# (S-4) The Many Colors of Sunlight

An introduction to color and to both line spectra and continuous spectra, with applications to sunlight.

Part of a high school course on astronomy, Newtonian mechanics and spaceflight
by David P. Stern

 This lesson plan supplements: "The Many Colors of Sunlight," section #S-4: on disk Sun4spec.htm, on the web           http://www.phy6.org/stargaze/Sun4spec.htm "From Stargazers to Starships" home page and index: on disk Sintro.htm, on the web           http://www.phy6.org/stargaze/Sintro.htm

 (Optional)         If time allows, students can be shown how a diffraction grating works.     The grating acts like many closely spaced slits: the light hitting between the slits is scattered irregularly, and only what hits the slits goes through. If light acts as a wave, one can show mathematically that each slit acts as a new source of the wave. (By the way--the "slits" are really the ridges between the grooves of the grating, which transmit light like a windowpane, not the grooves themselves)     Suppose light arrives at the grating from a direction perpendicular to it. Waves have peaks and valleys, and when the arriving wave-front is at a peak, all slits also start their "local waves" with a peak.     Suppose we continue in the same direction 1, 2, 3... wavelengths. The wave from each slit will then also have a peak at those locations. These peaks would be in the same distances if the wave passed intact through the grating, as if it wasn't there, suggesting that much of the wave goes straight through, with no modification. But wait! If each slit is the source of a wave spreading in all directions, what about the part spreading in slanted directions?    Consider the part spreading at an angle θ to the original direction of light. The wave front of a wave moving in that direction would be along the drawn slanted line. However, the distances of the points on that line from the various slits--each a separate "light source"--are all different! If at the slits the wave has a peak, at the wavefront, different parts of it are in different parts of the cycle. They are at a peak if the distance to a slit is an exact multiple Nλ of the wavelength (N is some whole number), at a peak in the opposite direction if the distance is (N+0.5)λ, and in other parts of the cycle for other distances. The sum total--say 2000 slits, 2000 different distances--is close to zero, so we get very little light scattered in the direction of θ. (That cancellation of peaks is called "destructive interference between the waves.")     Except... if the angle θ is such that the distances of the wave-front from two neighboring slits differ by exactly one wavelength λ . In that case, the distances from the next slits in line are 2λ, 3λ ... and so forth, and the waves continue propagating "in step." That is "constructive interference" between the waves, and in those directions, you will see a fairly bright beam of light.
As the second drawing shows, if D is the spacing between two neighboring slits, this requires

D sinθ = λ

Note that the angle θ at which the light undergoes constructive interference depends on the wavelength λ, that is, on the spectral color of the light. Each color is therefore bent by a different angle--just as it is in a prism. Because most of the beam goes straight through, the light may not be as bright as in a prism, but the separation of neighboring colors may be much more sensitive.

 The important thing to note is that such behavior is only expected from a wave. This therefore suggests that light is a wave, even though (at this stage of the discussion--like scientists for most of the 19th century) nothing tells us what exactly forms its peaks and valleys

The above formula allows the light's wavelength to be calculated. For example: you observe the yellow line of sodium with a grating having 1000 lines per centimeter, and find that light is brightest at an angle θ =36°. What is the wavelength λ?

In fact, methods based on interference have measured wavelengths with such accuracy, that the international meter--originally defined by two scratches on a bar, kept in a vault in Paris--was at one time redefined in terms of the wavelength of a certain emission.

Laser disks for recording songs, videos or data for computers, shimmer in colors, because they contain many closely spaced grooves, which make them act like a grating. The light is reflected from the grooves (with the help of an aluminum backing), rather than passing through, but the effect is very similar.

Another interference effect are the colors seen when a thin layer of kerosene floats on a puddle of water--layers with a thickness of the order of a wavelength of light. Some light is reflected from the top of the kerosene layer, some from its bottom (which is the top of the water), and the two reflected waves interfere with each other. For some colors the interference is destructive, for others, constructive, leading to a shimmering of colors.

(end of optional section)

What does the spectrum of sunlight tell about the Sun?

• The continuous spectrum? ... It tells that the temperature of the photosphere is about 5780° Kelvin.

• The bright lines in the spectrum?... They tell us about the composition of the photosphere--mostly hydrogen, some helium, a bit of oxygen, carbon and heavier stuff (some lines, carefully recorded and analyzed, can also tell of the presence and strength of the local magnetic field).

• The dark lines of the spectrum?.... They identify cooler material in the higher levels of the photosphere.

• The spectrum of the corona, for instance, the presence of iron that has lost 13 electrons? ... It tells us the corona is very hot, and provides an estimate of its temperature.

• How was helium discovered? (The teacher can tell more about the discovery. The helium line was in the yellow part of the spectrum, and at first some astronomers credited it to sodium--but it had a slightly different wavelength, and it was gradually recognized that in no way could sodium produce it.)

Guides to teachers...       A newer one           An older one             Timeline         Glossary

Author and Curator:   Dr. David P. Stern
Mail to Dr.Stern:   audavstern("at" symbol)erols.com .

Last updated: 20 November 2004