A diffraction grating is used to observe light of wavelength 400 nm. The light illuminates 100 slits of the grating. What is the minimum wavelength difference that can be resolved when the second order of diffraction is viewed? 

A. 1 nm 

B. 2 nm 

C. 4 nm 

D. 8 nm

B

In two different experiments, white light is passed through a single slit and then is either refracted through a prism or diffracted with a diffraction grating. The prism produces a band of colours from M to N. The diffraction grating produces a first order spectrum P to Q.

What are the colours observed at M and P?

A

This has low discrimination and the difficulty index suggests candidates found it hard with the incorrect option C being the most popular. The spreading of colours and formation of a spectrum (or rainbow) is something that is covered during an introductory course in physics and then developed in refraction and diffraction.

A train moving at speed u relative to the ground, sounds a whistle of constant frequency f as it moves towards a vertical cliff face.

The sound from the whistle reaches the cliff face and is reflected back to the train. The speed of sound in stationary air is c.

What whistle frequency is observed on the train after the reflection?

A.  $\frac{(c+u)}{(c-u)}f$

B.  (c + u)f

C.  (c – u)f

D.  $\frac{(c-u)}{(c+u)}f$

A

For fringes to be observed in a double-slit interference experiment, the slits must emit waves that are coherent.

What conditions are required for the frequency of the waves and for the phase difference between the waves so that the waves are coherent?

B

Two points illuminated by monochromatic light are separated by a small distance. The light from the two sources passes through a small circular aperture and is detected on a screen far away.

Two points illuminated by monochromatic light are separated by a small distance. The light from the two sources passes through a small circular aperture and is detected on a screen far away.

C

Light of wavelength λ is incident normally on a diffraction grating that has a slit separation of $\frac{7\lambda }{2}$. What is the greatest number of maxima that can be observed using this arrangement? 

A. 4 
B. 6 
C. 7 
D. 9

C

Monochromatic light is incident on a double slit. Both slits have a finite width. The light then forms an interference pattern on a screen some distance away. Which graph shows the variation of intensity with distance from the centre of the pattern?

D

A particle is oscillating with simple harmonic motion (shm) of amplitude x₀ and maximum kinetic energy E_k. What is the potential energy of the system when the particle is a distance 0.20x₀ from its maximum displacement? 

A. 0.20E_k 

B. 0.36E_k 

C. 0.64E_k 

D. 0.80E_k

C

White light is incident normally on separate diffraction gratings X and Y. Y has a greater number of lines per metre than X. Three statements about differences between X and Y are

I.  adjacent slits in the gratings are further apart for X than for Y
II.  the angle between red and blue light in a spectral order is greater in X than in Y
III.  the total number of visible orders is greater for X than for Y.

Which statements are correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

B

Many candidates chose incorrect options. They need to be aware that there will usually be questions of this style and they need to practice them. The pattern of the answers is always the same and the best strategy is to try to identify a wrong answer which will then help to eliminate incorrect combinations.

A simple pendulum and a mass–spring system oscillate with the same time period. The mass of the pendulum bob and the mass on the spring are initially identical. The masses are halved.

What is $\frac{\mathrm{time} \mathrm{period} \mathrm{of} \mathrm{pendulum}}{\mathrm{time} \mathrm{period} \mathrm{of} \mathrm{mass}–\mathrm{spring} \mathrm{system}}$ when the masses have been changed?

A.  $\frac{\sqrt{2}}{2}$

B.  $1$

C.  $\sqrt{2}$

D.  $2$

C

Monochromatic light of wavelength $\lambda$ passes through a single-slit of width $b$ and produces a diffraction pattern on a screen. Which combination of changes to $b$ and $\lambda$ will cause the greatest decrease in the width of the central maximum?

C

Blue light is incident on two narrow slits. Constructive interference takes place along the lines labelled 1 to 5.

The blue light is now replaced by red light. What additional change is needed so that the lines of constructive interference remain in the same angular positions?

A. Make the slits wider

B. Make the slits narrower

C. Move the slits closer together

D. Move the slits further apart

D

Light is incident on a diffraction grating. The wavelength lines 600.0 nm and 601.5 nm are just resolved in the second order spectrum. How many slits of the diffraction grating are illuminated?

A. 20

B. 40

C. 200

D. 400

C

A transparent liquid forms a parallel-sided thin film in air. The diagram shows a ray I incident on the upper air–film boundary at normal incidence (the rays are shown at an angle to the normal for clarity).

Reflections from the top and bottom surfaces of the film result in three rays J, K and L. Which of the rays has undergone a phase change of $\pi$ rad?

A. J only

B. J and L only

C. J and K only

D. J, K and L

A

A mass–spring system oscillates vertically with a period of $T$ at the surface of the Earth. The gravitational field strength at the surface of Mars is $0.3 \text{g}$. What is the period of the same mass–spring system on the surface of Mars?

A.  $0.9T$

B.  $0.3T$

C.  $T$

D.  $3T$

C

Two lines X and Y in the emission spectrum of hydrogen gas are measured by an observer stationary with respect to the gas sample.

The emission spectrum is then measured by an observer moving away from the gas sample.

What are the correct shifts X* and Y* for spectral lines X and Y?

C

Which is correct for the tangential acceleration of a simple pendulum at small amplitudes?

A. It is inversely proportional to displacement.

B. It is proportional to displacement.

C. It is opposite to displacement.

D. It is proportional and opposite to displacement

D

A beam of monochromatic light is incident on a diffraction grating of N lines per unit length. The angle between the first orders is θ₁.

What is the wavelength of the light?

A.     $\frac{\sin {\theta }_1}{N}$

B.     N sin θ₁

C.     N sin$\left(\frac{{\theta }_1}{2}\right)$

D.     $\frac{\sin \left(\frac{{\theta }_1}{2}\right)}{N}$

D

A simple pendulum undergoes simple harmonic motion. The gravitational potential energy of the pendulum is zero at the equilibrium position. How many times during one oscillation is the kinetic energy of the pendulum equal to its gravitational potential energy?

A.  1

B.  2

C.  3

D.  4

D

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

What are the changes in the width and in the intensity of the central maximum of the diffraction pattern?

B

A simple pendulum bob oscillates as shown.

At which position is the resultant force on the pendulum bob zero?

A.     At position A

B.     At position B

C.     At position C

D.     Resultant force is never zero during the oscillation

D

Monochromatic light of wavelength λ in air is incident normally on a thin film of refractive index n. The film is surrounded by air. The intensity of the reflected light is a minimum. What is a possible thickness of the film?

A.     $\frac{\lambda }{4n}$

B.     $\frac{3\lambda }{4n}$

C.     $\frac{\lambda }{n}$

D.     $\frac{5\lambda }{4n}$

C

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

What is the expression for the wavelength of light used?

A.   $\frac{d\text{sin}\alpha }{2}$

B.   $\frac{d\text{sin}\beta }{2}$

C.   d sin α

D.   d sin β

B

An observer with an eye of pupil diameter $d$ views the headlights of a car that emit light of wavelength $\lambda$. The distance between the headlights is $L$.

What is the greatest distance between the observer and the car at which the images of the headlights will be resolved by the observer’s eye?

A.  $\frac{1.22\lambda }{Ld}$

B.  $\frac{1.22\lambda L}{d}$

C.  $\frac{Ld}{1.22\lambda }$

D.  $\frac{d}{1.22\lambda L}$

C

Despite option C being the most frequent (correct) response, both options A and B were effective distractors. A useful teaching point relating to this question relates to unit analysis; neither solution presented in option A or option D produce the correct units for distance, and could be eliminated from consideration on this basis.

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

The number of slits is increased keeping the width and the separation of the slits unchanged.

Three possible changes to the pattern are

I.   the separation of the primary maxima increases

II.  the intensity of the primary maxima increases

III. the width of the primary maxima decreases.

Which of the possible changes are correct?

A.   I and II only

B.   I and III only

C.   II and III only

D.   I, II and III

C

An object undergoing simple harmonic motion (SHM) has a period T and total energy E. The amplitude of oscillations is halved. What are the new period and total energy of the system?

C

A train is sounding its whistle when approaching a train station. Three statements about the sound received by a stationary observer at the station are:

I.   The frequency received is higher than the frequency emitted by the train.
II.  The wavelength received is longer than the wavelength emitted by the train.
III. The speed of the sound received is not affected by the motion of the train.

Which combination of statements is correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

B

A simple pendulum has a time period $T$ on the Earth. The pendulum is taken to the Moon where the gravitational field strength is $\frac{1}{6}$ that of the Earth.

What is the time period of the pendulum on the Moon?

A.  $T\sqrt{6}$

B.  $T$

C.  $\frac{\sqrt{6}}{6}T$

D.  $\frac{T}{6}$

A

A train approaches a station and sounds a horn of constant frequency and constant intensity. An observer waiting at the station detects a frequency f_obs and an intensity I_obs. What are the changes, if any, in I_obs and f_obs as the train slows down?

D

An unusual way of considering the Doppler effect, this had a very low discrimination index with the most popular answer A when D was correct. It is likely the candidates have confused what the train is producing – a constant intensity sound – and what the observer hears, Io, where the intensity is going to increase as the train approaches. This immediately eliminates options A and C.

A mass on a spring is displaced from its equilibrium position. Which graph represents the variation of acceleration with displacement for the mass after it is released?

D

Light of frequency 500 THz is incident on a single slit and forms a diffraction pattern. The first diffraction minimum forms at an angle of 2.4 x 10^–3 rad to the central maximum. The frequency of the light is now changed to 750 THz. What is the angle between the first diffraction minimum and the central maximum?

A.  1.6 × 10^–3 rad

B.  1.8 × 10^–3 rad

C.  2.4 × 10^–3 rad

D.  3.6 × 10^–3 rad

A

The four pendulums shown have been cut from the same uniform sheet of board. They are attached to the ceiling with strings of equal length.

Which pendulum has the shortest period?

D

Candidate answers were almost equally divided between responses B and D (correct). This question indirectly assesses experimental skills; how do we determine the effective length of a pendulum?

A mass oscillates with simple harmonic motion (SHM) of amplitude x_o. Its total energy is 16 J. 

What is the kinetic energy of the mass when its displacement is $\frac{x_0}{2}$?

A. 4 J

B. 8 J

C. 12 J

D. 16 J

C

A spring loaded with mass m oscillates with simple harmonic motion. The amplitude of the motion is A and the spring has total energy E. What is the total energy of the spring when the mass is increased to 3m and the amplitude is increased to 2A?

A. 2E

B. 4E

C. 12E

D. 18E

B

Monochromatic light is incident on two identical slits to produce an interference pattern on a screen. One slit is then covered so that no light emerges from it. What is the change to the pattern observed on the screen?

A. Fewer maxima will be observed.

B. The intensity of the central maximum will increase.

C. The outer maxima will become narrower.

D. The width of the central maximum will decrease.

A

Light passes through a diffraction grating. Which quantity must be decreased to improve the resolution of the diffraction grating?

A. The grating spacing

B. The number of grating lines illuminated by the light source

C. The number of grating lines per millimetre

D. The spectral order being observed

A

A train is approaching an observer with constant speed

                                                         $$\frac{c}{34}$$

where c is the speed of sound in still air. The train emits sound of wavelength λ. What is the observed speed of the sound and observed wavelength as the train approaches?

A

A beam of monochromatic light is incident on a single slit and a diffraction pattern forms on the screen.

What change will increase θ_s?

A.     Increase the width of the slit

B.     Decrease the width of the slit

C.     Increase the distance between the slit and the screen

D.     Decrease the distance between the slit and the screen

B

Monochromatic light of wavelength $\lambda$ in air is incident normally on a thin liquid film of refractive index $n$ that is suspended in air. The rays are shown at an angle to the normal for clarity.

What is the minimum thickness of the film so that the reflected light undergoes constructive interference?

A.  $\frac{\lambda }{4n}$

B.  $\frac{\lambda }{3n}$

C.  $\frac{\lambda }{2n}$

D.  $\frac{\lambda }{n}$

A

A mass at the end of a vertical spring and a simple pendulum perform oscillations on Earth that are simple harmonic with time period T. Both the pendulum and the mass-spring system are taken to the Moon. The acceleration of free fall on the Moon is smaller than that on Earth. What is correct about the time periods of the pendulum and the mass-spring system on the Moon?

B

Light of wavelength $\lambda$ is diffracted after passing through a very narrow single slit of width $x$. The intensity of the central maximum of the diffracted light is $I_0$. The slit width is doubled.

What is the intensity of central maximum and the angular position of the first minimum?

B

Option B was the most frequent (correct) selected by candidates. Interestingly, the more able candidates were distracted by option D, who were likely considering the intensity/amplitude relationship. As a result, this would be a good MC question for teaching purposes.

The headlights of a car emit light of wavelength 400 nm and are separated by 1.2 m. The headlights are viewed by an observer whose eye has an aperture of 4.0 mm. The observer can just distinguish the headlights as separate images. What is the distance between the observer and the headlights?

A. 8 km

B. 10 km

C. 15 km

D. 20 km

B

Response B was the most common (correct) response, with responses A and C as equally significant distractors.

Two stars are viewed with a telescope using a green filter. The images of the stars are just resolved. What is the change, if any, to the angular separation of the images of the stars and to the resolution of the images when the green filter is replaced by a violet filter?

A

Another question with a low discrimination index and candidates choosing all 4 responses with B the most popular. Remembering that angular separation is dependent on the stars position in space relative to each other so unlikely to have been changed by a coloured filter would have helped to eliminate A and D.

Sea waves move towards a beach at a constant speed of 2.0 m s^–1. They arrive at the beach with a frequency of 0.10 Hz. A girl on a surfboard is moving in the sea at right angles to the wave fronts. She observes that the surfboard crosses the wave fronts with a frequency of 0.40 Hz.

What is the speed of the surfboard and what is the direction of motion of the surfboard relative to the beach?

B

An object at the end of a spring oscillates vertically with simple harmonic motion (shm). The graph shows the variation with time $t$ of the displacement $x$ of the object.

What is the velocity of the object?

A. $-\frac{2\pi A}{T}\sin \left(\frac{\pi t}{T}\right)$

B. $\frac{2\pi A}{T}\sin \left(\frac{\pi t}{T}\right)$

C. $-\frac{2\pi A}{T}\cos \left(\frac{\pi t}{T}\right)$

D. $\frac{2\pi A}{T}\cos \left(\frac{\pi t}{T}\right)$ 

B

A transparent liquid film of refractive index 1.5 coats the outside of a glass lens of higher refractive index. The liquid film is used to eliminate reflection from the lens at wavelength λ in air.

What is the minimum thickness of the liquid film coating and the phase change at the liquid–glass interface?

D

Half of candidates (incorrectly) selected response B, suggesting that while they recognized the phase change of π, determining the minimum thickness of the thin film was challenging. The discrimination index was very low for this question.

A train travelling in a straight line emits a sound of constant frequency f. An observer at rest very close to the path of the train detects a sound of continuously decreasing frequency. The train is

A. approaching the observer at constant speed.

B. approaching the observer at increasing speed.

C. moving away from the observer at constant speed.

D. moving away from the observer at increasing speed.

D

Light of wavelength λ is normally incident on a diffraction grating of spacing 3λ. What is the angle between the two second-order maxima?

A.  ${\sin }^{-1}\frac{2}{3}$

B.  ${\sin }^{-1}\frac{4}{3}$

C.  $2{\sin }^{-1}\frac{2}{3}$

D.  >90° so no second orders appear

C

A stationary sound source emits waves of wavelength $\lambda$ and speed v. The source now moves away from a stationary observer. What are the wavelength and speed of the sound as measured by the observer?

A

Monochromatic light is incident on 4 rectangular, parallel slits. The first principal maximum is observed at an angle θ to the direction of the incident light. The number of slits is increased to 8 each having the same width and spacing as the first 4.

Three statements about the first principal maximum with 8 slits are

     I.     the angle at which it is observed is greater than θ

     II.     its intensity increases

     III.     its width decreases.

Which statements are correct?

A.     I and II only

B.     I and III only

C.     II and III only

D.     I, II and III 

C

The diagram shows the diffraction pattern for light passing through a single slit.

What is

                                      $\frac{\text{wavelength of light}}{\text{width of slit}}$

A. 0.01

B. 0.02

C. 1

D. 2

A

An ambulance siren emits a sound of frequency 1200 Hz. The speed of sound in air is 330 m s^–1. The ambulance moves towards a stationary observer at a constant speed of 40 m s^–1. What is the frequency heard by the observer?

A.   $\frac{1200\times 330}{370}$Hz

B.   $\frac{1200\times 290}{330}$Hz

C.   $\frac{1200\times 370}{330}$Hz

D.   $\frac{1200\times 330}{290}$Hz

D

A train is moving in a straight line away from a stationary observer when the train horn emits a sound of frequency $f_0$. The speed of the train is $0.10v$ where $v$ is the speed of sound. What is the frequency of the horn as heard by the observer?

A.  $\frac{0.9}{1}{f}_0$

B.  $\frac{1}{1.1}{f}_0$

C.  $\frac{1.1}{1}{f}_0$

D.  $\frac{1}{0.9}{f}_0$

B

A pendulum oscillating near the surface of the Earth swings with a time period T. What is the time period of the same pendulum near the surface of the planet Mercury where the gravitational field strength is 0.4g?

A.  0.4T

B.  0.6T

C.  1.6T

D.  2.5T

C

Light is incident on a diffraction grating. The wavelengths of two spectral lines of the light differ by $0.59 \mathrm{nm}$ and have a mean wavelength of $590 \mathrm{nm}$. The spectral lines are just resolved in the fourth order of the grating. What is the minimum number of grating lines that were illuminated?

A.  $25$

B.  $250$

C.  $1000$

D.  $4000$

B

A beam of light containing two different wavelengths is incident on a diffraction grating. The wavelengths are just resolved in the third order of diffraction.

What change increases the resolution of the image?

A.  Increasing the width of the incident beam

B.  Increasing the intensity of light

C.  Decreasing the number of lines per unit length in the diffraction grating

D.  Decreasing the order of diffraction

A

An object undergoes simple harmonic motion (shm) of amplitude $x$₀. When the displacement of the object is $\frac{x_0}{3}$, the speed of the object is $v$. What is the speed when the displacement is $x$₀?

A. 0

B. $\frac{v}{3}$

C. $\frac{\sqrt{2}}{3}v$

D. $3v$

A

In a Young’s double-slit experiment, the distance between fringes is too small to be observed.

What change would increase the distance between fringes?

A. Increasing the frequency of light

B. Increasing the distance between slits

C. Increasing the distance from the slits to the screen

D. Increasing the distance between light source and slits

C

On approaching a stationary observer, a train sounds its horn and decelerates at a constant rate. At time t the train passes by the observer and continues to decelerate at the same rate. Which diagram shows the variation with time of the frequency of the sound measured by the observer?

D