Wave Phenomena (DP IB Physics: HL): Exam Questions

A wave is moving along a rope under tension as shown.

Which graph correctly shows the variation with time of the displacement of particle K in the rope?

Two waves from individual point sources meet at a point.

For interference to be observed at the point, the waves must

The diagram shows the shape of the wavefront as a result of the diffraction of plane waves by two apertures.

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? 

A light ray is incident on an air–diamond boundary. The refractive index of diamond is greater than 1.

What changes to the speed, frequency, and wavelength of the light wave would be observed as it passes from the air to the diamond?

The effect of a double slit on monochromatic light is observed using the setup shown in the diagram.

Interference fringes are seen on the screen.

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

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

Which of the following arrangements would produce a fringe spacing of ?

Which of the following processes changes the frequency of a wave?

Young’s double-slit experiment is set up as shown, including a monochromatic source, a single slit, a double slit and a screen.

What is the purpose of the single slit in this experiment?

Two point sources, S₁ and S₂, emit identical sound waves of intensity .

The waves leaving S₁ and S₂ are in phase and arrive at point X. The wavelength of the sound is 3.0 m. Point X is 18.0 m from S₁ and 10.5 m from S₂.

What intensity of sound would be heard by a person standing at point X?

Which diagram shows the path of visible light as it travels through a glass prism?

The angle of incidence should always be measured between

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 shows an arrangement for a two-slit interference experiment.

Coherent light of frequency 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 observed at point O, and the next bright fringe is observed at point P. The speed of light is .

The distance S₂P – S₁P is equal to

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

Monochromatic light is incident on the slits, which are considered to be infinitely narrow point sources. An interference pattern is observed on a screen, and a central maximum is observed at point O.

Which graph shows the intensity distribution of light on the screen?

A beam of monochromatic light is incident on a double slit. The slit separation is , and the distance between the slits and the screen is . The angle between the central maximum and first-order maxima is , as shown.

What is the wavelength of the light?

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

If and  are tripled, and  is doubled, what is the new distance between consecutive fringes?

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  and the slit width is . In Diagram 2, the wavelength of light is  and the slit width is .

Which expression correctly links the wavelength and slit width of the two interference patterns?

Three statements about single-slit diffraction are:

I. Blue light produces a wider central maximum than red light.

II. The wider the slit, the narrower the central maximum for light of a constant wavelength.

III. The narrower the slit, the greater the intensity of the central maximum for light of a constant wavelength.

Which statements are correct?

Four diffraction experiments are performed using diffraction gratings with 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?

White light is diffracted through a single slit.

Which graph indicates the correct positions of red (R), violet (V) and white (W) light on the intensity pattern observed on a screen?  

Light is incident on a single slit and forms a diffraction pattern.

The experiment performed several times using light of different wavelengths, slits of different widths and placed at different distances from the screen.

Which change would decrease the width of the central maximum?

A parallel beam of coherent light of wavelength  is incident on a rectangular slit of width . After passing through the slit, the light is incident on a screen a distance  from the slit, where .

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

In a single-slit diffraction experiment, the first diffraction minimum is observed at an angle from the central maximum. The intensity of the central maximum is . The same light source is used throughout the experiment.

What changes to  and would be observed if a narrower slit were used?

Light incident on a single slit produces a diffraction pattern. The angle between the centre of the pattern and the first minimum is . The slit width is then halved and the frequency of light is doubled. 

What is the new angle between the centre of the pattern and the first minimum?

The intensity pattern of monochromatic light of wavelength is projected onto a screen, as shown.

What combination produces this pattern?

Red light is incident on a diffraction grating, a double-slit and a single-slit. The patterns produced on a screen 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 ripple tank is used to demonstrate the movement of progressive waves. In the tank, a wave is set in motion from left to right.

The displacement of points X and Y on the wave at time = 0 are indicated.

Which graph represents the variation with time of the displacement of points X and Y?

Two loudspeakers, X₁ and X₂, emit a continuous sound of the same frequency.

Loudspeaker X₁ is positioned to the left of loudspeaker X₂, and both loudspeakers are positioned parallel to the detection line AB. When a microphone is moved from left to right along the line AB, a minimum is first detected at P, followed by a maximum at Q, with another minimum at R, and a maximum at S. PQRS are all equidistant, and X₁S = X₂S.

Which of the following expressions correctly represents the wavelength of the sound waves?

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.

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

Where:

• 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

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

What is the path difference between the 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 a ray of light passes from material A to material B, the direction of the ray bends away from the normal. The refractive indices of materials A and B are  and , respectively.

Which of the following statements is true? 

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? 

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?

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

What is the ?

An interference pattern is observed on a screen when monochromatic light is incident on two identical slits.

If one of the slits were blocked, which change to the pattern would be observed?

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 is incident on a rectangular slit of width . The angle of the diffraction minimum at X is .  

What is the energy of the photons arriving 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  nm is incident on a rectangular slit of width  µm. After passing through the slit the light is incident on a screen a distance  m away. 

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

A beam of light of wavelength  is incident normally on a slit of width . After passing through the slit, the light is incident on a screen a distance  from the slit, where .

What is the total width of the first two maxima?

A beam of photons 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 beam remains the same. 

What are the changes to the total number of photons incident every second on the screen and the angular size of the central maximum of the diffracted beam?

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

What is the wavelength of the light source?

The diagram 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 at the centre of the first observed beam at position Z is and the grating has 1562 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 550 nm.

When a screen is placed 1.2 m from the grating, the distance between the central maximum and the first maximum on the screen is 0.40 m.

What is the number of slits per mm for this diffraction grating?