Wave Phenomena (HL IB Physics)

Two microwave transmitters are arranged to ensure that their waves undergo superposition and create a stationary wave made up of nodes and antinodes.

Which line correctly identifies the formula and a likely value for the minimum distance between the nodes of the stationary wave?

	formula	distance /cm
A.		30
B.		0.05
C.		30
D.		0.05

Two pulses are travelling towards each other.

What is a possible shape observed when the pulses undergo superposition?

Unpolarised light of intensity I₀ is incident on the first of two polarising sheets. Initially the transmission axes are parallel.

­­Which sheet must be rotated and by what angle so that light of intensity I₀ emerges from the second sheet?

You may use the fact that

cos 45 =

cos 60 = 

cos 90 = 0

The graph shows the displacement y, with distance x, of air molecules vibrating due to a sound wave of frequency 261 Hz travelling to the right.

Positive values of y indicate displacement of the particles to the right.

Which row correctly shows the positions of a compression (C) and rarefaction (R) at the moment shown and then 3.8 × 10⁻³ seconds later?

In a Young’s double-slit experiment, the spacing of the double slits is d and the distance between the slits and the screen on which fringes are formed is D. When monochromatic light of wavelength λ is incident on the slits the distance between adjacent fringes on the screen is s.

Which row shows another arrangement that produces a fringe spacing of s?

	Wavelength of the light	Distance between the slits and the screen	Spacing of double Slits
A.		2D	4d
B.		2D	2d
C.		2D	2d
D.		2D	8d

K is the source of a wave of frequency 25 Hz.

The wave travels to point M by two routes, K → L → M and K → M. The speed of the wave is 15 m s⁻¹.

What is the path difference between the two waves at M in terms of the wavelength λ of the waves?

The diagram below shows an arrangement used to investigate double slit interference using microwaves.

The diagram below shows the view from above:

The microwaves from the transmitter are polarised. These waves are detected by the aerial in the microwave detector (probe). The aerial is a vertical metal rod.

The detector is moved along the dotted line UY. As it is moved, maximum and minimum signals are detected. Maximum signals are first detected at points V and W. The next maximum signal is detected at the position X.

The distances between each of the two slits, S₁ and S₂ and the microwave receiver when the aerial is in position X are S₁X = 0.3335 m and S₂X = 0.3615 m

Select the three correct reasons that explain why the signal strength falls to a minimum between U and V, and between V and W.

Our fingerprints are made up of a series of ridges on the end of the finger. These ridges can be ‘read’ by electronic devices.

The diagram below shows a certain type of fingerprint detector below, which works by scattering light when pressure is applied to a plastic screen. The ridges of the fingerprint press the plastic film against the glass when the finger is pressed to the screen.

When not in use, the plastic screen and the glass have a small air space between them. The diagram below shows the two possible paths for the light when the finger is pressed down.

Which row in the table correctly describes the properties of the fingerprint detector that cause the bright and dark patches on the image produced by the camera?

A sound source X₁ is positioned w cm to the left of sound source X₂. Both sound sources are y m below the detection line AB. AB runs parallel to X₁X₂ . When a sound detector is slowly moved along the line AB, a maxima is first detected at P, followed by a minima at Q, with another maxima at R and a minima at S. PQRS are all equidistant apart with X₁ S = X₂ S.

Which one of the following is a correct expression for the wavelength of the sound?

A ray of light is incident on a material made from three layers, each having a different optical density, so that in each layer the light travels at a different speed.

• For layer 1: refractive index = n₁ and the speed of light = c₁
• For layer 2: refractive index = n₂ and the speed of light = c₂
• For layer 3: refractive index = n₃ and the speed of light = c₃
• Angle of incidence = i
• Angle of refraction = r

This is illustrated in the diagram below:

Which is the correct expression for c₃, the speed of light in the third layer?

Diamonds are highly valued because of their sparkle. This is caused by total internal reflection, which reflects most of the light that falls onto a cut diamond out of the face we see. Fake gems, called ‘paste’, are often used in jewellery because they are cheaper. However, paste gems sparkle much less than real diamonds.

The diagrams show a possible path of light through a real diamond, and another through a fake.

If:

• n = refractive index;
  • n_d is the refractive index of the diamond
  • n_f is the refractive index of the fake
• v = speed of light
  • v_d is the speed of light in the diamond
  • v­­_f is the speed of light in the fake

Which row in the table contains only statements which must be true?

A double slit interference experiment is conducted using monochromatic light of wavelength λ. The centre of the observed pattern is a bright fringe.

What is the path difference between two waves which interfere to give the second dark fringe from the centre?

A student is investigating the interference of waves. They set up coherent waves produced at points S and T and travel outwards in all directions.

The line XY is halfway between S and T and perpendicular to the joining line S and T. The distance XY is much greater than the distance ST.

