TOPIC 12: SUPERPOSITION (INCOMPLETE)

Question 1

[Definition] Principle of Superposition

Answer 1

The principle of superposition states that when two or more waves meet and overlap, the resultant displacement is the vector sum of the displacement of each individual wave

Question 2

Are the waves’ travel altered after they meet and overlap?

Answer 2

NO!

Question 3

[Definition] Interference

Answer 3

An interference pattern is a pattern of maxima and minima,

which results from 2 or more waves meeting and overlapping such that the resultant displacement is the vector sum of the displacement of each individual wave

*depending on context, may need to bring in additional details provided in qn

Question 4

Odd / Even number integer of phase difference

Answer 4

Even number: Meet in-phase, Constructive interference

Odd number: Meet anti-phase, Destructive interference

Question 5

Standard answering for why particles at rest / describe and explain intensity at X

Answer 5

1. Find path difference
2. Find phase difference
3. Explain in words
   - Waves from X and Y meet and overlap at point Z in phase / anti-phase,
   - undergo constructive / destructive interference,
   - since waves individually have same amplitude at Z,
   - vector sum of displacements is 0

Question 6

[Definition] Diffraction

Answer 6

Diffraction is the spreading of a wave into the geometric shadow when it passes through a slit or past an edge of an obstacle

Question 7

When is diffraction most significant?

Answer 7

When size of the aperture (or obstacle) is the same order of magnitude as the wavelength of the wavelength

Question 8

Phrasing for describing / explaining changes to (diffraction) pattern

Answer 8

SAO / SOA

1. Separation of fringes
   - distance between central bright fringe and first minima increase or decrease / central maxima is broader or narrower
2. Amplitude of waves
   - (Intensity ∝ Amplitude²)
   - Intensity increase or decrease
3. Overlap of diffracted waves
   - Less or more spreading of the waves

Question 9

[Formula] Single-Slit Diffraction

Answer 9

sin θ = λ / b

Question 10

[Definition] Rayleigh Criterion

Answer 10

The Rayleigh Criterion states that the limit for which 2 sources of light can be just distinguished is when

the first minima of the diffraction pattern of one source coincides with the central maximum of the diffraction pattern of the other source

Question 11

[Formula] Rayleigh Criterion

Answer 11

θ = λ / b
+
s = rθ

Question 12

Conditions for coherent waves

Answer 12

1. Waves of the SAME TYPE meet and overlap
2. Waves from sources with CONSTANT PHASE DIFF
3. If waves are transverse, they are either unpolarised or polarised IN THE SAME PLANE

Note:
4. For good contrast, maxima to be as high intensity and minima to be as low intensity

Question 13

[Formula] Double-Slit Interference

Answer 13

x = λD / a

Question 14

What is single slit envelope?

Answer 14

Single slit diffraction observed over and above the double slit interference pattern

Question 15

[Formula] Diffraction Grating

Answer 15

d sinθ = nλ

d = unit length / N

Question 16

Wavelength or red and blue light?

Answer 16

Red light ( λ ≈ 700 nm)
Blue light ( λ ≈ 400 nm)

Question 17

What is formula for single slit / double slit / diffraction grating used for respectively?

Answer 17

Single slit: Position of first minima
Double slit: Fringe separation
Diffraction grating: Position of nth order maxima

Question 18

[Definition] Stationary Waves

Answer 18

A stationary wave is formed when two waves

of the same type, same amplitude, same frequency, wavelength and speed,

travelling in opposite directions towards each other,

meet and overlap to superpose across a length

Question 19

Free VS Fixed End: Difference in resultant displacement at boundary and phase change of refleced wave

Answer 19

Free end:
Maximum amplitude, meet in-phase,
Δϕ = 0

Fixed end:
No displacement, meet in anti-phase,
Δϕ = π