IB Physics HL C.3 Wave Phenomena

[Maximum number: 2]

A converging lens is placed between an object and a screen. An image of the object is formed on the screen.

(a)

Draw a ray to locate the focal point of the lens. Label this point with the letter F .

[ 1 ]

(b)

The lens suffers from spherical aberration.

[ 1 ]

(i)

Draw lines to complete the rays in the diagram.

[ 1 ]

[Maximum number: 12]

Monochromatic light enters the base of a plastic beaker that contains water with an oil layer floating on it. A student draws a diagram to show the directions the light takes as it passes through the layers. The student's diagram has one error at position A and one error at position B. The refractive indices of the materials are shown on the diagram.

The light is refracted at an angle of $32^{\circ}$ when it enters the plastic layer as shown.

(a)

Identify, with a reason, the error in the student's diagram for

[ 4 ]

(i)

light crossing the plastic-water interface (position A).

[ 2 ]

the angle of refraction ought to be greater than the angle of incidence OR the ray should refract away from the normal
because ray goes from high refractive index/<<optically>> more dense/slower medium to
low refractive index/optically less dense/faster medium

Marking guidance:

Do not allow use of e.g $n_{1}$
unless medium one is
described e.g. $n_{\text {air }}$

(ii)

light at the water-oil interface (position B).

[ 2 ]

(b)

Calculate the angle of incidence at the air-plastic interface.

[ 2 ]

Use of Snell's Law « $\frac{\sin i}{\sin r}=\frac{1.60}{1}$ »
$i=\sin ^{-1} \ll 1.60 \times \sin 32^{\circ}>=58<^{\circ} \gg$

'Use of' requires a substitution NOT just a statement of a formula

Marking guidance:

Accept 1.0 rad (unit must be included to show a deliberate attempt to use rad rather than a calculator mistake)

(c)

Calculate the critical angle for the plastic-water interface.

[ 2 ]

$\begin{aligned} \frac{\sin i}{\sin r}=\frac{1.33}{1.60} \text { and } \sin r=1 i=\text { «sin }{ }^{-1} 0.831 »=56 \text { " }^{\circ} \text { » } \end{aligned}$

Accept 0.98 rad (unit required)

(d)

Monochromatic light of wavelength $6.3 \times 10^{-7} \mathrm{~m}$ in air is incident from above at a normal to the oil layer. Rays on the diagram are shown at near-normal incidence for clarity. Three positions X, Y and Z are shown on the diagram.

[ 4 ]

(i)

Identify, with a reason, a position at which there is a phase change of $180^{\circ}$ .

[ 1 ]

(ii)

Determine the minimum thickness of the oil layer for which light is not reflected. State your answer to an appropriate number of significant figures.

[ 3 ]

Use of $2 d \mathrm{n}=m \lambda$ $2.1 \times 10^{-7}$ «m»

any answer to 2 s.f.

'Use of' requires a substitution
NOT just a statement of a formula

[Maximum number: 12]

A beam of coherent monochromatic light from a distant galaxy is used in an optics experiment on Earth.

(a)

The beam is incident normally on a double slit. The distance between the slits is 0.300 mm . A screen is at a distance D from the slits. The diffraction angle $\theta$ is labelled.

[ 6 ]

(i)

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

[ 3 ]

superposition of light from each slit / interference of light from both slits with path/phase difference of any half-odd multiple of wavelength/any odd multiple of $\pi$ (in words or symbols), producing destructive interference

(ii)

Outline why the beam has to be coherent in order for the fringes to be visible.

[ 1 ]

(iii)

The wavelength of the beam as observed on Earth is 633.0 nm . The separation between a dark and a bright fringe on the screen is 4.50 mm . Calculate D.

[ 2 ]

evidence of solving for D: $D=\frac{s d}{\lambda}$ $D=\frac{4.50\times10^{-3}\times0.300\times10^{-3}}{633.0\times10^{-9}}\times2=4.27\ \mathrm m$

(b)

The graph of variation of intensity with diffraction angle for this experiment is shown.