Which line or lines would an interference pattern be seen along?

When moving from material A to material B, the direction of a ray of light moves away from the normal. If n_A and n_B are the refractive indices of materials A and B respectively, then which of the following statements is true in this situation? 

The diffraction pattern for light passing through a single slit is shown on the graph below.  

What is the ?

Monochromatic light is incident on two slits that are identical. An interference pattern is produced on a screen some distance away. Upon returning to the experiment a Physicist notices that there are fewer maxima now present on the screen.

What aspect of the equipment set up has been changed?

When monochromatic light is incident on a single slit a diffraction pattern forms on a screen. The width of the slit is increased. 

What are the changes in the width of the central and subsidiary maxima and in the intensity of the central and subsidiary maxima of the single slit diffraction pattern?

A beam of photons moving in the direction shown is incident on a rectangular slit of width, b. The angle produced at X by the interference pattern of the photons diffracting through the slit is θ. 

What is the component of the energy of the photons at point X on the screen?

A beam of light of wavelength λ is incident upon a single slit of width w. After passing through the slit, the light is incident on a screen at a distance Q from the slit. 

Which of the following changes, carried out separately, will result in an increased width of the central maxima observed on the screen?

A parallel beam of coherent light of wavelength p nm is incident on a rectangular slit of width p µm. After passing through the slit the light is incident on a screen a distance p m away. 

What is the width of the central maximum of the diffraction pattern as measured on the screen?

A parallel beam of light of wavelength 400 nm is incident normally on a slit of width b. The distance between the slit and the screen is 0.2 m and the distance of the second order of maximum from the centre of the screen is 10 mm. 

What is the width of the slit?

A parallel beam of light of wavelength λ passes through a slit of width b. The transmitted light is collected on a screen D m away where D ≫ b.

What is the distance between the two second-order minima?

Radiation is incident on a single rectangular slit. The diffracted beam that emerges from the slit is incident on a screen. Both the slit width and the wavelength of the radiation are tripled. The intensity of the radiation remains the same. 

Which answer option correctly describes the total number of photons incident every second on the screen and the angular width of the central maximum of the diffracted beam?

A monochromatic source of light of wavelength λ is incident on a single slit of width b. The interference pattern is visible on the screen where the angle of the third minima is θ.

What is the wavelength of the light?

Monochromatic light of wavelength λ is incident on a double slit. The resulting interference pattern is observed on a screen a distance p from the slits. The distance between consecutive fringes in the pattern is 21 mm when the slit separation is q.

λ and q are tripled and p is doubled. 

What is the new distance between consecutive fringes?

The figure below shows a spectrometer that uses a diffraction grating to split a beam of light into its constituent wavelengths and enables the angles of the diffracted beams to be measured.

Light with a particular wavelength is passed through the diffraction grating. The angle of diffraction θ at the centre of the observed beam at Z in the image above is 45⁰ where sin(45) =  and the grating has 1000 lines per mm.

A dark fringe is observed at position W, with the central maximum at the straight-through position.

How many orders of maxima of this light are present at this wavelength?

A diffraction grating is illuminated normally with light of wavelength 5 x 10^-7m.

When a screen is 1 m from the grating, the distance between the zero and first-order maxima on the screen is 0.20 m.

You may need to use the following values in your calculation:

What is the number of lines per mm of the diffraction grating?

A Physicist carried out Young's double slit experiment using a monochromatic beam. The diagram shows the equipment set-up and the pattern produced with a ruler next to it. 

What is the wavelength of the monochromatic beam? 

The diagram below shows an arrangement used to investigate double-slit interference using microwaves.

The diagram below shows the view from above.

The microwaves from the transmitter are polarised. These waves are detected by the aerial in the microwave detector. The aerial is a vertical metal rod.

The detector is moved along the dotted line HL. As it is moved, maximum and minimum signals are detected. Maximum signals are first detected at points I and J. The next maximum signal is detected at position K.

The distances between each of the two slits, S₁ and S₂ and the microwave receiver when the aerial is in position K are S₁K = 0.1115 m and S₂K = 0.0315 m

 Which of the following reasons explains why the signal strength falls to a minimum between H and I, and between I and J?

White light is passed through a double slit and an interference pattern is observed on a screen 2.0 m away. The separation between the slits is 0.5 mm. The first violet and red fringes are formed 2.0 mm and 3.0 mm respectively away from the central white fringe.

What are the wavelengths of the violet and red light?

Two waves from individual point sources meet at a point X. Which of the following conditions is necessary for interference to be observed at point X?

This diagram below shows two apertures through which planar waves are passed as they are moving to the left. The wavefronts show crests moving in phase. Given this information, at which point will the amplitude of the waves be a minimum?

A flat plate made of glass has a refractive index of n = 1.52. What is the speed of light within this material? 

