Activity 5
Interference and Spectra
Background Information
Interference is a wave phenomena. It is easy to observe interference in water waves with a ripple tank (see Water Waves at end of Activity 5). The observation of this effect in light proves that light has wave properties. Moreover, it demonstrates that the statement “light travels in straight lines” is an oversimplification that describes the particle behavior of light but not all of the wave behavior. Light can also bend (slightly) around the edge of an object and spread out when passing through a single slit, effects called diffraction. In fact, light will diffract even when passing through a slit many times larger than its wavelength. This diffraction is what makes interference possible, since otherwise the light energy would continue straight ahead, without spreading out to form the interference pattern.
The drawing shows coherent light—light of the same phase—illuminating two closely-spaced slits.
The pattern observed on a distant screen is a series of spots, and the closer together the slits, the further apart the spots. Notice that in the drawing, the rays going to the slits are shown as parallel (even though they meet on the screen), an approximation resulting from the small slit spacing. Each slit has a path length to a point on the screen, and the difference in path length determines the relative phases at that point. The difference in path length is d sin (u). When this difference is an integral number of wavelengths, the light from the two slits reinforces and produces a bright spot, called a maxima.
d sin(θ) = n λ , n = 0, 1, 2, 3 . . .
Halfway between the maxima, the light from the two slits cancels to produce a minima, where there is no light. If x is the distance from the center of the pattern to a bright spot and L is the distance from the slits to that spot on the screen (see drawing on page 324), then:
sin (θ) = x/L
d (x / L) = n λ
For the first bright spot,
d (x / L) = λ
The above derivation is for a two-slit system. It turns out that increasing the number of slits—making a grating—serves mostly to brighten and sharpen the pattern, narrowing each bright spot, and improving the accuracy of the measurement. The interference pattern of a grating, with thousands of slits per centimeter, is described by the same equation above. In Activity 6 (and in one of the Additional Activities presented for Activity 5), students will calculate with the equation above as a part of their experiment.
The grating spectroscope spreads out light according to wavelength in the regular way described by the equation d sin(θ) = n λ. The larger the wavelength, the larger the angle. If the students look at an incandescent bulb through the spectroscope, they see a continuous spectrum. The bulb’s hot filament emits light through the range of visible wavelengths. However, the spectra of the spectrum tubes consists of a number of bright lines. The lines are produced from atomic transistions in the atoms of the gas inside the tube. Since the energy of these atoms is quantized, these transitions can produce only a small number of different energies and, according to Λ E = h v, only a small number of wavelengths. Each element has a unique spectra, including infrared, ultraviolet, and x-ray lines.
Astronomers observe spectra from stars and galaxies. Analysis of these spectra can reveal the atoms, and even the molecules, that exist on these objects, which can be many millions of light-years away. The element helium was discovered, in just this way, on the Sun, even before it was found on Earth.
Interference and Spectra
Background Information
Interference is a wave phenomena. It is easy to observe interference in water waves with a ripple tank (see Water Waves at end of Activity 5). The observation of this effect in light proves that light has wave properties. Moreover, it demonstrates that the statement “light travels in straight lines” is an oversimplification that describes the particle behavior of light but not all of the wave behavior. Light can also bend (slightly) around the edge of an object and spread out when passing through a single slit, effects called diffraction. In fact, light will diffract even when passing through a slit many times larger than its wavelength. This diffraction is what makes interference possible, since otherwise the light energy would continue straight ahead, without spreading out to form the interference pattern.
The drawing shows coherent light—light of the same phase—illuminating two closely-spaced slits.
The pattern observed on a distant screen is a series of spots, and the closer together the slits, the further apart the spots. Notice that in the drawing, the rays going to the slits are shown as parallel (even though they meet on the screen), an approximation resulting from the small slit spacing. Each slit has a path length to a point on the screen, and the difference in path length determines the relative phases at that point. The difference in path length is d sin (u). When this difference is an integral number of wavelengths, the light from the two slits reinforces and produces a bright spot, called a maxima.
d sin(θ) = n λ , n = 0, 1, 2, 3 . . .
Halfway between the maxima, the light from the two slits cancels to produce a minima, where there is no light. If x is the distance from the center of the pattern to a bright spot and L is the distance from the slits to that spot on the screen (see drawing on page 324), then:
sin (θ) = x/L
d (x / L) = n λ
For the first bright spot,
d (x / L) = λ
The above derivation is for a two-slit system. It turns out that increasing the number of slits—making a grating—serves mostly to brighten and sharpen the pattern, narrowing each bright spot, and improving the accuracy of the measurement. The interference pattern of a grating, with thousands of slits per centimeter, is described by the same equation above. In Activity 6 (and in one of the Additional Activities presented for Activity 5), students will calculate with the equation above as a part of their experiment.
The grating spectroscope spreads out light according to wavelength in the regular way described by the equation d sin(θ) = n λ. The larger the wavelength, the larger the angle. If the students look at an incandescent bulb through the spectroscope, they see a continuous spectrum. The bulb’s hot filament emits light through the range of visible wavelengths. However, the spectra of the spectrum tubes consists of a number of bright lines. The lines are produced from atomic transistions in the atoms of the gas inside the tube. Since the energy of these atoms is quantized, these transitions can produce only a small number of different energies and, according to Λ E = h v, only a small number of wavelengths. Each element has a unique spectra, including infrared, ultraviolet, and x-ray lines.
Astronomers observe spectra from stars and galaxies. Analysis of these spectra can reveal the atoms, and even the molecules, that exist on these objects, which can be many millions of light-years away. The element helium was discovered, in just this way, on the Sun, even before it was found on Earth.