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

Two microwave transmitters are placed 15 cm apart and connected to the same source. A receiver is placed 70 cm away and moved along a line parallel to the transmitter.

The microwaves emitted by the source have a frequency of 120 GHz. The receiver detects alternating maxima and minima of intensity.

Explain the formation of the intensity maxima and minima.

Outline why the two sources must be coherent for the maxima and minima to be detected.

The receiver initially detects an intensity maximum at a point equidistant from the sources. Two minima, X₁ and X₂, are detected on either side of this maximum.

Calculate, in radians, the angular separation of X₁ and X₂.

A beam of monochromatic light is incident upon two slits. The distance between the slits is 0.4 mm.

A series of bright and dark fringes appear on the screen. Explain how a bright fringe is formed.

Monochromatic light is incident on the double-slits, and the distance from the screen is 0.64 m. The distance between the bright fringes is 9.3 × 10^–4 m.

Calculate the wavelength of the incident light.

The wavelength of the incident light is halved, and the distance between the slits is doubled.

Outline the effect on the separation of the fringes of the interference pattern.

One of the slits is covered so it emits no light.

Describe how this changes the pattern's appearance and the intensities observed on the screen.

Light is incident upon a piece of glass.

The angle of incidence is less than that of the critical angle. The refractive index of the glass is 1.50.

Explain what is meant by the 'critical angle' and what will occur at angles that are above and below the critical angle.

The angle of incidence for this situation is 34°.

Determine the angle of refraction to the nearest degree.

The refracted light travels within the glass for 5 m.

Determine the time that the light will take to travel this distance in the glass.

The light continues within the glass until it strikes the side perpendicular to the original side of entry.

Show that the light will not emerge from the side of the glass.

The diagram shows a cross-section through a step-index optical fibre.

Beam A is incident at the end of the optical fibre at an angle of 12.6° to the normal and refracts into the core at 6.89° to the normal.

Calculate the refractive index of the core.

Beam A travels through the air-core boundary and experiences total internal reflection.

On the diagram, show the path of this ray down the fibre and label the angle of reflection.

Beam B is incident at the same end of the fibre. It refracts through the air-core boundary and then refracts again when it hits the core-cladding boundary at an angle of 51.8°, traveling along the boundary.

Calculate the refractive index of the cladding.

A different step-index optical fibre is built with the same core as that in part (a) but with a different material used for the cladding.

The speed of light in the new cladding material is 1.54 × 10⁸ m s⁻¹.

Explain why this new cladding material would not be suitable for sending signals through the step-index optical fibre. Use a calculation to support your answer.

A beam of microwaves is incident normally on two very narrow slits, S1 and S2.

When a microwave receiver is initially placed at W, which is equidistant from the slits, an intensity maximum is observed. The receiver is then moved towards Z along a line parallel to the slits. Intensity maxima are also observed at X and Y, with one minimum between them. W, X and Y are consecutive maxima.

Explain the formation of

(i) the intensity maxima at W, X, and Y

[2]

(ii) the intensity minima between W, X, and Y.

[2]

The distance from S1 to Y is 1.482 m, and the distance from S2 to Y is 1.310 m.

Calculate the wavelength of the microwaves.

On the axes, sketch the intensity variation for the points W, X and Y.

The two narrow slits are replaced by two rectangular slits of finite size.

State one feature of the intensity pattern that will remain the same and one that will change.

A laboratory ultrasound transmitter emits ultrasonic waves of wavelength 0.7 cm through two slits. A receiver, moving along line AB, parallel to the line of the slits, detects regular rises and falls in the strength of the signal.

A student measures a distance of 0.39 m between the first and the fourth maxima in the signal when the receiver is 1.5 m from the slits.

The ultrasound transmitter is a coherent source.

Explain what is meant by the term coherent source.

Explain why the receiver detects regular rises and falls in the strength of the signals as it moves along the line AB.

Calculate the distance between the two slits.

One of the slits is now covered. No other changes are made to the experiment.

State and explain the difference between the observations made as the receiver is moved along AB before and after one of the slits is covered.

A beam of monochromatic light of frequency 2.44 × 10¹⁵ Hz is incident normally on a single rectangular slit.

