CAIE A-Level Physics 8.3 Interference

Practise analysing coherent-source interference, path and phase differences, experimental conditions and quantitative fringe patterns.

Exam points

define interference and coherence and identify constructive or destructive regions from phase or path difference
interpret two-source interference experiments across water, sound, light or microwaves and state the required conditions
calculate double-slit fringe spacing, wavelength, slit separation or screen distance using λ = ax/D

Covered syllabus points

8.3.1—The terms interference and coherence 8.3.2—Experiments that demonstrate two-source interference 8.3.3—The conditions required if two-source interference fringes are to be 8.3.4—Λ = ax / D for double-slit interference using light

[Maximum number: 4]

(a)

Two sources $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ of sound waves are positioned as shown in Fig. 5.2.

Fig. 5.2 (not to scale)

The sources emit coherent sound waves of wavelength 0.85 m . A sound detector is moved parallel to the line $S_{1} S_{2}$ from a point X to a point Y. Alternate positions of maximum loudness L and minimum loudness Q are detected, as illustrated in Fig. 5.2.

Distance $S_{1} X$ is equal to distance $S_{2} X$ . Distance $S_{2} Y$ is 7.40 m.

[ 4 ]

(i)

Explain what is meant by coherent waves.

[ 1 ]

(ii)

State the phase difference between the two waves arriving at the position of minimum loudness Q that is closest to point X.
phase difference =

[ 1 ]

$180^{\circ}$

A1

(iii)

Determine the distance $S_{1} Y$ .
distance = m

[ 2 ]

path difference $=2 \lambda$ or $\mathrm{S}_{1} \mathrm{Y}-\mathrm{S}_{2} \mathrm{Y}=2 \lambda$

C1

$\begin{aligned} \text { distance } =7.40+(0.85 \times 2) =9.1 \mathrm{~m} \end{aligned}$

A1

[Maximum number: 8]

(a)

Interference fringes may be observed using a light-emitting laser to illuminate a double slit. The double slit acts as two sources of light.

Explain

[ 1 ]

(i)

the reason why a double slit is used rather than two separate sources of light.

[ 1 ]

(b)

A laser emitting light of a single wavelength is used to illuminate slits $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ , as shown in Fig. 6.1.

Fig. 6.1 (not to scale)

An interference pattern is observed on the screen A B. The separation of the slits is 0.48 mm . The slits are 2.4 m from AB . The distance on the screen across 16 fringes is 36 mm , as illustrated in Fig. 6.2.

Fig. 6.2

Calculate the wavelength of the light emitted by the laser.
wavelength = m

[ 3 ]

$x=\lambda D / a$

C1

$\lambda=\left(36 \times 10^{-3} \times 0.48 \times 10^{-3}\right) /(16 \times 2.4)$

C1

$=4.5 \times 10^{-7} \mathrm{~m}$

A1

(c)

Two dippers $\mathrm{D}_{1}$ and $\mathrm{D}_{2}$ are used to produce identical waves on the surface of water, as illustrated in Fig. 6.3.

Fig. 6.3 (not to scale)

Point P is 7.2 cm from $D_{1}$ and 11.2 cm from $D_{2}$ .
The wavelength of the waves is 1.6 cm . The phase difference between the waves produced at $\mathrm{D}_{1}$ and $\mathrm{D}_{2}$ is zero.

[ 4 ]

(i)

State and explain what is observed at P .

[ 2 ]

no movement of the water/water is flat/no ripples/disturbance

B1

the path difference is $2.5 \lambda$ or the phase difference is $900^{\circ}$ or $5 \pi \mathrm{rad}$

B1

(ii)

State and explain the effect on the answer to (c)(i) if the apparatus is changed so that, separately,
1. the phase difference between the waves at $\mathrm{D}_{1}$ and at $\mathrm{D}_{2}$ is $180^{\circ}$ ,
2. the intensity of the wave from $D_{1}$ is less than the intensity of that from $D_{2}$ .

[ 2 ]

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Covered syllabus points

8.3 Interference question 1

Question (a)

Question (i)

Question (ii)

Question (iii)

8.3 Interference question 2

Question (a)

Question (i)

Question (b)

Question (c)

Question (i)

Question (ii)