IB Physics HLTopic 3 — Oscillations & WavesPaper 1 & 2At a boundary~13 min read
Reflection, Refraction & Transmission
Look at a window at night and you see two things at once: the street outside, and your own face. Some of the light went through the glass and some bounced back off it. That’s the whole of this page. A wave arriving at a boundary between two materials has a few options — bounce, cross over, bend, or be soaked up — and usually it does several at once.
📘 What you need to know
At a boundary a wave can be reflected, refracted, transmitted or absorbed
Reflection: the wave bounces back into the original medium, obeying i = r
All angles are measured from the normal — the line at 90° to the boundary
Refraction: the wave crosses the boundary and changes direction, because it changes speed
Into a denser medium → slower, bends towards the normal. Into a less dense medium → faster, bends away
When a wave refracts, v and λ change but f never does
These behaviours happen for all waves — transverse and longitudinal
A wave meets a boundary
Whenever a wave arrives at the boundary between two materials, four things can happen to it — usually a mixture of them:
Reflected — it bounces back into the material it came from
Transmitted — it carries on through into the new material
Refracted — it crosses over and changes direction
Absorbed — some of its energy is taken by the material
Wave hits boundary
splits into
Reflected bounces back
+
Transmitted often refracted
+
Absorbed energy taken
One word of vocabulary first: in optics a transparent material is called a medium. Two or more of them are media. The incident ray is the one travelling towards the boundary.
Reflection
Definition — reflection
A wave hits a boundary between two media and does not pass through, but bounces back into the original medium
Reflection follows one beautifully simple rule, and it works for light, sound, water waves — everything:
The law of reflection
angle of incidence i = angle of reflection r
Both angles are measured from the normal, never from the boundary itself. The law of reflection says they are equal: i = r.
Nothing about the wave itself is altered by reflecting. It stays in the same medium, so its speed, wavelength and frequency are all unchanged — only its direction is different. (Some energy may still be absorbed or transmitted at the same time, which is why a reflection is usually dimmer than the original.)
Refraction
Definition — refraction
The change in direction of a wave as it passes through a boundary between media of different densities
Why does it bend? Because the wave changes speed, and the two ends of a wavefront don’t reach the boundary at the same instant. One side slows down first while the other is still going fast, and the whole wavefront swings round.
Picture a toy car rolling diagonally off a smooth floor onto a carpet. The wheel that reaches the carpet first slows down while the other wheel is still racing along — so the car turns. A wavefront does exactly this at a boundary. No mystery, just one side slowing before the other.
Going into a denser medium the wave slows down and bends towards the normal, so r < i. The faint dashed line shows where it would have gone without bending.
Which way does it bend?
Less dense → denser (air into glass): the wave slows down, the angle of refraction is smaller, and the ray bends towards the normal.
Denser → less dense (glass into air): the wave speeds up, the angle of refraction is larger, and the ray bends away from the normal.
The special case: hitting the boundary head-on
If the ray travels along the normal — striking the boundary at 90° to its surface — the wave passes straight through with no change of direction. There’s nothing to turn it: the whole wavefront crosses the boundary at the same instant, so both sides slow down together. It still slows and its wavelength still shrinks; it just doesn’t bend.
What changes, and what doesn’t
This is the sentence to memorise: when a wave refracts, its speed and wavelength change, but its frequency stays the same. The frequency is set by the source that made the wave, and the boundary has no say in it.
Refraction and the wave equationv = fλ , with f constantv down ⇒ λ down
That’s why light doesn’t change colour when it enters water. Colour is set by frequency, and frequency doesn’t budge.
Refraction of water waves
Water waves refract too, but here the “different media” are regions of different depth. As waves move from deep water into shallow water there is more drag from the seabed and less room to oscillate, so they slow down.
Slower waves with the same frequency must have a shorter wavelength — so the wavefronts bunch closer together. And if they meet the boundary at an angle, they bend towards the normal, giving r < i.
Crossing into shallow water the wavefronts crowd together (shorter λ) and swing round towards the normal, so r < i. The spacing where the wavefronts meet the boundary is identical on both sides — they have to join up.
Transmission and absorption
Definition — transmission
A wave passes through a substance and appears on the far side of the boundary
Transmission is the broad term: it simply means the wave got through, the opposite of being reflected. Refraction is one kind of transmission — the kind where the wave also changes direction because the two media have different densities.
As it passes through a material a wave can be partly absorbed. Energy is transferred to the material, so the transmitted wave has a smaller amplitude than the one that went in. Its frequency, though, is untouched.
