Waves and optics

Question 1

What is a wave?

Answer 1

A disturbance in a medium which transfers energy without transferring mass.

Question 2

What is the amplitude, wavelength, and frequency of a wave?

Answer 2

Amplitude - The maximum displacement of a particle from its equilibrium position.

Wavelength - The minimum distance between two points on the wave that are in phase.

Frequency - No. of complete waves the pass a point per second

Question 3

What is the phase difference for two points on a wave that are:
- in phase?
- in antiphase?
- out of phase?

Answer 3

Points seperated by an integer multiple of wavelengths (λ, 2λ, 3λ, etc) will be in phase.
Δø = 0, 2π, 4π, 6π, etc.

Points seperated by an odd integer number of half wavelengths (λ/2, 3λ/2, 5λ/2, etc) will be in antiphase.
Δø = π, 3π, 5π, etc.

Any other Δø is described as being “out of phase”.

Question 4

What is the equation for the phase difference between two points on a progressive wave?

Answer 4

phase difference (rad.) = 2pi x separation between points/wavelength
Δø = 2π x Δd/λ

Question 5

What are the wave equations? (3)

Answer 5

f = 1/T
v = fλ
c = fλ

Question 6

How do you calculate phase differences on a stationary wave?

Answer 6

Δø = no. of nodes between points x π

Question 7

Describe the nature of a longitudinal wave and give 2 examples

Answer 7

Direction of the oscillation of particles is parallel to the direction of energy transfer
- Sound Waves
- Seismic P-Waves

Question 8

Describe the nature of a transverse wave and give 2 examples

Answer 8

Direction of the oscillation of particles is perpendicular to the direction of energy transfer
- Electromagnetic waves
- Seismic S-Waves

Question 9

What is the speed of an electromagnetic wave in a vacuum?

Answer 9

3x10^8 ms-1

Question 10

What does it mean for a wave to be polarised, and what type of waves can be polarised?

Answer 10

To polarise a wave is to limit the direction of the oscillation of particles to only one direction. All particles will then oscillate in the same plane.

Only applies to transverse waves, particularly EM waves.

Question 11

What are some applications of polarisers?

Answer 11

Sunglasses - Polarising filters reduce the glare
EM Transmission - Arials for radio, satellite signals
Polarimetry - Measuring concentration of certain chemicals

Question 12

What is the principle of superposition?

Answer 12

When two waves of the same type meet, the overall displacement at any point is the sum of the individual displacements of the waves at that point.
“The waves superpose”

Question 13

What is a stationary wave and how are they formed?

Answer 13

• Formed when two waves with the same frequency travelling in opposite directions superpose
• At some points, the waves superpose in phase, producing antinodes.
• At other points, the waves always superpose in antiphase, producing nodes.
• The frequency/wavelength of the stationary wave is the same as that of the progressive waves that form it.
• Stationary waves store energy instead of transferring it like progressive waves

Question 14

What is a node and why is it formed?

Answer 14

Nodes are regions where there is no vibration from the equilibrium position.
They are formed when two waves superpose in antiphase.

Question 15

What is an antinode and why is it formed?

Answer 15

Antinodes are regions where amplitude is at a maximum.
They are formed when two waves superpose in phase.

Question 16

How do the wavelengths of the harmonics on a string compare to the length of a string?

Answer 16

λₙ = 2L / n, where L is the length of the string

Question 17

How can the frequencies of the harmonics on a string be calculated?

Answer 17

fₙ = n x f₁

Question 18

What are the differences between progressive and stationary waves?

Answer 18

Progressive Waves:
- Every point has the same amplitude
- Δø = 2π x Δd/λ
Stationary Waves:
- Amplitude varies from a maximum at an antinode to a minimum at a node
- Δø = no. of nodes between points x π

Question 19

What is the first harmonic equation?

Answer 19

f₁ = 1/2L x √(T/μ)
where f₁ is the frequency of the first harmonic (m)
L is the vibrating length of the string (m)
T is the tension in the wire (N)
μ is the mass per unit length, kg.m⁻¹

Question 20

What factors of the string determine the frequency of its first harmonic?

Answer 20

• Length
• Thickness
• Material
• Tension

Question 21

What is the range of visible wavelengths and in what order are the colours found?

Answer 21

400 - 700 nanometres
violet is found at the 400 end
red is found at the 700 end

Question 22

What does it mean for a light source to be monochromatic?

Answer 22

Single wavelength

Question 23

What does it mean for two light sources to be coherent?

Answer 23

• Same frequency/wavelength
• Constant phase relationship

Question 24

What is the relationship between path difference and phase difference?

Answer 24

Δø = 2π x Δd/λ
where Δø is the phase difference (rad.)
Δd is the path difference (m)

I REALISED WHAT THIS IS SAYING IT JUST MEANS THAT THEY’RE PROPORTIONAL
so if Δø = 2π, Δd = 1 (i think?) (both of those are in phase)
and if Δø = π, Δd = 1/2

Question 25

What assumptions are made when deriving the double slit formula?

Answer 25

- The light is monochromatic - Each slit acts as a source of coherent waves

Question 26

What is the double slit formula?

