Waves properties of lightMfd 2007

The nature of light

Sir Isaac Newton (1642-1727) believed that light consisted of particles or corpuscles.

The Dutch scientist, Christian Huygens (1629-1695), agreed with the wave nature of light and was able to explain reflection and refraction by using the properties of waves.

However, none of these scientists had enough influence to seriously challenge people's belief in Newton's theory of light as particles, until Thomas Young carried out his experiments with light.

For more than three hundred years, the nature of light has been the subject of arguments between scientists. Some have thought that light behaves as waves, others that light behaves as particles.

Refraction is a wave phenomenon

Thomas Young

Thomas Young carried out many investigations into different areas of science. In 1800 he published a paper on sound and light which was presented to the Royal Society.

This paper provided experimental evidence which could only be explained by the wave theory of light.

However, no-one appreciated the importance of his discoveries until Augustin Fresnel repeated many of them 14 years later.

Interference of waves

When two waves meet their amplitudes add together giving a resultant wave at the point where they meet.

If their amplitudes are both positive a larger wave results. This is called constructive interference or reinforcement.

If the amplitude of one wave is positive but the other is negative, the amplitude of the waves is reduced. This is called destructive interference.

Interference is a wave phenomenon

Interference in water waves

Conditions for constructive interference

Path difference for constructive interference = mλ where m = 0, 1, 2, 3, ...

Constructive interference occurs between two waves, when the path difference is always a whole number of wavelengths.

Conditions for destructive interference

Path difference for destructive interference = mλ + λ/2 where m = 0, 1, 2, 3,

Destructive interference occurs, the path difference is always a whole number of wavelengths plus half a wavelength.

Diffraction is the spreading of waves around an obstacle.

A slit can be thought of as a narrow space between two obstacles.

Diffraction

Huygen’s Principle

“Every point on an advancing wavefront is the source of a secondary circular wavelet. The new wavefront is the tangent to these circular wavelets” 1650

Huygen's Principle

Huygen suggested that the behavior of waves can be explained by considering that each point on a wave front produces semi-circular wavelets and a new wave front is the result of the addition of all the wavelets.

Monochomatic light is light of one wavelength only.

Waves are coherent if there is a constant phase difference between them, ◦ i.e. if at one point in time the phase

difference between the waves is λ/2 then the phase difference continues to be λ/2 as the waves advance. This can only occur when the waves have the

same frequency◦ Most light sources produce waves which are

not monochromatic and coherent.

Monochromatic and coherent light

Young’s experiment

Young’s double slit experiment

Interference pattern

Double Slit Interference

Diffraction of a very narrow slit

Single Slit Interference

Thomas Young was the first person to discover a method of producing two sources of light which would emit coherent waves.

Thomas Young first demonstrated this apparatus in 1801. It clearly shows interference patterns of light which can only be explained if light is behaving as waves.

Young's double slit experiment

The production of an interference pattern by the double slit apparatus

Formation of a bright fringe in the centre of the pattern of the double slit apparatus

Calculating the fringe separation for the double slit apparatus

Derivation of the equations dsin = mλ and y = λL/d

Derivation of the equations dsin = mλ and y = λL/d

Example 10.1

10.1Solution

Interference and the speckle effect of laser light

When laser light falls onto a surface which appears to be smooth, e.g. a whiteboard or mirror, a small spot of light is produced. When this spot of light is magnified, it can be seen that it is not a solid spot of light but has dark and light areas

Areas of annulment and reinforcement will occur because the light is initially in phase. Reflection from different parts of the surface will cause the light to travel different distances. If the path difference is a whole number of wavelengths, reinforcement will occur, producing a light area. If the path difference is a whole number of wavelengths plus an extra half wavelength, annulment will occur, producing a dark area.

Transmission diffraction grating

A transmission diffraction grating consists of a large number of equally spaced slits. The slits are very narrow. 600 slits per cm is a common number, giving a spacing of 1.7 x 10-5 m betweenadjacent slits. The slits are usually spaces between lines ruled on glass or plastic.Light is scattered inside the uneven surface of the ruled lines and does not pass directly through.However, the light does pass directly through the spaces between the lines.

Interference of light passing through a transmission diffraction grating

Each slit in the diffraction grating acts as the source of semi-circular wavelets which spread out in a similar way to the double slit apparatus, as described in Huygens's principle.However, constructive interference, producing maxima, occurs only at particular angles from theoriginal direction of the light.

. At all other angles there is destructive interference between the waves from each slit and the waves from at least one other slit. The waves which destructively interfere may be some distance away from each other on the grating, but because there are so many slits destructive interference occurs at almost all angles. So most of the screen is dark.

The monochromatic light is either shone first through a single slit which produces coherent light, or laser light is used. The coherent waves then pass through the diffraction grating. The diffracted rays are focused by a lens so that they form an image on the screen. For certain angles, which fit the relationship dsin = mλ, maxima will be seen as bright sharp lines on the screen.

An angle of 0° produces a very bright central maximum called the zero order maximum, at other angles, less bright maxima are produced. The maxima occur symmetrically in pairs, one of each pair on either side of the zero order maximum. As the maxima get further away from the centre, they decrease in brightness and they become further away from each other when projected onto a flat screen.

For the zero order maximum, m = 0, for the first order maximum, m = 1, etc. The greatest angle at which a maximum can occur is 90°.

Calculating the angles at which maxima occur

Example 10.2

A spectrometer is an instrument which allows the measurement of the positions of maxima produced by a diffraction grating

Spectrometer

A diffraction grating and spectrometer are being used to determine the wavelength of light. The diffraction grating has 300 lines per millimetre. The angle between the zero order maximum and the first order maximum is found to be 8.2°. Find the wavelength of the light.

Example 10.3 - Method 1

Method 2

This second method easily demonstrated using a laser, for which the light is already coherent. Therefore it is not necessary to pass the laser light through a single slit to produce coherent light1. Shine laser light through a can be diffraction grating, of known slit

separation, onto a screen such as a whiteboard. 2. Measure the distance from the diffraction grating to the screen, L;3. Measure the distance from the zero order maximum to the first order

maximum, y.4. Calculate using trigonometry.5. Calculate X from d sin = mλ6. Repeat the measurements for other maxima and average the results for λ .

Example 10.4 - Method 2

Interference using white light