What is the condition for **constructive** interference in terms of optical path difference?

Constructive interference occurs when

**Optical path difference = mλ**

Stationary waves can only be formed by interference at very specific frequencies.

What name is given to these frequencies?

Resonant frequencies.

A **polariser** and **analyser** combination can be used to increase or decrease the transmission of a light wave.

What would be observed if a laser beam was shone through a polariser and then an analyser which were at 90 degrees to each other?

There would be no light transmission through the polariser and analyser combination.

The relationship shown below can be used to determine the wavelength of a laser going through a double slit.

Define each of the quantities in the relationship.

Δx = distance between adjacent bright fringes (m)

λ = Wavelength of the laser light (m)

D = distance from double slit to screen (m)

d = distance between slits (m)

Under which condition will a wave undergo a phase change of λ/2 upon reflection?

The wave will be travelling from a medium with a lower refractve index and reflected by a medium with a higher refractive index.

What is the condition for** destructive** interference in terms of phase?

Two waves **meet** completely out of phase by half a wavelength- crest meets trough.

The phase difference Φ = π radians.

An experiment designed to show 'thin wedge' interference is set up as shown below:

What is the relationship used to describe thin wedge interference, and what does each quantity represent?

∆x = distance between bright fringes (m)

λ = wavelength of light (m)

l = length of 'wedge' (m)

d = height of 'wedge' at end (m)

What is the condition for **destructive** interferece in terms of optical path difference?

Constructive interference occurs when

**Optical path difference = (m+1/2) λ**

What is the relationship between the brewster angle and the refractive index of a material?

n = tan i_{p}

Plane polarised light can be produced by partial reflection from a glass surface as shown below.

The reflected ray will be plane polarised if the angle of incidence is equal to the brewster angle (i_{p}).

What condition must be met to find the brewster angle, and produce plane polarised light?

The angle between the reflected and refracted rays must be **90 degrees** as shown below. This will produce a reflected ray which is plane polarised parallel to the surface of the glass.

A stationary wave is formed in a piece of elastic string under tension, created by a vibration generator set to 250Hz as shown below.

The distance between adjacent nodes is 0.15m

- Determine the wavelength of this wave.
- Determine the speed of this wave.

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- The wavelength of the wave is
**0.3m** (The distance between nodes is equal to half a wavelength).
- The speed of the wave = frequency x wavelength

**0.3m**(The distance between nodes is equal to half a wavelength).= 250 x 0.3

**= 75 ms ^{-1}**

What does it mean if a wave is said to be **plane** **polarised**?

If the oscillations of the wave medium are restricted to one dimension only the wave is said to be **plane polarised.**

What is the relationship between geometrical path length and optical path length?

Optical path length = n x geometrical path length.

What is the unit of phase angle, Φ?

Radians (rad).

Shown below is an example of interference by division of amplitude- a lens is 'bloomed' with a non-reflective coating.

Derive the expression **d = λ/4n** where 'd' is the thickness of coating required to give destructive interference.

**Optical PD = λ/2** for destructive interference

also from the diagram, **Optical PD = 2nd**

therefore

2nd = λ/2

**d = λ/4n**

What is the relationship between the **optical path difference **and the **phase difference** (Ф) of two coherent waves of wavelength λ?

phase difference Ф (in radians) = (2π/λ) x optical path difference

What is meant by two waves being **coherent**?

The two waves have a **constant phase relationship** (that is the phase difference between any given point on each wave remains constant),

What effect would having a thinner 'wedge' (d) have on the spacing between bright fringes (∆x) in the following experiment?

A thinner wedge would make the spacing further apart.

The relationship shown below can be used to determine the wavelength of a laser going through a double slit.

What effect would be seen on the interference pattern if light of a shorter wavelength was used?

The distance between adjacent bright fringes, Δx, would be smaller (the fringes would be closer together).

How could you calculate the optical path difference if you know the optical path lengths of two coherent waves?

Optical path difference is the difference between the two optical path lengths.

What is the relationship between the energy transferred by a wave and the amplitude of the wave?

The energy transferred by a wave is proportional to the ampltude squared of the wave.

E = kA^{2}

or

E_{1}A_{1}^{2 }= E_{2}A_{2}^{2}

On a stationary wave, what is meant by the term **antinode**?

A point on the stationary wave pattern where there is maximum disturbance/maximum displacement.

What is the condition for **constructive** interference in terms of phase?

Two waves **meet** completely in phase- crest meets crest.

The phase difference Φ = 0 radians.

On a stationary wave, what is meant by the term **node**?

A point on the stationary wave pattern where there is no disturbance/zero displacement.

A stationary wave pattern is shown below.

What is the wavelength of the wave?

**The wavelength is 1m.**

(There are three half-wavelengths in 1.5m)

The phase difference (Φ) between two points on a travelling wave separated by a distance of half a wavelength (x = λ/2) is equal to how many radians?

Φ = x/λ x 2π

so if x = λ/2

**Φ = π radians.**

The relationship describing a travelling wave is shown below.

y = 4.0 sin2π(8t – 5x)

What is the relationship describing a reflected wave of the same type with** half the amplitude**, travelling in the **opposite direction**?

**y = 2.0 sin2π(8t + 5x) **

Any periodic (repeating) waveform can be created by adding a combination of sine and cosine waves together.

What is the name given to the process of adding waves together?

Superposition of waves

Explain, in terms of waves, how a stationary wave is produced.

Stationary waves are formed by the interference of two waves, of the same frequency and amplitude, travelling in opposite directions.

Interference can be produced by two methods, division of wavefront and division of amplitude.

Give example(s) of an experiment demonstrating

- Interference by division of wavefront
- Interference by division of amplitude