A diffraction pattern is observed on a screen located 3.75 m from the slit. The distance on the screen from the central maximum to the first minimum is 0.25 cm.

Calculate the width of the slit. 

Three diffraction patterns, X, Y, and Z, are produced from three wavelengths of light, λ, 5λ and 10λ, passing through a single slit.

(i) State the wavelength of light that produced diffraction patterns X, Y, and Z. 

[2]

(ii) Explain which pattern has the highest intensity at the central maximum and state how to increase the intensity at the central maximum.

[2]

The variation of intensity with position on the screen is shown.

The width of the slit is reduced.

Sketch, on the same axes, the variation of intensity with position on the screen for the narrower slit.

Plane wavefronts of monochromatic light of wavelength λ are incident on a rectangular slit of width b. The light is brought to a focus after passing through the slit on a screen at a distance D from the slit as shown in the diagram below. 

The width of the slit is comparable to the wavelength of the light and b ≪ D. The point X on the screen is opposite the centre of the slit.  

The variation of the intensity incident on the screen with angle θ is shown on the graph below.

Outline why maximum and minimum values of intensity are observed on the screen at different values of .

In a single-slit diffraction experiment, the slit width is 0.030 mm and the wavelength of the light incident on the slit is 525 nm.

Calculate the angle of diffraction for the second maxima.

The single slit of width b is replaced by three rectangular slits, also of width b. The intensity distribution of a single slit is shown by the dotted line.

Sketch, on the axes, the intensity distribution for the three slits. 

A rectangular slit has width b and is comparable to the wavelength λ of plane wavefronts of monochromatic light incident upon it. After passing through the slit, the light is brought to a focus on a screen. 

The diagram shows a line normal to the plane of the slit, drawn from the centre of the slit to the screen is labelled PQ. The points X and Y are the first points of minimum intensity as measured from point Q. 

The diagram also shows two rays of light incident on the screen at point X. Ray RX leaves one edge of the slit and ray PX leaves the centre of the slit. The angle φ is small. 

On the diagram, label two angles of diffraction.

Derive an expression, in terms of λ, for the path difference RT between the rays RX and RT.

Describe the changes in the experimental setup that would decrease the width of the central bright maximum.

In a certain demonstration of single-slit diffraction λ = 400 nm, b = 0.12 mm, and the screen is a long way from the slit. 

Calculate the angular width of the central maximum of the diffraction pattern on the screen.

Monochromatic light is incident normally on four, thin, parallel, rectangular slits. 

The graph shows the variation with diffraction angle θ of the intensity of light I on a distant screen. 

I₀ is the intensity of the light in the middle of the screen from one slit. Intensity I is directly proportional to the square of amplitude A.

State the value of the light intensity in terms of I₀  when θ = 0 and explain where this value comes from.

The width of each slit is 2.0 µm. 

Use the graph to estimate the wavelength of the light.

Use the graph to calculate the number of lines per metre on the diffraction grating. 

The four slits are now changed for a grating where the number of slits becomes very large. The separation of the slits and their width stays the same.

State two changes to the graph that will appear as a result of this modification.

Monochromatic light is incident on a double-slit diffraction grating. After passing through the slits the light is brought to a focus on a screen. The intensity distribution of the light on the screen is shown in the diagram below. 

The double-slit diffraction grating is now changed to a grating with many narrower slits, the same widths as the slits above. 

Sketch the new intensity pattern for the light between points C and D on the screen. 

The wavelength of the monochromatic light incident on the diffraction grating is 550 nm. The slit spacing of the diffraction grating is 1.34 × 10⁻⁶ m.

Calculate the angle between the two second-order maxima. 

Calculate the total number of orders of diffracted light that can be observed on the screen. 

Two sources of light now replace the light incident on the diffraction grating. One is the same as the wavelength of the previous source and the other has a slightly longer wavelength. 

Compare and contrast the new intensity pattern with the original. Comment on the intensity of the central maxima and the width of all maxima. 

Two coherent sources, A and B, which are in phase with each other, emit microwaves of wavelength 40.0 mm. The amplitude of waves from source B is twice that of source A. 