[ 3 ]

(i)

Calculate the angular separation between the central peak and the missing peak in the double-slit interference intensity pattern. State your answer to an appropriate number of significant figures.

[ 3 ]

$\begin{aligned} \sin\theta=\frac{4\times633.0\times10^{-9}}{0.300\times10^{-3}} \\ \theta=0.00844 \end{aligned}$

(c)

The air between the slits and the screen is replaced with water. The refractive index of water is 1.33 .

[ 3 ]

(i)

Calculate the wavelength of the light in water.

[ 1 ]

$\frac{633.0}{1.33}=476\ \mathrm{nm}$

(ii)

State two ways in which the intensity pattern on the screen changes.

[ 2 ]

[Maximum number: 1]

A beam of coherent monochromatic light from a distant galaxy is used in an optics experiment on Earth.

The air between the slits and the screen is replaced with water. The refractive index of water is 1.33 .

Calculate the wavelength of the light in water.

$\frac{633.0}{1.33}=476\ \mathrm{nm}$

[Maximum number: 2]

Monochromatic light enters the base of a plastic beaker that contains water with an oil layer floating on it. A student draws a diagram to show the directions the light takes as it passes through the layers. The student's diagram has one error at position A and one error at position B. The refractive indices of the materials are shown on the diagram.

The light is refracted at an angle of $32^{\circ}$ when it enters the plastic layer as shown.

Calculate the critical angle for the plastic-water interface.

$\begin{aligned} \frac{\sin i}{\sin r}=\frac{1.33}{1.60} \text { and } \sin r=1 i=\text { «sin }{ }^{-1} 0.831 »=56 \text { " }^{\circ} \text { » } \end{aligned}$

Accept 0.98 rad (unit required)

[Maximum number: 2]

Two loudspeakers, A and B, are driven in phase and with the same amplitude at a frequency of 850 Hz . Point P is located 22.5 m from A and 24.3 m from B. The speed of sound is $340 \mathrm{~ms}^{-1}$ .

When both loudspeakers are operating, the intensity of sound recorded at Q is $I_{0}$ . Loudspeaker B is now disconnected. Loudspeaker A continues to emit sound with unchanged amplitude and frequency. The intensity of sound recorded at Q changes to $I_{\mathrm{A}}$ .

Estimate $\frac{I_{\mathrm{A}}}{I_{0}}$ .

the amplitude of sound at Q is halved

«intensity is proportional to amplitude squared hence» $\frac{I_{A}}{I_{0}}=\frac{1}{4}$

[Maximum number: 1]

A beam of coherent monochromatic light from a distant galaxy is used in an optics experiment on Earth.

The beam is incident normally on a double slit. The distance between the slits is 0.300 mm . A screen is at a distance D from the slits. The diffraction angle $\theta$ is labelled.

Outline why the beam has to be coherent in order for the fringes to be visible.

[Maximum number: 3]

A beam of coherent monochromatic light from a distant galaxy is used in an optics experiment on Earth.

The beam is incident normally on a double slit. The distance between the slits is 0.300 mm . A screen is at a distance D from the slits. The diffraction angle $\theta$ is labelled.

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

superposition of light from each slit / interference of light from both slits with path/phase difference of any half-odd multiple of wavelength/any odd multiple of $\pi$ (in words or symbols), producing destructive interference

[Maximum number: 3]

A student investigates how light can be used to measure the speed of a toy train.

Light from a laser is incident on a double slit. The light from the slits is detected by a light sensor attached to the train.

The graph shows the variation with time of the output voltage from the light sensor as the train moves parallel to the slits. The output voltage is proportional to the intensity of light incident on the sensor.

Explain, with reference to the light passing through the slits, why a series of voltage peaks occurs.

[Maximum number: 1]

A student investigates how light can be used to measure the speed of a toy train.

