Quanta and Waves part II

Question 1

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

Answer 1

Constructive interference occurs when

Optical path difference = mλ

Question 2

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

What name is given to these frequencies?

Answer 2

Resonant frequencies.

Question 3

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?

Answer 3

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

Question 4

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.

Answer 4

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)

Question 5

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

Answer 5

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

Question 6

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

Answer 6

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

The phase difference Φ = π radians.

Question 7

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?

Answer 7

∆x = distance between bright fringes (m)

λ = wavelength of light (m)

l = length of ‘wedge’ (m)

d = height of ‘wedge’ at end (m)

Question 8

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

Answer 8

Constructive interference occurs when

Optical path difference = (m+1/2) λ

Question 9

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

Answer 9

n = tan i_p

Question 10

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?

Answer 10

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.

Question 11

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

1. Determine the wavelength of this wave.
2. Determine the speed of this wave.

Answer 11

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

= 250 x 0.3

= 75 ms^-1

Question 12

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

Answer 12

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

Question 13

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

Answer 13

Optical path length = n x geometrical path length.

Question 14

What is the unit of phase angle, Φ?

Answer 14

Radians (rad).

Question 15

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.

Answer 15

Optical PD = λ/2 for destructive interference

also from the diagram, Optical PD = 2nd

therefore

2nd = λ/2

d = λ/4n

Question 16

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

Answer 16

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

Question 17

What is meant by two waves being coherent?

Answer 17

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

Question 18

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

Answer 18

A thinner wedge would make the spacing further apart.

Question 19

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?

Answer 19

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

Question 20

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

Answer 20

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

Question 21

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

Answer 21

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

E = kA²

or

E₁A₁² = E₂A₂²

Question 22

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

Answer 22

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

Question 23

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

Answer 23

Two waves meet completely in phase- crest meets crest.

The phase difference Φ = 0 radians.

Question 24

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

Answer 24

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

Question 25

A stationary wave pattern is shown below.

What is the wavelength of the wave?

Answer 25

The wavelength is 1m.

(There are three half-wavelengths in 1.5m)

Question 26

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?

Answer 26

Φ = x/λ x 2π

so if x = λ/2

Φ = π radians.

Question 27

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?

Answer 27

y = 2.0 sin2π(8t + 5x)

Question 28

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?

Answer 28

Superposition of waves

Question 29

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

Answer 29

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

Question 30

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

Give example(s) of an experiment demonstrating

1. Interference by division of wavefront
2. Interference by division of amplitude

Answer 30

1. Young’s double slit experiment, experiments using gratings.
2. ‘Bloomed’ lenses, thin film interference, ‘wedge’ fringes, newton’s rings.