Unlock access to content

Select one option:

Free of charge

Unlock the chapter "Interference"

Unlock access to the solution of problems in this chapter.
Free of charge Price: 3.00 £

Continue »

Subscribe to OpenProf If you do not get a better grade, you get your money back!

Unlock access to all problems solutions.
Available from 8.25 £ / month.

Continue »

Solved problems for the chapter:

Interference

View the theory »

Introduction to Light

1. Speed of light

2. Wavelength and frequency of light

3. Sources of light

3.1. Light sources based on black body radiation

3.2. Light emission due to changes in the energy levels of atoms

4. Luminous intensity and illuminance

5. Light perception

6. Forum

View the theory »

Refraction, Diffraction, and Interference of sound

1. Diffraction

1.1. Huygens principle

2. Interference

2.1. Wave amplification (Constructive interference)

2.2. Waves attenuation (Destructive interference)

3. Refraction of sound

3.1. Change in wavelength

3.2. Law of refraction

4. Forum

↓ Show theory [2] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:interference/4073/

Example 1.

A beam of laser light passes perpendicularly through a slit which is wide.

Which of the options below is correct?

There is no light wave after the slit.
Light will pass through the slit without changing direction.
We get a spherical wave of light after the slit.
We get attenuations and amplification of light after the slit.

Example 2.

A speaker emits a tone of 440 Hz. The sound spreads to the listener directly and through the reflection from the wall. Assuming that the amplitudes of the direct and reflected waves are the same and the speed of wave propagation is 360 m/s, what is the path difference between the reflected and the direct waves in order for the two waves to cancel out?

Two speakers, 0.5 m apart, stand in a horizontal plane. The speakers emit a 1.4 kHz tone coherently. In the space in front of the speakers, the sound alternately amplifies and attenuates. At a distance of 10 m from both speakers (point A in the picture) is the central sound amplification.

Why does this amplification occur?
What is the distance of the first amplification from the central amplification (distance of point B from A)?
How many times is the sound amplified to the left and right of the speaker?

Two wave sources emit coherent waves. Which condition must be correct for the coherent waves?

The waves are emitted in phase.
The waves are emitted and move in opposite directions.
The waves are emitted with a constant phase difference.
The waves are emitted with the same amplitude.

A student sets up an experiment to investigate double-slit interference. The student uses light of a single wavelength from a laser to illuminate a double slit so that a pattern of interference fringes is observed on the screen.

The student finds that the fringes are very close together. What could the student decrease in order to increase the separation of the fringes on the screen?

the distance from the laser to the double slit
the distance from the double slit to the screen
the separation of the slits
the wavelength of the light from the laser

Coherent visible light of a single frequency is incident normally on a double slit. This produces a pattern of bright and dark interference fringes on a screen, as illustrated below.

There are seven bright fringes.

Explain how the pattern of bright and dark interference fringes is formed.
The distance between the centres of bright fringe X and bright fringe Y in the pattern is . The slit spacing is . The distance from the slits to the screen is . Calculate the wavelength of the light incident on the slits.
The light is replaced by different visible light with a shorter wavelength. State how the new fringe separation will compare to the original fringe separation.

Microwaves are emitted from two sources at points X and Y. The two waves meet at point Z. The diagram shows the paths of the two waves.

The waves emitted from points X and Y are coherent. What is a direct consequence of the two waves being coherent?

There is a constant difference in the path lengths YZ and XZ.
There is a constant difference in phase between the two waves at Z.
There is a constant non-zero difference in frequency of the two waves at Z.
There is a constant non-zero difference in amplitude of the two waves at Z.

Interference fringes of separation are observed on a screen at a distance of from a double slit that is illuminated by yellow light of wavelength . At which distance from the double slit would interference fringes of the same separation be observed when using blue light of wavelength ?

Waves are emitted from two coherent sources. Which statement about the waves must be correct?

They are in phase.
They are transverse waves.
They have a constant phase difference.
They have the same amplitude.

10.

Observable interference fringes are produced using light from a double slit. The intensity of the light emerging from each slit is initially the same. The intensity of the light emerging from one of the slits is now reduced. How does this affect the interference pattern?

The bright fringes and the dark fringes all become brighter.
The bright fringes and the dark fringes all become darker.
The bright fringes become brighter and the dark fringes become darker.
The bright fringes become darker and the dark fringes become brighter

11.

Coherent light is incident normally on two identical slits X and Y. The diffracted light emerging from the slits superposes to produce an interference pattern on a screen positioned at a distance of from the slits. The figure below shows the arrangement and the central part of the interference pattern of bright and dark fringes formed on the screen.

