UNIT 4, Wave Nature of Light Wave Basics; 9.2 Diffraction; 9.2 Interference9.5Double Slit Int.; 10.1 Polarization; 10.2 Single Slit; 10.3 Diffraction Grating

Light is energy and it is also a messenger: it carries information from distant stars and other celestial objects. This information arrives, as visible light, and as electromagnetic radiations, such as radio waves, X rays, and cosmic rays. Fibre optics, lasers, and light-emitting diodes used in communication use light for operation. CDs, DVDs, and holography use the wave aspect of light. How is the light energy transmitted from its source? Wave or Particle? This chapter looks at the WAVE MODEL of LIGHT The wave theory of light has led to the development of our whole communications field, from the wireless telegraph, to radio, to TV, to satellite communications. Key Terms: Waves: are travelling disturbance, and they carry energy from one location to another. Dispersion of light: is the separation of light into the colours of spectrum when passing through a prism. Diffraction & Interference are properties of all waves, as are Refraction & Reflection Diffraction, the spreading or bending of a wave after encountering a barrier. It is the interference effect from waves originating from a single source or wavefront. Interference: superposition effect originating from two or more discrete sources of waves. Diffraction of waves from two or more sources Diffraction Grating: multiple slits, device for producing spectra by diffraction and for measurement of wavelength. The surface of the device is ruled with close, equally spaced, parallel lines for the purpose of resolving light into spectra. It is diffraction of waves from multiple sources. (Transmission Gratings are transparent (this chapter) and Reflection grating is mirrored) Examples of Wave Motion A stone is dropped into a still lake, a person shouts to someone across the room, a string is plucked and vibrates visibly, and oscillating electrons in an antenna send out radio waves to stereo receivers. Three categories of waves: Mechanical waves are waves that are governed by Newton’s laws. They require a physical medium in which to travel. E.g., water waves, sound waves, vibrating air columns in musical instruments, and waves travelling in springs.

Electromagnetic waves are waves that can travel through a vacuum, such as outer space. Electromagnetic waves all travel at speed of light. E.g., Visible light is an example of this type of wave, along with infrared, ultraviolet, radio, and cosmic rays. These are Transverse waves.

Matter waves are a model that amalgamates the particle and wave theories of energy and matter. Particles such as electrons, protons, neutrons, and other subatomic particles can all behave like waves. E.g., electrons producing interference patterns similar to those of visible light or x-rays.

Water waves

sound-wave collector

radio-wave receiver

Water waves are a combination of the action of both kinds of waves, transverse and longitudinal. The particles of water move in circular paths, so sometimes they are parallel to the direction of wave motion, and at other times they are perpendicular to the direction of wave motion. People sitting in a boat find themselves moving in a circular clockwise path, in the direction of wave motion

Two Types of Wave Motions: Transverse waves, the particle motion is perpendicular to the direction of wave velocity. Longitudinal waves, particle motion is parallel to the direction of wave velocity. Both types of waves are: Travelling waves because their energy travels from one point to another, and Periodic waves because their cycles or patterns are repeated by the action at the wave source.

Interference of Light (Basics, Wave 1D, 2D): Interference: superposition effect originating from two or more discrete sources of waves. Diffraction, on the other hand, is the interference effect from waves originating from a single source or wavefront.

INTERFERENCE THEORY: Combining two or more WAVES to produce a SINGLE WAVE is called SUPERIMPOSITION. As the wave meet the AMPLITUDES of the WAVES combine.

CONSTRUCTIVE INTERFERENCE, when the AMPLITUDES are in SAME direction (waves are in-phase), they are ADDED. DESTRUCTIVE INTERFERENCE, when the APLITUDES are in OPPOSITE directions (waves not in-phase) they CANCEL out, or SUBTRACT.

When two waves arrive at one spot in phase (shifted by nλ , where n is an integer), the net effect is constructive interference and a maximum occurs (pl. maxima). When two waves arrive out of phase (shifted by 1 1 or

2 2n nλ λ + −

, the net effect is destructive interference and a minimum occurs.

The term node (nodal lines) is sometimes used to refer to a minimum.

Path Difference (Phase-Shift): Waves from two different sources travel a different distance to the observer. The waves may arrive at the same point shifted relative to one another. This effect was called a PHASE SHIFT.

Interference in two dimensions: Two sources producing waves at the same time. Where two crests or two troughs overlap, maxima occur. Where a crest and a trough overlap, minima occur.