When a light ray enters a denser medium and refracts, some of the characteristics of the wave will change. Which of the following options is correct about this change?

The effect of a double slit on monochromatic light is observed by the set up in the diagram below.

Interference fringes are seen on the screen.

Which of the following changes would increase the distance between the adjacent fringes?

Which of the following options will alter the frequency of a wave?

Young’s double-slit experiment is setup as shown, including a monochromatic source, a single slit, a double slit and a screen. What is the purpose of the double slit in this experiment?

Identical waves that begin propagation at the same time leave from two different sources and arrive at the same point – point X. The first source is 18 m from point X. The second source is 10.5 m from point X. The waves of both sources have a wavelength of 3 m. What is observed at X?

Which of the following images shown below best represents the path of visible light traveling through a glass prism?

The angle of incidence should always be measured between:

In two separate experiments, monochromatic light is incident on a single slit. The diagrams show the interference patterns obtained on a screen far from the slit. In diagram 1, the wavelength of light is λ₁ and the slit width is b₁. In diagram 2, the wavelength of light is λ₂ and the slit width is b₂.

What is the correct expression linking wavelength and slit width of the two interference patterns?

Which of the statements are true for single-slit interference? 

1. Blue light produces a larger angle of diffraction than red light
2. The smaller the slit width, the larger the angle of diffraction for a constant wavelength 

Several diffraction experiments are performed with light diffracted through different numbers of slits. Which row. in the table below, correctly matches the number of slits and the intensity pattern observed on the screen?

Monochromatic light is incident on a narrow rectangular slit in an optical experiment. The diffracted light is observed on a distant screen. The graph below shows how the intensity of light varies with position on the screen.

The width of the slit is increased. The original diffraction pattern is shown by the solid line.

Which graph shows how the intensity of light observed varies with position on the screen? 

The diagram shows the diffraction pattern for light travelling through a single slit of width 2.0 mm. 

What is the wavelength of the light used?

White light is diffracted through a single slit.

Which row in the table indicates the correct positions of red (R), violet (V) and white (W) light on the intensity pattern seen on a screen?  

A single slit diffraction pattern is performed several times using light of different colours, slits of different widths and different distances to the screen. Which change will decrease the width of the central peak?

A parallel beam of coherent light of wavelength λ is incident on a rectangular slit of width b. After passing through the slit the light is incident on a screen a distance D from the slit where D is much greater than b.  

What is the width of the central maximum of the diffraction pattern as measured on the screen? 

In a diffraction experiment with a single slit, the first minimum is observed at a diffraction angle θ. The intensity of the central maximum of the diffraction pattern is I. The light source stays the same. What is the effect on I and θ of reducing the slit width?

A single slit produces a diffraction pattern. The angle from the centre of the pattern to the first minimum point is Y. The slit width is then halved and the frequency of light is doubled. 

What is the new angle from the centre of the pattern to the first minimum point?

Waves emitted from sources V and W are initially in phase and have equal wavelengths. Point A is not equidistant between V and W. The waves interfere destructively at point A, where the path difference is 0.30 m.  

 What is the maximum possible value of the wavelength of the waves?

The diagram below shows an arrangement for a two-slit interference experiment. Coherent light of frequency f is incident on two narrow parallel slits S₁ and S₂. An interference pattern is observed on a screen a distance away. The central bright fringe is at O and the next bright fringe is at P. The speed of light is c.

The distance S₂P – S₁P is equal to

The interference of light waves is observed using a double-slit arrangement as shown below.

Which of the following best shows the intensity distribution of light at point O on the screen?

In an experiment, light incident on a diffraction grating has a first maximum of the second order in the same location as the first minimum of a single slit diffraction pattern. The light source and the distance from the slits to the screen are kept the same. 

What is the relationship between the slit separation d and the slit width b? 

The graph shows the intensity pattern from the interference of monochromatic light passing through N slits. 

Which row gives the correct value of N and the correct relationship between the slit separation d and the wavelength λ?

	N	Relationship
A.	6	d =
B.	6	d = 2λ
C.	4	d = 2λ
D.	4	d =

Red light is incident on a diffraction grating, a double-slit and a single-slit. The patterns produced on a screen some distance away are shown below.

Which row in the table correctly identifies patterns p, q and r?

The graph shows the variation with diffraction angle of the intensity of light when monochromatic light is incident on a diffraction grating. 

The number of slits is reduced to less than 20. The width and the separation of the slits remain the same. 

Three possible changes to the pattern are: 

I. The intensity of the primary maxima increases 

II. The width of the primary maxima increases 

III. Secondary maxima are seen between the primary maxima 

Which of the possible changes are correct?

A beam of monochromatic light is incident normally on a double slit. The slit spacing is d. The angles between the different orders are shown on the diagram. 

What is the expression for the wavelength of light used?