A detector is placed at the point P where it is 0.93 m from A and 1.19 m from B. The centre axis is normal and a bisector to the straight line joining A and B. 

With reference to the phase of the microwaves, deduce the magnitude of the detected signal at P and explain your reasoning.

Deduce, with suitable calculations, how the detected signal varies as the detector is moved from P to O.

The source B is altered such that it emits waves that are 180° out of phase with source A. 

Deduce the type of interference that now occurs at point P and explain your reasoning. 

A ray of light passes from air into a glass prism.

As the light ray passes through the prism, it emerges back into the air.

Calculate the critical angle from the glass to the air.

The prism is rotated and one side is coated with a film of transparent gel. A ray of light strikes the prism, at an angle of incidence of 38°, and continues through the glass to strike the glass–gel boundary at the critical angle.

Calculate the refractive index of the gel.

A ray of light now strikes the prism at an angle of incidence which means that it now refracts straight through the gel at the glass–gel boundary.

Without calculation, explain how the critical angle for the glass–gel boundary differs from the critical angle for the gel–air boundary.

The diagram shows a cross–section through an optical fibre used in an endoscope. The critical angle is 7% lower than the 75º angle to the normal at the core–cladding boundary. The refractive index of the cladding is 1.4.

Calculate the angle of incidence at the air–core boundary.

Complete the graph to show how the refractive index changes with radial distance along the line ABCD in Figure 2.

The diagram below shows an arrangement for observing the interference pattern produced by laser light passing through two narrow slits S₁ and S₂.

The distance S₁S₂ is d, and the distance between the double slit and the screen is D where D ≫ d, so angles θ and ϕ are small. M is the midpoint of S₁S₂ and it is observed that there is a bright fringe at point A on the screen, a distance f_n from point O on the screen. Light from S₁ travels a distance S₂Y further to point A than light from S₁.

The wavelength of light from the laser is 650 nm, and the angular separation of the bright fringes on the screen is 5.00 × 10⁻⁴ rad.

Calculate the distance between the two slits.

A bright fringe is observed at A. 

(i) Explain the conditions required in the paths of the rays coming from S₁ and S₂ to obtain this bright fringe. 

[2]

(ii) Determine an equation for the distance S₂Y in terms of and .

[1]

Determine an expression for

(i) in terms of , and

[2]

(ii) in terms of and .

[2]

Some students in a lab are performing a single-slit diffraction investigation. They have a green laser but they do not know the exact wavelength of the light. 

Describe which measurements the students can take and how they can use them to calculate the wavelength.

The students recorded the following information:

Calculate the wavelength of the laser and give its fractional uncertainty.

Single-slit diffraction patterns provide evidence for light as a wave. 

The images below show the diffraction of light around a small circular object. 

Suggest how the images provide evidence for light as a wave.

The image shows a diffraction pattern from a single rectangular slit.

Sketch the diffraction pattern if the slit width was 20% smaller.

Monochromatic light from a single source is incident on two thin parallel slits. 

The following data are available: 

• Distance from slits to screen = 4.5 m

• Wavelength = 690 nm

• Slit separation = 0.13 mm

The intensity, I of the light on the screen from each slit separately is I₀. 

Sketch, on the axis, a graph to show variation with distance p on the screen against the intensity of light detected on the screen for this arrangement.

State and explain the changes that will occur to the diffraction pattern when the number of slits is increased from two to three.

Monochromatic light of wavelength is normally incident on a diffraction grating. The light waves are diffracted through an angle to form a first-order diffraction maximum.

The diagram shows two adjacent slits of the diffraction grating labelled A and B. Point C is also labelled.

The separation of adjacent slits is .

Show that for the first-order diffraction maximum

Monochromatic light of wavelength 545 nm is normally incident on a diffraction grating. The diffraction maxima are observed on a screen, and their angle to the central beam is determined.

The graph shows the variation of  with the order  of the maximum. The central order corresponds to  = 0.

Determine a mean value for the number of slits per millimetre of the grating.

A beam of light containing all the wavelengths in the range 500 nm to 600 nm is incident normally on the diffraction grating.

Determine the largest order of the diffraction pattern in which all the wavelengths in the incident beam are present.