LIGHT SPECTRUM: If the composition of the light is a series of discrete frequencies, the resulting pattern is called a line spectrum . If the range of frequencies is extensive, then the pattern is called a continuous spectrum

'minium' or nodal line

1D2D

Single Diffraction & Weak Interference Double Diffraction & Strong Interference

Bright

nodal line

Diffraction Light is a transverse electromagnetic wave. Reflection, refraction, diffraction, and interference are phenomena observed with all waves. A periodic mechanical wave is a periodic disturbance that moves through a medium. The medium itself goes nowhere. The individual atoms and molecules in the medium oscillate about their equilibrium position, but their average position does not change. As they interact with their neighbors, they transfer some of their energy to them. The neighboring atoms in turn transfer this energy to their neighbors down the line. In this way the energy is transported throughout the medium, without the transport of any matter. Each point on a wavefront can therefore be considered a point source for the production of new waves. In three dimensions, these new waves are spherical waves called wavelets, that propagate outward with the speed characteristic of waves in the medium. The wavelets emitted by all points on the wavefront interfere with each other to produce the traveling wave. This is called Huygens' principle. It also holds for electromagnetic waves. When studying the propagation of light, we can replace any wavefront by a collection of sources distributed uniformly over the wave front, radiating in phase. When light passes through a small opening, comparable in size to the wavelength λ of the light, in an otherwise opaque obstacle, the wavefront on the other side of the opening resembles the wavefront shown above. The light spreads around the edges of the obstacle. This is the phenomenon of diffraction. Diffraction is a wave phenomenon and is also observed with water waves in a ripple tank shown above Diffracted Wave does interferes due to the ‘wavelet’ of the ‘new wavefromt’ colliding, which is very weak. This interference results in a bright maxima at the centre and number of destructive dark interference patterns separated by very weak constructive patterns. Diffraction Basics: Shadows form because light travels in straight lines, the property called the rectilinear propagation of light. When a solid, thin object is illuminated by a monochromatic source of light, instead of producing the expected outline of the object, a shadow with a series of fringes appears.

Diffraction

Diffraction

Wide Interference band of light

The bright region in the centre of the shadow area caused by diffraction around an opaque object is referred to as Poisson’s bright spot. Sound waves can bend around corners and large objects such as trees because their wavelengths are comparable to the size of these objects. Light has a wavelength in the range of 710 m− . The diffraction of light waves can only be observed through experimentation.

Interference Two or more waves traveling in the same medium travel independently and can pass through each other. In regions where they overlap we only observe a single disturbance called interference. When two or more waves interfere, the resulting displacement is equal to the vector sum of the individual displacements. If two waves with equal amplitudes overlap in phase, i.e. if crest meets crest and trough meets trough, then we observe a resultant wave with twice the amplitude called constructive interference. If the two overlapping waves, however, are completely out of phase, i.e. if crest meets trough, then the two waves cancel each other out completely, This is called destructive interference. Interference patterns are only observed if the interfering light from the various sources is coherent, i.e. if the phase difference between the sources is constant. Splitting the light from a single source into various beams guaranties coherence. Light from two different light bulbs is incoherent and will not produce an interference pattern. Lasers are sources of monochromatic, (single wavelength), coherent light. Two lasers can maintain a constant phase difference between each other for relatively long time intervals. The double slit If light is incident onto an obstacle which contains two very small slits a distance d apart, then the wavelets emanating from each slit will constructively interfere behind the obstacle.

If we let the light fall onto a screen behind the obstacle, we will observe a pattern of bright and dark stripes on the screen. This pattern of bright and dark lines is known as a fringe pattern. The bright lines indicate constructive interference and the dark lines indicate destructive interference. The bright fringe in the middle of the diagram above is caused by constructive interference of the light from the two slits traveling the same distance to the screen. It is known as the zero-order fringe. Crest meets crest and trough meets trough. The dark fringes on either side of the zero-order fringe are caused by destructive interference. Light from one slit travels a distance that is 1/2 wavelength longer than the distance traveled by light from the other slit. Crests meet troughs at these locations. The dark fringes are followed by the first-order fringes, one on each side of the zero-order fringe. Light from one slit travels a distance that is one wavelength longer than the distance traveled by light from the other slit to reach these positions. Crest again meets crest forming a bright fringe. The diagram shows the geometry for the fringe pattern. If light with wavelength λ passes through two slits separated by a distance d, we will observe constructively interference at certain angles. These angles are found by applying the condition for constructive interference, which is (path difference)

sin , where m=0,1,2,..., (for BRIGHT fringe)md mθ λ= The angles at which dark fringes occur can be found be applying the condition for destructive interference, which is