Light from a laser is incident on a double slit. The light from the slits is detected by a light sensor attached to the train.

The graph shows the variation with time of the output voltage from the light sensor as the train moves parallel to the slits. The output voltage is proportional to the intensity of light incident on the sensor.

The slits are separated by 1.5 mm and the laser light has a wavelength of $6.3 \times 10^{-7} \mathrm{~m}$ . The slits are 5.0 m from the train track. Calculate the separation between two adjacent positions of the train when the output voltage is at a maximum.

$s=\frac{\lambda D}{d}=\frac{6.3\times10^{-7}\times5.0}{1.5\times10^{-3}}=2.1\times10^{-3}\ \mathrm{m}$

[Maximum number: 3]

This question is about the motion of a ship and observing objects from it.

A security camera on the ship captures an image of two green lamps on the shore. The lamps emit light of wavelength 520 nm .

The camera has a circular aperture of diameter 6.2 mm . The lamps are separated by 1.5 m . Determine the maximum distance between the camera and the lamps at which the images of the lamps can be distinguished.

use of $\theta=\frac{1.22 \lambda}{d}$ ;
$\left(\frac{1.22 \times 520 \times 10^{-9}}{6.2 \times 10^{-3}}\right)=1.02 \times 10^{-4} ;$
distance $=\left(\frac{1.5}{1.02 \times 10^{-4}}=\right) 1.47 \times 10^{4} \mathrm{~m} ;$

Marking guidance:

Award [2 max] if distance is $1.79 \times 10^{4} m$ (ignoring factor of 1.22) in second marking point.

[Maximum number: 2]

A student investigates how light can be used to measure the speed of a toy train.

Light from a laser is incident on a double slit. The light from the slits is detected by a light sensor attached to the train.

The graph shows the variation with time of the output voltage from the light sensor as the train moves parallel to the slits. The output voltage is proportional to the intensity of light incident on the sensor.

As the train continues to move, the first diffraction minimum is observed when the light sensor is at a distance of 0.13 m from the centre of the fringe pattern.

(not to scale)

Determine the width of one of the slits.

angular width of diffraction minimum $=\frac{0.13}{5.0}=0.026\ \mathrm{rad}$

slit width $=\frac{\lambda}{d}=\frac{6.3\times10^{-7}}{0.026}=2.4\times10^{-5}\ \mathrm{m}$

[Maximum number: 2]

A student investigates how light can be used to measure the speed of a toy train.

Light from a laser is incident on a double slit. The light from the slits is detected by a light sensor attached to the train.

The graph shows the variation with time of the output voltage from the light sensor as the train moves parallel to the slits. The output voltage is proportional to the intensity of light incident on the sensor.

As the train continues to move, the first diffraction minimum is observed when the light sensor is at a distance of 0.13 m from the centre of the fringe pattern.

(not to scale)

Suggest the variation in the output voltage from the light sensor that will be observed as the train moves beyond the first diffraction minimum.

[Maximum number: 3]

Two sources of light produce an interference pattern on a screen.

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

Considers the largest wavelength $\boldsymbol{O} \boldsymbol{R} \quad \theta=90^{\circ}$ $d \sin \theta=n \lambda \Rightarrow n=\frac{10^{-3}}{580} \frac{\sin 90^{\circ}}{650 \times 10^{-9}}=2.65$

So the second order/ n=2

Award [2] if smallest wavelength
used and an answer of n=3.

IB Physics HL C 3 Wave Phenomena Questions

Exam points

Covered syllabus points

Covered syllabus points

Question 1

Question (a)

Question (b)

Question (i)

Question 2

Question (a)

Question (i)

Question (ii)

Question (b)

Question (c)

Question (d)

Question (i)

Question (ii)

Question 3

Question (a)

Question (i)

Question (ii)

Question (iii)

Question (b)

Question (i)

Question (c)

Question (i)

Question (ii)

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14