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Waves
• Progressive waves• Transverse and longitudinal waves
• Polarization• Determination of speed, frequency and wavelength
• Electromagnetic spectrum
When are waves formed?
• When there is a disturbance in the medium.
As the wave passes through, the particles in the air oscillate back and forth about their equilibrium positions but it is the disturbance which travels, not the individual particles in the medium.
Progressive waves
• Waves which move energy from place to place
Transverse and longitudinal waves
Graphical representation
of waves
Terms• Amplitude
• Wavelength
the maximum displacement of a particle in a wave from its equilibrium position. It is measured in metres (m).
the distance between two neighboring points which are vibrating together in exactly the same way on a wave (i.e. one full wave). It is measured in metres (m).
• Time period: The period of the wave is the time for a particle in the wave to complete one vibration.
• Frequency: The number of complete vibrations per unit time.
Phase• A term used to describe the relative positions
of the crests and troughs of two waves of the same frequency.
http://www.acoustics.salford.ac.uk/feschools/waves/super.htm
Intensity
• Amount of energy passing through unit area per unit time.
• For a wave of amplitude A and frequency f, the intensity is proportional to .
• For a point source the wave will be a spherical wave.
Intensity is proportional to 1/
Wave equation
Polarization
The vibrations in the rope will only pass through the narrow gap in the railings if the vibrations are parallel to the individual rails. Thus an up and down vibration is transmitted through the vertical railings, but is stopped by the horizontal ones.
• The condition for a wave to be plane polarized is for the vibrations to be in just one direction normal to the direction in which the wave is traveling.
• Polarisation can be applied only to transverse waves and not longitudinal waves.
Polarizing light waves
The light that you see all around you, from the sun and from light bulbs etc, is made up of many electromagnetic waves all travelling independently in different directions. This is called unpolarised light.
Polaroid filter. This kind of filter is made up of parallel strands of long molecules. Let's think of a polaroid where these strands are horizontal. The energy of the horizontal components of light is absorbed by the strands, so this part cannot pass through. The vertical components can pass through, however, because the horizontal strands cannot absorb their energy.
POLARISATION BY REFLECTION: Reflected light is partly plane-polarised depending on the incident angle.
Electro-magnetic WavesAll the waves in the electromagnetic spectrum...• travel the same speed in a
vacuum;• can be reflected, refracted,
diffracted and polarised;• are transverse waves.• Em spectrum pg no. 251 in text
book
Principle of superposition
The principle of superposition may be applied to waves whenever two (or more) waves travelling through the same medium at the same time. The waves pass through each other without being disturbed. The net displacement of the medium at any point in space or time, is simply the sum of the individual wave displacements
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INTERFERENCE animation water ripples and light
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Interference animation sound
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Interference
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When two progressive waves of the same type coincide, they superpose. The results of the superposition (addition) is interference.
Interference Constructive and Destructive Interference
Two waves (top and middle) arrive at the same point in space.
The total wave amplitude is the sum of the two waves.
The waves can add constructively or destructively
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Two waves can have an infinite variety of relationships in phase. To describe them, we use the idea of phase angle.
In order to form an interference pattern, the incident light must satisfy two conditions:
(i) The light sources must be coherent. (ii) The light must be monochromatic.
Light emitted from an incandescent lightbulb is incoherent because the light consists of waves of different wavelengths and they do not maintain a constant phase relationship. Thus, no interference pattern is observed.
Coherent sources• Two sources of light are said to be coherent if
the waves emitted from them have the same frequency and are 'phase-linked'; that is, they have a zero or constant phase difference.
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Young’s Double Slit Experiment
Interference of light waves was first demonstrated by Thomas Young in 1801.
When two small apertures are illuminated with coherent light, an interference pattern of light and dark regions is observed on a distant screen:
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Light
(resourcefulphysics.org)
Path Difference
We can understand the interference pattern as resulting because light from the two apertures will, in general, travel a different distance before reaching a point on the screen. The difference in distance is known as the path difference.
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Light
P
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Red filtered light from
Animation
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Constructive interferencePath difference = whole number of wavelength
Destructive interferencePath Difference= odd number of half wavelengths
Determining wavelength
• λ = ax/D
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a is the distance between the center of slits
Research
These soap bubbles exhibit brilliant colors when exposed to sunlight. (credit: Scott Robinson, Flickr)Explain this phenomenon in your notebook
Write observations for the following in your notebook.Do not forget to copy question
Look at a light, such as a street lamp or incandescent bulb, through the narrow gap between two fingers held close together. What type of pattern do you see? How does it change when you allow the fingers to move a little farther apart? Is it more distinct for a monochromatic source, such as the yellow light from a sodium vapor lamp, than for an incandescent bulb?
DiffractionDiffraction manifests itself in the apparent bending of waves around small obstacles and the spreading out of waves past small openings.
Diffraction
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Diffraction refers to various phenomena which occur when a wave encounters an obstacle. It is described as the apparent bending of waves around small obstacles and the spreading out of waves past small openings.
While diffraction occurs whenever propagating waves encounter such changes, its effects are generally most pronounced for waves where the wavelength is on the order of the size of the diffracting objects.
Diffraction Grating
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An optical device consisting of an assembly of narrow slits or grooves, which by diffracting light produces a large number of beams which can interfere in such a way as to produce spectra
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Diffraction Grating Formula
Constructive interference only occurs along a few precise directions, one of which is shown in the diagram. Light from A must be in phase with light from B, and this can only happen when the path difference is a whole number of complete wavelengths (even number of half-wavelengths).
AC = n λ, where n = 0, 1, 2, 3… Now: AC = d sinθ Where is θ the angle of diffraction.
d sin θ = nλ The term n is called the spectrum order. If n = 1, we have the first diffraction maximum. Sin θ can never be greater than 1, so there is a limit to the number of spectra that can be obtained.
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