1 1sin , OR sin , where n=0,1,2,... (for DARK firnge)2 2n nd n d nθ λ θ λ = − = +

If the interference pattern is viewed on a screen a distance L from the slits, then the wavelength can be found from the spacing of the fringes using sine value. We have (For L>>z, sin = tan = z/L)n nθ θ where z is the distance from the center of the interference pattern to the nth bright line in the pattern. The single slit When light passes through a single slit whose width w is on the order of the wavelength of the light, then we observe a single slit diffraction pattern. Huygen's principle tells us that each part of the slit can be thought of as an emitter of waves. All these waves interfere to produce the diffraction pattern. Consider a slit of width w as shown in the diagram below. For light leaving the slit in a particular direction, we may have destructive interference between the ray at the top edge (ray 1)and the middle ray (ray 5). If these two rays interfere destructively, so do rays 2 and 6, 3 and 7, and 4 and 8. In effect, light from one half of the opening interferes destructively and cancels out light from the other half. Ray 1 and ray 5 are half a wavelength out of phase if ray 5 must travel 1/2 wavelength further than ray 1. We need ( / 2)sin ( / 2), where n=0,1,2,...

sin , for destructive interference (DARK)n

n

w nw n

θ λθ λ

==

If the interference pattern is viewed on a screen a distance L from the slits, then the wavelength can be found from the spacing of the fringes using sine value. We have (For L>>z, sin = tan = z/L)n nθ θ

Diffraction grating Diffraction patterns can be produced by a single slit or by two slits. When light encounters an entire array of identical, equally-spaced slits, called a diffraction grating, the bright fringes, which come from constructive interference of the light waves from different slits, are found at the same angles they are found if there are only two slits. But the pattern is much sharper. The figure below shows the interference pattern for various numbers of slits. The width of all slits is 50 micrometers and the spacing between all slits is 150 micrometers. The location of the maxima for two slits is also the location of the maxima for multiple slits. The single slit pattern acts as an envelop for the multiple slit patterns. The bright fringes, which come from constructive interference of the light waves from different slits, are found at the same angles they are found if there are only two slits. But the pattern is much sharper. Why? For two slits, there is one single position between bright peaks, where the interference is totally destructive. Between the zero-order and first-order fringes, there is one position which requires that one of the waves travels exactly 1/2 wavelength further than the other to reach it. For three slits, however, there are two positions where destructive interference takes place. One is located at the point where the path lengths differ by 1/3 of a wavelength, while the other is located where the path lengths differ by 2/3 of a wavelength. For 4 slits, there are three positions, for 5 slits there are four positions, etc. For a diffraction grating with a large number of slits, the pattern is sharp because of the many positions of completely destructive interference between the bright, constructive-interference fringes. Diffraction gratings, like prisms, disperse white light into its component colors. The spectral pattern is repeated on either side of the main pattern. These repetitions are called "higher order spectra". There are often many of them, each one fainter than the previous one.

http : / / electron9.phys.utk.edu

Diffraction Grating Applications: A spectroscope uses a diffraction grating to separate light into very narrow bands of specific colours (wavelengths) that you analyze. Spectroscopes can analyze Sun’s absorption spectra. The core of the Sun emits a continuous spectrum. However, atoms and molecules in the Sun’s outer atmosphere absorb specific wavelengths, causing the Sun’s spectrum to have several narrow black lines. Atoms and molecules also absorb light at the same wavelengths at which they emit it. Therefore, by identifying the wavelengths of light that have been absorbed by the Sun’s outer atmosphere, physicists are able to identify the atoms that are present in Sun’s atmosphere. Analysis of the Sun’s absorption spectrum reveals that at least two thirds of all elements present on Earth are present in the Sun. This technique is used to identify the composition of stars throughout our galaxy. An instrument called a “spectrophotometer” is used in chemistry and biochemistry laboratories to identify and measure compounds in solutions. A spectrophotometer has a diffraction grating that separates white light into all wavelengths. You can select a specific wavelength and send it through a sample of a solution. The spectrophotometer then measures the amount of light of the wavelength that is absorbed by the sample and you can then calculate the concentration of the compound in the solution.

