if = 90 between two filters, then no light will make it past the second one. At other angles light will pass through both, changing the orientation of its electric field each time. So, what if we arranged several polarizing filters so that the angle between any two consecutive filters is less than 90? The answer is that light twists its way through the filters, even if the angles between the filters adds up to 90. With each pass the light is oriented in a new direction, and this new orientation has a component parallel to the orientation of the next filter.
Recall that a black body is an ideal absorber of all incident radiation. A hot black body is also a perfect emitter--radiation is the result of its temperature, and since none of this is absorbed, it is a perfect emitter of radiation. A black body emits all wavelengths of light but not equally; there is always a wavelength in which the radiation peaks. The hotter the black body, the
smaller the peak wavelength. Objects around you are cool, so their peak is in the infrared. The sun is hot enough to peak in the visible spectrum (all other wavelengths are emitted too but at lower intensities).
In the late 19th century classical physics had predicted something impossible: as the temperature rises, the intensity of the peak radiation approaches infinity (red dashed line). The theory did match experimental data for large wavelengths but failed for small ones. This was known as the “ultraviolet catastrophe.”
In 1900 Max Planck came up with a revolutionary way to resolve the problem by assuming that energy came in discrete amounts (quanta). This was the beginning of quantum mechanics. Each quantum of light is called a photon, and its energy is given by E = hf, where fis the frequency of the radiation and h is the constant of proportionality called Plank’s constant. The formula states that higher frequency light has proportionally more energy per photon. Einstein lent credence to Plank’s ideas by explaining the photoelectric effect in a similar manner. Robert Millikan did a series of experiments involving the photoelectric effect and calculated the constant: h = 6.62610-34 Js.
Before Planck light was considered to be a wave. Today we know it can be interpreted as either a particle or a wave. As a wave, bright light can be explained as a large amplitude in the electric and magnetic fields. As a particle, bright light would be explained by a large number of photons.
Lamps, flashlights, etc… all produce light. But this light is released in many directions, and the light is very weak and diffuse. In coherent light the wavelength and frequency of the photons emitted are the same. The amplitude may vary. Such things as lasers and holograms are composed of coherent light.
Laser stands for light amplification by stimulated emission of radiation. A laser is a device that creates and amplifies a narrow, intense beam of coherent, monochromatic (one wavelength) light. Here’s how they work.
There are 2 primary states for an atom, an excited state and a ground state. The ground state is the lowest energy, most stable state. In the excited state electrons are in a higher energy level. In a laser, the atoms or molecules of a crystal (such as ruby) or of a gas, liquid, or other substance are excited in the laser cavity so that more of them are at higher energy levels (excited state) than are at lower energy levels. When an excited electron drops back to a lower energy level, a photon of a particular wavelength is released. This photon stimulates other electrons to emit photons. All these photons are in phase.
As with any type of wave, light waves can interfere with one another. The interference of two or more waves will carry the whole information about all the waves. It is on this basis that holograms work. Holograms make use of lasers and they work in the following fashion: (Explanation on next slide.)
Light wave interference
As the laser hits the beam splitter, it is split in two. The object beam heads towards the object of interest, while the reference beam heads toward a mirror. The beams are identical until the object beam shines on the object. There some of the light is absorbed; some is reflected toward the film. After reflecting off the mirror, the reference beam is reunited with the object beam on the film. Because one beam interacted with the object and the other didn’t, the two beams will be out of phase and interfere with one another. This interference pattern is imprinted upon the holographic film plate, creating the holographic image.
This pattern records the intensity distribution of the reflected light just as an ordinary camera does. However, it also records the phase distribution. This means that it contains information about where the waves are in their oscillating cycles as they strike the film. To determine this the object beam must be compared with the reference beam. This is accomplished via the interference. Also unlike an ordinary photo, a hologram contains all its information in every piece of it.
When viewed in coherent light the object appears in 3-D and viewing a hologram from different angles will reveal the object from different angles.