The one constant: reflect it, refract it, transmit it, absorb half of it — the frequency never changes. Speed, wavelength, direction and amplitude are all fair game; f is fixed by the source.
Reflection vs refraction
Feature
Reflection
Refraction
Crosses the boundary?
No — stays in medium 1
Yes — enters medium 2
Direction
Changes, with i = r
Changes, bending towards or away from the normal
Speed
Unchanged
Changes
Wavelength
Unchanged
Changes
Frequency
Unchanged
Unchanged
Happens for
All waves
All waves
🧭 Deciding which way a ray bends
Draw the normal at the point where the ray hits, at 90° to the boundary.
Ask: is medium 2 denser? If yes the wave slows down; if no it speeds up.
Slower → bends towards the normal. Faster → bends away from the normal.
Check the special case: if the ray came in along the normal, it goes straight on, no bending at all.
WE 1
A ray of light strikes a plane mirror so that it makes an angle of 25° with the surface of the mirror. Determine the angle of reflection, and the angle between the incident and reflected rays.
Step 1 — angles are measured from the normal, not the surfacei = 90 − 25 = 65°Step 2 — apply the law of reflection
r = i
Step 3 — the two rays sit either side of the normalangle between rays = 65 + 65 = 130°r = 65°, rays 130° apartAnswering 25° is the trap. Always convert a “with the surface” angle using 90 − θ first.
WE 2
Light of frequency 5.0 × 1014 Hz travels from air, where its speed is 3.00 × 108 m s⁻¹, into glass, where its speed is 2.0 × 108 m s⁻¹. Calculate its wavelength in each medium.
Step 1 — the frequency is the same in both media
f = 5.0 × 10¹⁴ Hz throughout.
Step 2 — wavelength in air, λ = v / fλ = (3.00 × 10⁸) / (5.0 × 10¹⁴) = 6.0 × 10⁻⁷ mStep 3 — wavelength in glassλ = (2.0 × 10⁸) / (5.0 × 10¹⁴) = 4.0 × 10⁻⁷ m600 nm in air, 400 nm in glassThe light slowed down, so λ shrank in the same proportion. It is still the same colour — f never changed.
WE 3
Water waves of frequency 8.0 Hz have a wavelength of 4.0 cm in deep water and 2.5 cm in shallow water. Calculate the speed in each region, and state how the waves bend on entering the shallow water at an angle.
Step 1 — deep water, v = fλv = 8.0 × 0.040 = 0.32 m s⁻¹Step 2 — shallow water (same frequency!)v = 8.0 × 0.025 = 0.20 m s⁻¹Step 3 — the waves slow down, so they bend towards the normal0.32 m s⁻¹ then 0.20 m s⁻¹; bends towards the normalShallow water acts like the “denser” medium here: slower, shorter λ, and r < i.
💡 Top tips
Always draw the normal first — every angle in this topic is measured from it.
If a question gives the angle to the surface, convert with 90 − θ before doing anything else.
Slower means towards the normal. Tie the bend to the speed, not to a memorised phrase about density.
Refraction always involves transmission; reflection never does.
Keep the wavefront spacing constant within one medium, and closer together in the slower medium.
When there are two boundaries, the refracted ray at the first becomes the incident ray at the second. Label them clearly.
⚠ Common mistakes
Measuring angles from the boundary instead of the normal
Mixing up reflection and refraction — refraction crosses the boundary, reflection does not
Saying the frequency changes on refraction — it never does
Thinking a ray along the normal doesn’t slow down — it does; it just doesn’t bend
Claiming refraction only happens to light — sound and water waves refract too
Forgetting that a reflected wave keeps its speed and wavelength, since it never left the medium
Quick recap: At a boundary a wave may be reflected (bounces back, i = r, nothing else changes), refracted (crosses over and bends because it changes speed), transmitted (gets through) or absorbed (loses amplitude). Into a slower medium it bends towards the normal; into a faster one, away. Throughout it all, v and λ may change but f never does.
So far the wave has met a flat wall. What if it meets a gap, or the edge of an obstacle? Instead of bouncing or bending, it spreads out and curves round the corner — that’s diffraction, and it’s the next page. Later, in Refraction of Waves, we’ll put numbers on the bending with refractive index and Snell’s law.
Rays, normals and bending got you stuck?
Book a free meeting and we’ll work through boundary diagrams and past-paper refraction questions together.