Answer 26

W = λD/s Where W = fringe width(m) λ is wavelength (m) D is slit-to-screen seperation (m) s is seperation

Question 27

What is the path difference equation?

Answer 27

When the path difference is equal to nλ (n = integer), the rays from every slit will superpose in phase producing a maximum. sinθ = Δd/d where: Δd = path difference d = grating spacing

Question 28

# T What is diffraction?

Answer 28

The spreading out of waves after passing through an opening or around an obstacle.

Question 29

What is the pattern observed when monochromatic light is shone through a single slit?

Answer 29

- Each slit acts as a source of coherent waves. These waves diffract after passing through each slit and superpose with one another. - Bright patches (maxima) form when waves suerpose in phase, causing constructive interference. - Dark patches (minima) form when waves superpose in antiphase, causing destructive interference - As the orders increase, the fringes become progressively dimmer

Question 30

What is the pattern observed when white light is shone through a single slit?

Answer 30

- Bright central white 0ᵗʰ order beam - Higher orders are split into spectra, with violet closest to the centre and red furthest from the centre - As the orders increase, the maxima become wider - Higher order maxima may overlap and longeer wavelengths may not be seen

Question 31

How does the width of the central maximum vary with the slit width?

Answer 31

The width of the central maximum is inversely proportional to the slit width. Narrower slit = wider central maximum, but dimmer pattern

Question 32

How does single slit diffraction affect the pattern from a double slit experiment?

Answer 32

Due to single slit diffraction, a real double slit experiment will see the fringe intensity decrease from the centre. (its the graph with the graph within a graph if you get what i mean)

Question 33

What is the relationship between the grating spacing and the number of lines per metre?

Answer 33

d = 1/(no. of lines per metre) where d is the grating spacing

Question 34

What is the equation for the highest order maximum seen?

Answer 34

nₘₐₓ = d/λ, rounded down where nₘₐₓ is the max order d is the grating spacing λ is the wavelength

Question 35

What are some uses of diffraction gratings?

Answer 35

- Determining the wavelength of an unknown source of light - Spectrometry - astrophysics - identifying the composition of stars - Spectrometry - chemistry - identifying chemical composition of a sample - Select a specific wavelength from a spectrum - Entertainment (lightshows, etc)

Question 36

What is the diffraction grating formula?

Answer 36

sin(θₙ) = nλ/d n.λ = d.sin(θₙ) where: θₙ = angle between 0ᵗʰ and nᵗʰ orders d = grating spacing (m) λ = wavelength (m) n = order

Question 37

What is refraction?

Answer 37

The bending of light when it crosses the boundary between two transparent median of different refractive indices, at an angle to the normal

Question 38

What is the refractive index of a material and how is it calculated?

Answer 38

A measure of how much the speed of light is reduced within a given medium compared to its speed in a vacuum. Only the wavelength changes, not the frequency Refractive index = wavelength in a vaccum / wavelength in the medium

Question 39

Name some of the refractive indices you should expect for air, water, glass and diamond (TAZARLORD REFERENCE?)

Answer 39

- Air - 1 - Water - 1.33 - Glass - 1.5 - Diamond - 2.4

Question 40

Which angle is used in Snell's Law calculations?

Answer 40

The angle between the light ray and the normal

Question 41

What is total internal reflection (TIR)?

Answer 41

Occurs when: - The angle of incidence is greater than the critical angle (θ₁ > θ꜀) - Light travels from a denser medium to a less dense medium (refractive indices) (n₁ > n₂)

Question 42

What is the critical angle?

Answer 42

(AI Generated answer FUCK THIS TOPIC) Definition of Critical Angle: The critical angle is the angle of incidence in the denser medium at which the angle of refraction in the less dense medium is 90 degrees. At this angle, the refracted ray travels along the boundary between the two media. If the angle of incidence is greater than the critical angle, total internal reflection occurs, and no light is refracted into the less dense medium. If the angle of incidence is less than the critical angle, the light is partially refracted and partially reflected.

Question 43

What are the two components of a fibre optic cable and their functions?

Answer 43

Core - Where the light travels through. Has a higher refractive index than the cladding. Cladding - Promotes TIR at core-cladding boundary, protects the core from scratches, prevents 'cross talk' (where signals cross from one core to a neighboring core in the bundle)

Question 44

What is material dispersion, why does it occur and how can it be mitigated?

Answer 44

Transparent materials have different refractive indices for different frequencies of light. Generally, shorter wavelengths = higher refractive index. Different refractive indices mean that idfferent colours travel at different speeds down an optical fibre. Limiting material dispersion - use monochromatic signals

Question 45

What is modal dispersion, why does it occur and how can its effects be mitigated?

Answer 45

Light rays taking different paths ("modes") down the cable of different lengths, and therefore taking different times. Limiting modal dispersion - use narrower cores, make the n(cladding) close to n(core) so that θ꜀ is big, limiting the potential of different modes

Question 46

What happens when n₁ > n₂, and when n₂ > n₁?

Answer 46

n₂ > n₁ = ray reflects towards the normal n₁ > n₂: - θ₁ < θ꜀ = ray reflects away from the normal - θ₁ = θ꜀ = ray refracts along the boundary - θ₁ > θ꜀ = ray undergoes TIR