SPH4U Grade 12 Physics Waves and Light Test

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

  • 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