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The Wave Aspect of Light: Interference

We know that visible light is the type of electromagnetic wave to which our eyes respond. Like all other electromagnetic waves, it obeys the equation

c = f λ, c = f λ, size 12{c=f`λ,} {}

27.1

where $c = 3 \times 10^{8} m/s c = 3 \times 10^{8} size 12{c=3 times "10" rSup { size 8{8} } `"m/s"} {}$ is the speed of light in vacuum, $f f size 12{f} {}$ is the frequency of the electromagnetic waves, and $λ λ size 12{λ} {}$ is its wavelength. The range of visible wavelengths is approximately 380 to 760 nm. As is true for all waves, light travels in straight lines and acts like a ray when it interacts with objects several times as large as its wavelength. However, when it interacts with smaller objects, it displays its wave characteristics prominently. Interference is the hallmark of a wave, and in Figure 27.3 both the ray and wave characteristics of light can be seen. The laser beam emitted by the observatory epitomizes a ray, traveling in a straight line. However, passing a pure-wavelength beam through vertical slits with a size close to the wavelength of the beam reveals the wave character of light, as the beam spreads out horizontally into a pattern of bright and dark regions caused by systematic constructive and destructive interference. Rather than spreading out, a ray would continue traveling straight ahead after passing through slits.

Making Connections: Waves

The most certain indication of a wave is interference. This wave characteristic is most prominent when the wave interacts with an object that is not large compared with the wavelength. Interference is observed for water waves, sound waves, light waves, and (as we will see in Special Relativity) for matter waves, such as electrons scattered from a crystal.

Part a of the figure shows a thin bright orange laser beam emitted from an observatory traveling in a straight line up into a starry sky. Part b of the figure shows a horizontal pattern of orange red spots produced when a laser beam has passed through a grid of slits. The central spot is the brightest and the spots get dimmer as you move away from the center..

Figure 27.3 (a) The laser beam emitted by an observatory acts like a ray, traveling in a straight line. This laser beam is from the Paranal Observatory of the European Southern Observatory. (credit: Yuri Beletsky, European Southern Observatory) (b) A laser beam passing through a grid of vertical slits produces an interference pattern—characteristic of a wave. (credit: Shim'on and Slava Rybka, Wikimedia Commons)

Light has wave characteristics in various media as well as in a vacuum. When light goes from a vacuum to some medium, like water, its speed and wavelength change, but its frequency $f f size 12{f} {}$ remains the same. (We can think of light as a forced oscillation that must have the frequency of the original source.) The speed of light in a medium is $v = c / n v = c / n size 12{v=c/n} {}$ , where $n n$ is its index of refraction. If we divide both sides of equation $c = f λ c = f λ size 12{c=f`λ} {}$ by $n n size 12{n} {}$ , we get $c / n = v = f λ / n c / n = v = f λ / n size 12{c/n=v=f`λ/n} {}$ . This implies that $v = f λ_{n} v = f λ_{n} size 12{v=f`λ rSub { size 8{n} } } {}$ , where $λ_{n} λ_{n} size 12{λ rSub { size 8{n} } } {}$ is the wavelength in a medium and that

λ_{n} = \frac{λ}{n}, λ_{n} = \frac{λ}{n}, size 12{λ rSub { size 8{n} } = {  {λ}  over  {n} } ,} {}

27.2

where $λ λ size 12{λ} {}$ is the wavelength in vacuum and $n n size 12{n} {}$ is the medium’s index of refraction. Therefore, the wavelength of light is smaller in any medium than it is in vacuum. In water, for example, which has $n = 1 . 333 n = 1 . 333 size 12{n=1 "." "333"} {}$ , the range of visible wavelengths is $(380 nm) /1 . 333 (380 size 12{ $ "380"`"nm" $ "/1" "." "333"} {}$ to $(760 nm) /1 . 333 (760 size 12{ $ "760"`"nm" $ "/1" "." "333"} {}$ , or $λ_{n} = 285 to 570 nm λ_{n} = 285 size 12{λ rSub { size 8{n} } ="285"`"to"`"570"`"nm"} {}$ . Although wavelengths change while traveling from one medium to another, colors do not, since colors are associated with frequency.