Wave Nature of Light

In Grade 10 we learnt about electromagnetic radiation and that visible light is a small part of the EM spectrum. EM radiation is a wave so we should see diffraction for visible light when it strikes a barrier or passes through a slit. In everyday life you don't notice diffraction of light around objects or when light passes through an open door or window. This is because the wavelength of light is very small and the "slits" like doors and windows are quite large.

We can put some everyday numbers into \[\text{diffraction}\propto \frac{\lambda}{w}\] to see how much diffraction we expect. White light is combination of light of many different colours and each colour has a different frequency or wavelength. To make things simpler lets just think about one colour, green light has a wavelength of \(\text{532} \times \text{10}^{-\text{9}}\) \(\text{m}\). If a wavefront of green light struck the wall of a house with an open door that is \(\text{1}\) \(\text{m}\) wide what would we expect to see?

\begin{align*} \text{diffraction} &\propto \frac{\lambda}{w} \\ & \propto \frac{\text{532} \times \text{10}^{-\text{9}}\text{ m}}{\text{1}\text{ m}} \\ &\propto \text{532} \times \text{10}^{-\text{9}} \end{align*}

A diffraction grating reflecting green light.

The result is a very small number so we expect to see very little diffraction. In fact, the effect is so small that we cannot see it with the human eye. We can observe diffraction of green light but for us to get \(\text{diffraction} \propto 1\) we need the wavelength and slit width to be the same number. So we know the effects of diffraction should become noticeable when the wavelength and slit width are similar. We can't change the wavelength of green light but there are objects called diffraction gratings that have very narrow slits that we can use to study the diffraction of light. We let wavefronts of green light strike a diffraction grating and then put a screen on the other side. We can see where the intensity of the the light on the screen is large and where it is small. For green light on a particular diffraction grating the pattern of green light on the screen looks like:

Blue light with a wavelength of \(\text{450} \times \text{10}^{-\text{9}}\) \(\text{m}\) and the same diffraction grating will produce:

Example: Diffraction

Question

Two diffraction patterns are presented, determine which one has the longer wavelength based on the features of the diffraction pattern. The first pattern is for green light:

The second pattern is for red light:

The same diffraction grating is used in to generate both diffraction patterns.

Step 1: Determine what is required

We need to compare the diffraction patterns to extract information about the relative wavelengths so we can decide which one is longer. We know that the diffraction pattern depends on wavelength and slit width through: \[\text{diffraction}\propto \frac{\lambda}{w}\]

The diffraction grating is the same in both cases so we know that the slit width is fixed.

Step 2: Analyze patterns

By eye we can see that the red pattern is wider than the green pattern. There is more diffraction for the red light, this means that:\begin{align*}\text{diffraction}_{red} &> \text{diffraction}_{green}\\\frac{\lambda_{red}}{w} &> \frac{\lambda_{green}}{w}\\\lambda_{red} &> \lambda_{green}\end{align*}

Step 3: Final answer

The wavelength of the red light is longer than that of the green light.

Wave Nature of Light