# Diffraction of Light and Young's Double Slit Experiment

This is part of the HSC Physics course under the topic Light: Wave Model.

### HSC Physics Syllabus

• conduct investigations to analyse qualitatively the diffraction of light

• conduct investigations to analyse quantitatively the interference of light using double slit apparatus and diffraction gratings dsinθ=mλ (ACSPH116, ACSPH117, ACSPH140)

### What is Diffraction?

Diffraction is the scattering behaviour a wave exhibits when it travels through a small opening or around the end of an object.

When light passes through an aperture, slit or around a bend/edge of an object, it also experiences this scattering effect, causing it to propagate outward. The scattering process bends light’s direction of propagation. The degree of bend is dependent on the relative difference between its wavelength and size of the slit.

• If the slit size is smaller than or equal to light’s wavelength, considerable diffraction occurs. Smaller the slit, greater the degree of diffraction.
• If the slit size is larger than light’s wavelength, diffraction still occurs but is unnoticeable to the naked eye.
Examples of diffraction can be seen in all types of waves, including all electromagnetic waves, sound waves or waves observed in water. • Diffraction of light creates a unique repeating pattern

Diffraction of light creates a repeating pattern where a white band is observed centrally and bands of rainbow are dispersed away from the centre, each separated by dark space.

The ‘resolution’ of each rainbow band become more diffuse and weaker the further away it from the central white band.

### Huygens' Wave Model of Light

Huygens’s wave model of light is commonly used to understand the effect of diffraction. In the 17th century, Christiaan Huygens proposed that when a wave reaches an opening, its wavefront can be perceived as individual points emitting spherical secondary wavelets. When light travels through a slit, some of these wavelets are obstructed and can no longer propagate. As a result, the new wavefront is formed from the interference between wavelets that managed to pass through the opening. The absence of wavelets on the periphery causes the wavefront to scatter and propagate outward.

Huygens' wave model of light also provides a plausible explanation to why waves diffract around an edge of an opaque material. This is due to the propagation of some wavelets being obstructed by the object.

### Diffraction Pattern through a Double Slit

In 1818, Fresnel improved Huygens’s theory by adding his theory of interference. Together, their theories could explain both the effect of diffraction and presence of dark fringes. Fresnel proposed that the diffraction pattern obtained from white light is a result of constructive and destructive interference between secondary ‘wavelets’ emitted from the original wavefront.

• When waves are out of phase, they undergo destructive interference. This results in dark fringes or ‘minima’ of diffraction.
• When waves are in phase, they undergo constructive interference. This results in spectral bands or ‘maxima’ of diffraction. The intensity of each spectral band decreases away from the centre. This is because the diffracted ray of light is lower in intensity the greater the angle of diffraction from the midline (θ).

### Young's Double-slit Experiment

In 1801, Thomas Young conducted an experiment using a double-slit apparatus. A monochromatic light source was shone through two narrow slits separated by a very small distance. A viewing screen was set-up directly behind the double-slit apparatus. Newton's corpuscular (particle) model of light and Huygens' wave model of light made different predictions regarding the pattern of light formed on the screen. Young's observations supported the wave model of light.

If light was a particle or consisted of particles, only light particles which pass through the slits would be observed on the viewing screen

However, Young instead observed multiple bright bands/spots on the viewing screen rather than just two. These spots spanned a larger distance than that between the slits and had alternating dark and bright spots (minima and maxima).

Young’s qualitative observations showed that light cannot be particle in nature as this would otherwise produce only two bright bands directly behind the two slits.

### Analysis of Diffraction Pattern

In addition, the bright spots showed varying intensity and their position can be calculated for a given wavelength of light. Constructive interference produce maxima

When the difference in phase between two waves are exactly one wavelength apart, they will undergo constructive interference.

$$d\sin{\theta} = m\lambda$$

Where d is the distance between two slits and m is the ‘order’ of interference.

m = 0, ±1, ±2...

The order of interference begins with 0 which corresponds to the central band on the viewing board. The intensity of band decreases with higher orders of interference.

Destructive interference produce minima

When the difference in phase between two waves are exactly or a multiple of half a wavelength apart, they will undergo destructive interference.

$$d\sin{\theta} = (m+\frac{1}{2})\lambda$$

Where d is the distance between two slits and m is the ‘order’ of interference. m = 0, 1, 2, 3...

Number of Maxima

For a particular wavelength of light and distance (d) between slits, the number of orders (m) of bright spots (maxima) is finite. A maximum cannot form more than 90 degrees from the midline between the two slits. Thus, the angle at which the furthest maximum is formed must be smaller than 90º.

Substitute an angle of 90º into the diffraction equation, the greatest order is given by

$$m = \frac{d}{\lambda}$$

This equation will often produce a number with decimal places. The greatest order is the largest integer lower than the calculated value.

#### How can we change the number of bright spots present?

• For a given wavelength, we can increase the separation distance between slits. However, this does not always work as when separation distance becomes too large, the interference between waves becomes negligible. This results in two bright spots being formed for a double slit experiment.
• For a given separation distance, we can decrease the wavelength of light to increase the number of maxima present.
• Both slit separation distance and wavelength can be manipulated to produce varying number of bright spots and dark fringes.

### Diffraction Grating

Diffraction of light produces a similar array of bright and black spots when more than 2 slits are used. Increased number of slits produces diffraction bands with greater resolution.

This is because as the number of slits increases, so does the number of waves being directed at the same angle (or same position on the viewing board). This increases the intensity of bright spots as more waves experience constructive interference which leads to a greater amplitude.

In contrast, when waves do not exactly overlap at their crests or troughs, they will undergo destructive interference. The extent of destructive interference again increases with the number of slits. Greater the extent, more defined the black fringes are.

### Diffraction of White Light

Diffraction of white light produces repeating rainbow-like spectra. Within each spectrum, longer wavelength of visible light (red) is further away from the centre. This is because the angle of diffraction increases for light of longer wavelengths. Previous section: Applications of Spectroscopy

Next section: Particle and Wave Models of Light