Grade 12 Physics – Waves and Light
Waves in Two Dimension
- Amplitude: the height of a wave from the equilibrium to its crest or trough
- Wavelength: the length of one wave: related to the speed, denoted as λ (Lambda)
- Frequency: the number of times a wave occurs in a second (Hz)
- Period: amount of time it takes to complete a wave cycle
- Reflection: when a wave bounces off a surface, the angle of reflection is equal to the angle of incidence.
- A crest reflects off a slower medium becomes a trough
- Crests do not change if reflecting off a faster medium
- Refraction: when light passes through a new medium, it’s direction, wavelength, and speed changes. Frequency does not change between mediums.
- Wave Front: the leading edge of the wave
- Absolute Refractive Index: the index of refraction for light passing from air or a vacuum into a substance. (n1, n2)
- Index of refraction: n = n2 / n1
- How many times slower the wave travels in a medium
n1 / n2 = v1 / v2 = λ1 / λ2 = sinθ1 / sinθ2
- All periodic waves obey the universal wave equation:
v = fλ
- Partial Reflection: When some of the light is reflected and some passes through and is refracted
- Snell’s Law: angle of incidence over angle of refraction equals the index of refraction.
n = sinθi / sinθr
Diffraction of Water Waves
- Diffraction: Straight waves that pass through an opening will become a new source of its own
- Waves of longer wavelength has more diffraction than shorter wavelengths
- For waves observable: λ / w >= 1 : where w is the width of the opening
Interference of 2D waves
- 2 waves coming from 2 sources radiating out can create interferences to each other
- Waves must be the same frequency and wavelength
- They must be in-phase (beginning at the same time)
- Lines of constructive Interference are called Maxima Lines
- Lines of deconstructive Interference are called Nodal Lines or Minima Lines
- Increasing the frequency, lowering the wavelength increases the number of nodal lines
- Path Length Difference equation for 2D wave interferences:
| PnS1 – PnS2 | = (n – 1/2)λ
- Finding Angle of interference nodal lines:
sinθn = (n – 1/2)λ/d
- Where n is the number of nodal line and d is the distance between the sources
- Equation for waves that span a farther, longer distance
Xn / L = (n – 1/2) λ/d
- Where Xn is the perpendicular distance from the right bisector to Point Pn
- Where L is the distance from the midpoint between the sources to Point Pn
Light as a Particle/ Light as a Wave
- Newton’s Particle theory of light explained 4 properties of light:
- Rectilinear Propagation: great speed of light allowed light particles to travel at near straight lines for long distances: similarly to a bullet.
- Reflection: If vector components are used to break apart the velocity of lights, it can be explained how the angle of incidence = angle or reflection. Vx and Vy are reversed due to the reactive force of the horizontal surface.
- Refraction: Speed of the light, just as if it’s a ball, will swerve in the direction it originally was before it regains and aligns again as it moves through faster medium (or falling down a ramp at an angle)
- Dispersion: Different mass for each colour means some colours would have less momentum and would be diverted more easily, hence, white light spreading out into colours as we know it.
- However, it did not explain diffraction and partial reflection/refraction
- Huygens’ Wave theory of light assumed every point of the wave front was it’s own source of tiny wavelets, radiating at the same speed and tangent to the wave.
- Huygens explained the following light properties:
- Reflection: Waves obey the laws of optics and would reflect accordingly
- Refraction: Wavelengths of the waves are changed as they are slowed down through a different medium and will bend accordingly.
- Partial Reflection/Refraction: Combining reflective and refractive properties of waves, it is possible to explain partial reflection/refraction
- Diffraction: Lights showed interference through a double slit experiment also, proving they travelled in waves.
- Rectilinear Propagation: Huygens thought the light rays represented the direction of the motion of the wave front
Young’s Double Slit Experiment
- When wave interferences needed to be tested, 2 light sources would be out of phase and hard to sync
- Young thought of using 1 source, and instead use 2 slits to separate the source
- And as expected, nodal lines (dark fringes) and maxima lines were visible
sinθm = mλ / d
- Where m is for the maxima lines (1, 2, 3..) and d is the distance between sources
sinθn = (n – 1/2)λ/d
- Where n is for nodal lines, and d is the distance between sources
sinθn = Xn / L = (n – 1/2) λ/d
- All three parts are equal and can be used together, where L is the distance from midpoint to Point Pn on the nodal line
ΔX / L = λ / d
- Where ΔX is the distance between nodal lines
- Colour is dictated by the wavelength of light it produces. Each colour has its own interval of wavelengths.
Polarization of Light
- Light, being a transverse wave, will only travel through filters that are slitted in its direction.
- Light traveling through a polarizer will keep it in one direction
- Polaroids have small slits that only allow light to travel in one direction through it
- Scattering of light: light changes direction when it hits particles in the air
- Photo elasticity: materials that make patterns when they are bent or under stress, As light traveling through it are polarized as the molecules bend, patterns are seen.
- Monochromatic: single colour wavelength
- Polarization can be used to reduce glare as light reflected off a surface can become polarized
Diffraction of light through a single slit
- Based on Huygens’ theory that light is a wavefront with tiny wavelets, traveling in tangent and at the same speed as the wave, Interference can occur if the wave front is traveling at an angle through a slit
- Pairs of waves can interfere with each other, creating dark and bright fringes, radiating from the centre and losing energy as it radiates outwards.
- The smaller the slit, the larger the distance between Maxima and Minima, and vice versa
- For minima, dark fringes (!! Different formula from before!!)
sinθn = nλ / w
- Where n is the number of nodal lines, w is the width of the slit
- For maxima, bright fringes (!! Different from before !!)
sinθm = (m + 1/2)λ / w
- Where m is the number of maxima lines and w is the width of the slit
- The Separation between between adjacent maxima or minima is given as
Δy = λL / w central maxima: 2λ
- where L is the distance of the perpendicular bisector and w is the width of the slit
- Resolution: is the ability of an instrument to separate two closely spaced images, is limited by the diffraction of the light.
- Diffraction Grating: device with surface of equally spaced parallel lines resolving light into spectra; transmission gratings are transparent; reflection gratings are mirrored.
- Diffraction Gratings deliver brighter interference patterns than typical double slots, with maxima that are narrower and more widely spaced
- sinθm = mλ / d
- where d is the distance between adjacent gratings, and m is the order of Maxima
- Spectroscope: used to analyze light in a spectrum, uses a collimator to send light to grating
- grating splits light into its respective colours.
Interference through thin films
- Light reflects off a thin coat, some refracts into the coat, and reflects off the medium behind it, and bounces out of the thin coat, causing interferences
- Crests reflecting off a faster medium stays crest
- Crests reflecting off a slower medium becomes trough
- Thickness of the film is dictated by how it alters the wavelength, either by cutting it short by 1/2, 1/4 or 1 lambda.
t = λcoating / Amount of Coating distruption