The separation of the slits is . The distance between the centres of adjacent bright fringes is .

Calculate the wavelength of the light.
Light waves from slits X and Y in (a) arrive at a point between adjacent bright fringes on the screen. The figure below shows the variation of displacement with time for the waves arriving at the point where they meet.

A student makes two statements about the waves at this point:

Statement 1: ‘The phase difference between the waves is .’

Statement 2: ‘The amplitude of the resultant wave is zero.’
- Explain how statement 1 is correct.
- State and explain whether statement 2 is correct.
The width of each slit in (a) is decreased by the same amount. There is no change to the separation of the slits. Describe and explain the effect, if any, of this change on the appearance of the interference pattern.

12.

Two point sources, A and B, produce coherent electromagnetic waves. The waves from A and B are emitted in phase and have wavelength as shown in the figure below.

The waves in air have a wavelength of . An interference pattern is detected along a line parallel to AB and at a perpendicular distance of from AB. The spacing between adjacent interference maxima is .

Calculate the separation of the sources A and B.
State the principal region of the electromagnetic spectrum to which the waves belong.

13.

Light of a single frequency passes through two narrow slits and produces an interference pattern on a screen some distance away. The interference fringes are very close together. Which change would increase the distance between the fringes?

Increase the brightness of the light source.
Increase the distance between the slits and the screen.
Increase the distance between the two slits.
Increase the frequency of the light used.

14.

A teacher sets up the apparatus shown to demonstrate a double-slit interference pattern on a screen.

Which change to the apparatus will increase the fringe spacing?

decrease the distance
decrease the distance
decrease the distance
decrease the wavelength of the light

15.

An experiment is carried out to demonstrate double-slit interference using light of wavelength . The distance between bright fringes in the interference pattern is . What are possible values for the distance between the slits and the screen, and the slit separation?

	slit–screen distance	slit separation
A
B
C
D

16.

An arrangement for demonstrating interference using light is shown.

The wavelength of the light from the laser is . The light is incident normally on the double slit. The separation of the two slits is . The perpendicular distance between the double slit and the screen is .

Coherent light waves from the slits form an interference pattern of bright and dark fringes on the screen. The distance between the centres of two adjacent bright fringes is . The central bright fringe is formed at point P.

Explain why a bright fringe is produced by the waves meeting at point P.
Calculate distance

17.

In a two-source interference experiment, light of a single frequency is incident on a double slit. The light waves emerging from the slits are coherent. What is meant by coherent?

The waves are in phase.
The waves have a constant phase difference.
The waves have the same amplitude.
The waves interfere constructively wherever they overlap.

18.

When the light from two lamps falls on a screen, no interference pattern can be obtained. Why is this?

The lamps are not point sources.
The lamps emit light of different amplitudes.
The light from the lamps is not coherent.
The light from the lamps is white.

19.

A laser produces a beam of light of wavelength . The beam is incident normally on two slits that are a distance of apart. A screen is placed parallel to the slits. The bright interference fringes on the screen have a separation of . What is the distance between the screen and the two slits?

20.

An arrangement that uses a double slit to demonstrate the interference of light from a laser is shown.

The light from the laser has a wavelength of and is incident normally on the slits. The separation of the two slits is . The slits and screen are parallel and separated by a distance of .

An interference pattern of bright fringes and dark fringes is formed on the screen. The distance on the screen across 8 bright fringes is , as illustrated below.

The light waves emerging from the two slits are coherent. State what is meant by coherent.
Calculate the separation of the slits.

21.

A double-slit interference pattern using red light of wavelength has a fringe spacing of . Which fringe spacing would be observed for the same arrangement of apparatus but using blue light of wavelength ?

22.

Coherent light of wavelength is incident normally on a double slit of slit separation . A series of bright and dark fringes forms on a screen placed at a distance of from the double slit, as shown. The screen is parallel to the double slit.

Determine the distance between the centres of adjacent bright fringes on the screen.
The light of wavelength is replaced with red light of a single frequency. State and explain the change, if any, in the distance between the centres of adjacent bright fringes.

23.

Coherent monochromatic light illuminates two narrow parallel slits and the interference pattern that results is observed on a screen some distance beyond the slits. Which change increases the separation between the dark lines of the interference pattern?

using monochromatic light of higher frequency
using monochromatic light of a longer wavelength
decreasing the distance between the screen and the slits
increasing the distance between the slits