Luminous flux, , is the rate at which an object emits visible light (adjusted to the responsiveness of the human eye, which is most sensitive to yellow-green). It is measured in lumens. Imagine a light source in the center of a sphere. Luminous flux is the quantity of light that hits the surface of the sphere per unit time. The size of the sphere is irrelevant. If the sphere were larger, the same quantity of light would reach the surface every second, so the flux wouldn’t change. However, this light would be more spread out, so the illuminance of the surface would be less than it was with the same candle in the smaller sphere. Also called illumination, the symbol for
illuminance is E, not to be confused with energy, and is defined as luminous flux per unit of surface area: E = /S. The SI unit for illuminance is the lux, which is a lumen per square meter. The illuminance of the sun is about 100,000 lx (lux); for the full moon it’s about 0.2 lx. A common, non-SI unit for illuminance is the foot-candle, which is equivalent to about 10.8 lx.
1m 2m 3m 4mIlluminance vs. Distance
A point source at P radiates light in all directions. The pic below shows how light spreads out as it radiates. If the illuminance on the sheet 1m from P is 1 unit, then the illuminance on the sheet 2m from P is four times less. This is because doubling the distance increases the area by a factor of four over which the light is spread. Similarly, 3m from P the illuminance is nine times less, and 4m from P it’s 16 times less. Note the flux (amount of light) is not changing, but the illuminance is because the same amount is spread over different areas. In general, E is proportional to and inversely proportional to the square of the distance. This is reminiscent of Newton’s inverse square law for gravitation.
angle = 1 radianSolid Angles
We can measure ordinary, “flat” angles by the ratio of arc length of a circle to the radius of the circle. Imagine two radii shooting out from the center, subtending part of the circumference. By definition this ratio is the measure of the angle between the radii in radians. There are 2 radians in a circle since C = 2r.
Now imagine a sphere instead of a circle and a cone shooting out from the center rather than a two radii (the apex of the cone is at the center). Instead of part of a circum-ference, the cone subtends part of the surface area of the sphere. A solid angle (measured in steradians) is defined as the ratio of the subtended surface area of the of sphere to the square of its radius. This definition applies even if the subtended area is not circular. There are 4 steradians in a sphere since S = 4r2.
radius = 1 unit
1m 2m 3m 4mLuminous Intensity
Recall that illuminance is flux per unit area. A related quantity is luminous intensity, I, which is defined as flux per unit of solid angle. Thus, I= Ø /4, since there are 4 steradians in a sphere. You can think of luminous intensity as the amount of light contained within a cone whose apex is at the source. The same amount of light confined to a skinnier cone would mean a greater intensity. Just as the “flat” angle is independent of the size of the circle, the solid angle is independent of the size of the sphere. The intensity is the same at every sheet in the pic below. In a sphere 7m in radius, I is the flux that falls on a 49m2 surface on the sphere. The SI unit for intensity is the candela, cd. 1 cd = 1 lumen per steradian. A footcandle is the illuminance one foot away from a 1 candela source.
Light sources, like light bulbs, vary in efficiency. This means that some bulbs, e.g. fluorescent bulbs, will produce more light while using less energy. (They can do this by producing less waste heat.) The efficiency of a simple machine is the work done by the machine divided by the work put into it. In this context, efficiency is the rate at which light is produced by the bulb divided by the rate at which energy is used to produce that light: eff = Ø/P, where P is power. Note that both flux and power are rates, so eff is really “light over energy.” It is measured in lumens per watt. A typical candle has an efficiency of about 0.1 lumen / W. Incandescent bulbs are about 15 lumen / W, but a fluorescent bulb is closer to 70 lumen / W. A monochromatic source emitting light of around 555 nm in wavelength would be the ideal in terms of efficiency, with all of its radiation being visible to us instead of infrared (waste heat).
Numerous Images as well as information were obtained from the following sources: