Waves

Practice

Recall it first, then use it — testing yourself builds the memory, where rereading the notes above only feels easier.

Recall and application shuffled together — you have to work out what each item wants before you can answer it, which is the part the exam actually tests. Both kinds feed the same spacing schedule, so anything you miss comes back sooner.

Say the answer out loud before flipping — that attempt is where the learning happens, even when you get it wrong.

Exam-style only. Instant feedback, shuffled each attempt, best score saved on this device.

What actually comes up

Three questions every year, in a stable order: lenses/mirrors and ray diagrams (Question One or Two), refraction/total internal reflection (Question Two or Three), and a waves/interference/Doppler question wrapped in a real scenario. Lenses and refraction have appeared every year transcribed here, even though the topic is titled simply "Waves".

Across 4 years

The pattern — what to prepare

The 2025 paper ↗ Marking schedule ↗

Question One — Lenses

A data projector uses a concave lens (object 15 cm from a 10 cm focal length) and, in another model, a convex lens forming a real image twice the object size; an ultra-short-throw projector uses a concave mirror.

• Concave lens: object 15 cm, focal length 10 cm

• a Draw and label the image formed by the concave lens. Achieved
• b Calculate the magnification of the image, and fully describe its nature. Merit
• c Complete a ray diagram showing how a convex lens forms a real image twice the object size, showing any calculations used to place the object. Excellence
• d Complete a ray diagram for a concave mirror forming the image in an ultra-short-throw projector, and describe the nature of the image. Merit

Question Two — Refraction

A double-glazed window (refractive index 1.5) makes a laser bend; a red laser (wavelength 6.50×10⁻⁷ m in air, 4.64×10⁻⁷ m in glass) enters at 30°; increasing the angle eventually causes total internal reflection.

• Glass n = 1.5
• λ(air) = 6.50 × 10⁻⁷ m, λ(glass) = 4.64 × 10⁻⁷ m, incident angle 30°

• a Show the path of the ray crossing from glass to air. Achieved
• b Explain what a refractive index of 1.5 means, in terms of the speed of light in the glass. Achieved
• c Calculate the angle of refraction as red light passes from air into the glass, using the given wavelengths. Merit
• d Name the phenomenon occurring when the ray bounces off the inner glass surface, and describe the conditions needed for it. Merit

Question Three — Waves (Wi-Fi)

Wi-Fi access points on the same frequency cause interference; a satellite orbits at 550 km sending 0.025 m radio waves; Wi-Fi signals slow passing through walls, modelled as pulses on ropes of different density.

• Satellite height: 550 km, wavelength: 0.025 m
• Rope speeds: air 2 squares/s, wall 1 square/s

• a What type of wave is an electromagnetic wave? Achieved
• b Explain how two Wi-Fi access points on the same frequency create both strong and weak signal spots. Merit
• c Calculate how many radio waves reach the Earth in 2 hours. Merit
• d Describe how frequency changes as the Wi-Fi signal moves from air to wall, then draw the result of two colliding pulses after 3 seconds. Excellence

The 2022 paper ↗ Marking schedule ↗

Question One — Behaviour of light

Light travels from air into a glass block (n = 1.52) at an internal angle of 32°; a semi-circular block shows total internal reflection; a concave lens (focal length 3 cm) has a pin placed 7 cm away.

• n(glass) = 1.52, n(air) = 1.00, v(air) = 3.00 × 10⁸ m s⁻¹, internal angle 32°
• Concave lens: object 7 cm away, focal length 3 cm

• a Calculate the angle of incidence in air, given the angle inside the glass is 32°. Achieved
• b(i) State what happens to the speed of light as it enters the glass. Achieved
• b(ii) Calculate the speed of light within the glass block. Merit
• c(i) Identify the physics phenomenon occurring at the straight boundary of the semi-circular block. Achieved
• c(ii) Describe the two conditions required for this phenomenon to occur. Merit
• d Complete a ray diagram and use calculations to describe and explain why no image can be seen on a screen for a pin 7 cm from a concave lens of focal length 3 cm. Excellence

Question Two — Light waves and barriers

Purple light (7.5 × 10¹⁴ Hz) shines through gaps of different widths in a barrier, then through a double slit, forming a bright/dark pattern.

• Purple light frequency: 7.5 × 10¹⁴ Hz

• a Calculate the wavelength of the purple light. Achieved
• b Complete diagrams to show the effect of a gap on the waves, for a wide gap and a narrow gap. Achieved
• c Complete a labelled wave diagram to show how the double-slit pattern occurs. Merit
• d Use physics principles to describe and explain how the double-slit pattern is formed, naming the phenomenon and the conditions required. Excellence

Question Three — Light rays and pulses in a rope

A lamp is placed 3 cm from a convex lens (focal length 2 cm), then compared with a convex mirror of the same focal length and distance; pulses reflect off a rope's fixed and free ends; a concave mirror forms a virtual image.

• Object 3 cm from a convex lens/mirror, focal length 2 cm each

• a Complete a ray diagram for a lamp 3 cm from a convex lens of focal length 2 cm. Achieved
• b(i) Complete a ray diagram for the same lamp and distance in front of a convex mirror of the same focal length. Achieved
• b(ii) Describe the image produced by the convex mirror. Merit
• c Complete diagrams showing the reflected pulses from a fixed end and a free end of a rope. Merit
• d(i) Use a ray diagram to show how a concave mirror can create a virtual image. Achieved
• d(ii) Describe the position of the object relative to the concave mirror for a virtual image to form. Merit
• d(iii) Compare the similarities and differences of the concave mirror's virtual image with a virtual image formed by a convex mirror. Excellence

The 2024 paper ↗ Marking schedule ↗

Question One — Waves

A water tank with a shallow and deep end shows waves changing as they cross; guide ropes model a wave pulse crossing from a less dense to a more dense rope.

• 6 waves in 8.0 s; wavelength 4.0 cm shallow → 2.0 cm deep

• a Name the physics phenomenon causing the wave changes as it crosses the tank. Achieved
• b Calculate the final velocity of the waves at the deep end. Achieved
• c Describe and explain the phenomenon, including changes to wavelength, velocity, amplitude, and frequency. Merit
• d Complete a diagram showing the transmitted and reflected pulse at a rope-density boundary, and compare their velocities. Merit

Question Two — Mirrors and lenses

A curved mirror forms an enlarged, upright image; a candle in front of a convex lens forms an inverted, diminished image projected on a screen.

• Object 1.5 m tall, 0.90 m from a mirror with 2.0 m focal length
• Second case: object 4.0 m from a concave mirror with 2.0 m focal length

• a State the third property of an image already described as enlarged and upright. Achieved
• b Calculate the height of the image for a 1.5 m object, 0.90 m from a mirror with 2.0 m focal length. Merit
• c Complete a ray diagram to locate the image for an object 4.0 m from a concave mirror (2.0 m focal length), and state its three properties. Merit
• d State which image property allows projection onto a screen, complete a ray diagram for an inverted, diminished image, then explain how to make the image larger while keeping it projectable. Excellence

Question Three — Light

A fibre optic cable (glass core, cladding) transmits light; a beam passes from oil into air at 30° incidence.

• n(air) = 1.00; v(air) = 3.00 × 10⁸ m s⁻¹, v(oil) = 2.56 × 10⁸ m s⁻¹; incident angle 30°

• a State what the symbols n₁ and n₂ represent in the fibre-optic diagram. Achieved
• b Name the phenomenon that transmits light along the fibre, and state the conditions required for it. Achieved
• c Draw the refracted ray as light passes from oil to air, then calculate the angle of refraction. Merit
• d Describe and explain any changes to sound heard by people walking past two in-phase loudspeakers. Excellence

The 2023 paper ↗ Marking schedule ↗

Question One — Mirrors (the costume shop)

Students look into a concave mirror (25 cm focal length); Marco stands 40 cm away; Harvey later stands 10 cm away.

• Concave mirror focal length: 25 cm
• Marco: 40 cm from mirror
• Harvey: 10 cm from mirror

• a Define the term "real" as used for the image. Achieved
• b Complete a ray diagram to show how Marco's (40 cm) image forms. Achieved
• d For Harvey standing 10 cm from the mirror, use a ray diagram and calculate the image distance and magnification to describe and explain the nature of the new image. Excellence

Question Two — Refraction (the wishing pond)

Coins in a pond appear closer to the surface than they are; a light ray leaves water (n = 1.33) into air (n = 1.00) at 40°; a beam later passes from air into diamond.

• n(water) = 1.33, n(air) = 1.00, angle in water 40°

• a Name the physics phenomenon causing the coins to appear closer to the surface. Achieved
• b Calculate the angle θ at the surface as light leaves water into air at 40°. Merit
• c Calculate the speed of light in diamond, and state what happens to the frequency of light entering diamond. Merit
• d Show that the critical angle for diamond is 24.4°, then explain total internal reflection and define the critical angle. Excellence

Question Three — Lenses (the optician)

Two lenses of the same shape and material but different thickness are compared; a pair of convex lenses has a 30 cm focal length.

• a Compare the focal length of the thin lens to the thick lens (no calculation). Achieved
• b Complete a ray diagram to show the position and appearance of the image formed by a 30 cm focal-length convex lens. Merit

Grades above are read from each year's own Achievement/Merit/Excellence evidence statement, condensed to the actual task — the schedules also grade holistically per question on a 0–8 scale, not a fixed mark per bullet. Ray diagrams in the original papers are described here rather than reproduced, since the source OCR cannot represent diagrams.

Past exams & resources

⏱ Timed opens the paper and starts a countdown matching the exam length. Official NZQA PDFs. If a link 404s, that year’s paper may sit under a slightly different code: browse the NZQA subject page.