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 =- How many times slower the wave travels in a medium

**n**_{1 }**/ n**_{2 }**= v**_{1}** / v**_{2 }**= λ**_{1 }**/ λ**_{2 }**= sinθ**_{1}** / sinθ**_{2}

- 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 = sinθ**_{i}** / sinθ**_{r}

**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:

**| P**_{n}**S**_{1 }**– P**_{n}**S**_{2 }**| = (n – 1/2)λ**

- Finding Angle of interference nodal lines:

**sinθ**_{n }**= (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

**X**_{n}** / L = (n – 1/2) λ/d**

- Where X
is the perpendicular distance from the right bisector to Point P_{n }_{n} - Where L is the distance from the midpoint between the sources to Point P
_{n}

**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

**sinθ**_{m }**= mλ / d**

- Where m is for the maxima lines (1, 2, 3..) and d is the distance between sources

**sinθ**_{n }**= (n – 1/2)λ/d**

- Where n is for nodal lines, and d is the distance between sources

**sinθ**_{n }**= X**_{n}** / 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 P
_{n}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!!)

**sinθ**_{n }**= nλ / w**

- Where n is the number of nodal lines, w is the width of the slit
- For maxima, bright fringes (!! Different from before !!)

**sinθ**_{m }**= (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
**sinθ**_{m }**= 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 = **λ**_{coating }**/ Amount of Coating distruption**