Interference of Light (Young’s Double Slit Interference Experiment): Young’s Experiment : provides very strong evidence for the WAVE THEORY of LIGHT. If light has WAVE PROPERTIES then two light sources in-phase should produce a result similar to interference pattern of two water wave in-phase in a ripple tank. Light should be BRIGHTER in areas of CONSTRUCTIVE INTERFERENCE and DARK in areas of DESTRUCTIVE INTERERENCE. Young used one incandescent light source instead of two, directing its light through two pinholes placed very close together. The light was diffracted through each pinhole, so that each acted as a point source of light. Since the sources were close together, the spacing between the nodal lines or minimum was large enough to make the pattern of nodal lines visible. Since the light from the two pinholes originated from the same incandescent body, the two interfering beams of light were always in phase (coherent), and a single, fixed interference pattern could be created on a screen. Young’s experiment resolved the two major problems in observing the interference of light: (1) two sources were in phase, and (2) the distance between sources was small enough that a series of light and dark bands was created on a screen placed in the path of the light. These bands of bright and dark are called interference fringes or maxima and minima. Figure 3 shows light waves, in phase, emerging from slits S1 and S2, a distance d apart. Although the waves spread out in all directions after emerging from the slits, we will analyze them for only three different angles,θ . In Fig 3(a), where 0θ = , both waves reach the centre of the screen in phase, since they travel the same distance. Constructive interference therefore occurs, producing a bright spot at the centre of the screen.

In Fig 3(b), when the waves from slit S2 travel an extra distance of / 2λ to reach the screen in (b), the waves from the two sources arrive at the screen 180° out of phase. Destructive interference occurs, and the screen is dark in this region (corresponding to nodal line

1n = ). In Fig 3(c), as we move still farther from the centre of the screen, we reach a point at which the path difference is λ , as in (c). Since the two waves are back in phase, with the waves from S2 one whole wavelength behind those from S1, constructive interference occurs (causing this region, like the centre of the screen, to be bright).

For destructive interference for appropriate values of the path difference, 1sin2nd nθ λ = −

For constructive interference for appropriate values of the path difference, sin md mθ λ= Since the dark fringes created on the screen by destructive interference are very narrow in comparison with the bright areas, measurements are made with those nodal lines.

Also, sin nθ is best determined by using the ratio sin nn

xL

θ = , where nx is the distance of the nodal line from the centre line on the

screen, and L is the distance to the screen from the midpoint between the slits in Fig 4. (For L>>x , sin = tan = x /L)n n n nθ θ

Young’s Formula Conditions: (1) ∆x, distance between 2 ‘nodal lines’ or dark lines = distance between the centers of 2 bright lines. (2) Relationship is used for small values of θ

Polarization: Light emitted by the sun, by a lamp, or by a candle flame is unpolarized light. Such light waves are created by electric charges that vibrate in a variety of directions, thus creating an electromagnetic wave that vibrates in a variety of directions. This concept of unpolarized light is rather difficult to visualize. It is helpful to picture unpolarized light as a wave that has an average of half its vibrations in a horizontal plane and half of its vibrations in a vertical plane. If we remove one of the components of the electric field, we produce polarized electromagnetic waves. Polarization is the removal of one component of the electric field.

Polarized Lenses: When light strikes a horizontal surface such as hood of a car or body of water, the electric fields that are perpendicular to the surface are absorbed and parallel or horizontal electric fields are reflected. Polarized lenses in sunglasses are oriented so that they absorb horizontal electric field and pass vertical electric field. Photos of a pond taken with a polarizing filter absorb the bright glare of water surface allowing the fish beneath the surface to be clearly visible. 3-D glasses (movies): have their polarizing directions oriented at 90° to each other. The left eye receives images from the left projector only, and the right eye receives images from the right projector only. We thereby fool the brain into thinking that it’s receiving two images of the same object, one from each eye.The brain puts the “two images” together to produce stereoscopic images.

Thin Film Interference Application: A coating of appropriate thickness on the front surface of sunglasses can create destructive interference eliminating most of the damaging wavelength of UV..

EXAMPLES & PRACTICE, 9.5 Double Slit Interference

Visible Light Spectrum

Solar Spectrum

Sodium

Mercury

Lithium

Hydrogen

Diffraction Grating & EM Spectra

c f λ=