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