Waves: Reflection, Refraction, and the Rules That Govern Them

Quick answer: When a wave hits a boundary it either bounces off (reflection) or passes through and bends (refraction). Reflection always obeys one rule - the angle of incidence equals the angle of reflection, both measured from the normal, not the surface. Refraction happens because the wave changes speed in the new material: light entering something denser (air into glass) slows down and bends towards the normal; leaving it, light speeds up and bends away.

I lost marks on this exact topic in a mock - not because it is hard, but because I measured my angles from the glass surface, not the normal. So here are the rules, why they are true, and the traps that quietly cost marks in GCSE, IGCSE and CBSE papers.

First, the two kinds of wave

Before reflection and refraction make sense, you need to know what is moving.

• Transverse waves - the vibration is at 90 degrees to the direction of travel. Think of flicking a rope up and down while the wave moves forward. All light and the rest of the electromagnetic spectrum, water ripples and earthquake S-waves are transverse, and they have crests and troughs.
• Longitudinal waves - the vibration is along the same line the wave travels, making squashed-together compressions and spread-out rarefactions. Sound is the classic example; so are P-waves in a quake.

Both carry energy, not matter - the water in a ripple bobs up and down, it does not travel to the shore. And both can be reflected and refracted. Speed, frequency and wavelength are tied together by wave speed = frequency x wavelength, which explains refraction later.

Reflection: one rule, measured the right way

Draw a straight line at exactly 90 degrees to the surface where the ray lands - that line is the normal. Everything is measured from it.

• The angle of incidence (i) is between the incoming ray and the normal.
• The angle of reflection (r) is between the reflected ray and the normal.
• The law of reflection: i = r. Always.

The mistake that costs marks - and the one I made - is measuring from the mirror instead of the normal. If your incident ray is 30 degrees from the normal, it is 60 degrees from the surface; quote the 60 and you are wrong, even though the reflection itself was fine. In an AQA ray-box practical or a CBSE diagram question, draw the normal as a dashed line first, every time.

One nice consequence: a plane-mirror image sits the same size and upright, as far behind the mirror as the object is in front, and laterally inverted - which is why AMBULANCE is printed back-to-front on the vehicle.

Refraction: why light bends

Refraction is what happens when a wave crosses from one material into another and changes speed. That speed change is the cause of the bending - not the density on its own.

Picture a car driving at an angle off tarmac onto mud: the wheel that hits the mud first slows while the other still grips, so the car slews towards the mud. Light does the same:

• Going into a denser medium (air into glass, or air into water), light slows down and bends towards the normal. The angle of refraction is smaller than the angle of incidence.
• Coming back out into a less dense medium (glass into air), light speeds up and bends away from the normal. The angle of refraction is larger.
• If the ray travels along the normal (i = 0 degrees), it does not bend at all - but it still changes speed.

One more trap: the frequency stays the same. It is the speed and the wavelength that change together, because frequency is set by the source.

How strongly a material bends light is its refractive index, n. Two ways to write it:

• n = sin i / sin r (from the angles - this is Snell's law)
• n = c / v (speed of light in a vacuum divided by its speed in the material)

Glass is about 1.5 and water about 1.33 - numbers worth memorising for CBSE and IGCSE.

Worked example: a ray entering a glass block

A ray of light hits a glass block at an angle of incidence of 40 degrees. The refractive index of the glass is 1.5. Find the angle of refraction.

1. Write the rule. n = sin i / sin r.
2. Put in what you know. 1.5 = sin 40 / sin r.
3. Rearrange for sin r. sin r = sin 40 / 1.5.
4. Work out the top. sin 40 = 0.643, so sin r = 0.643 / 1.5 = 0.429.
5. Take the inverse sine. r = arcsin(0.429) = 25.4 degrees.
6. Sense-check. 25.4 is smaller than 40, so the ray bent towards the normal - exactly what should happen going into denser glass. If your answer came out bigger, you divided the wrong way.

Leaving the far side of a parallel-sided block, the ray bends away from the normal by the same amount, so it emerges parallel to the ray that went in, just shifted sideways - a detail examiners love to check. Want it walked through with your own numbers? Paste the question into /explain and it will rebuild each step; for the trig itself, /math-solver handles the arcsin.

A note on total internal reflection

Push the angle of incidence inside the glass higher and higher and the refracted ray bends further from the normal, until at one special angle - the critical angle - it grazes along the surface (angle of refraction = 90 degrees). Go past that and no light escapes at all: it reflects straight back inside. That is total internal reflection.

Two conditions, and you need both:

1. The light is going from a denser to a less dense medium (for example glass into air).
2. The angle of incidence is greater than the critical angle.

The critical angle comes from sin c = 1 / n. For glass (n = 1.5), sin c = 0.667, so c = 41.8 degrees. That is why a 45-degree prism reflects light inside binoculars and periscopes, why optical fibres pipe light around bends, and why a cut diamond (n = 2.42, critical angle just 24 degrees) traps light and sparkles.

Test yourself

1. A ray of light meets a mirror at 25 degrees to the mirror's surface. What is the angle of reflection?
2. Light passes from water into air. Does it bend towards or away from the normal, and does it speed up or slow down?
3. The critical angle of a glass is 42 degrees. Light inside the glass hits the boundary with air at 50 degrees. What happens?

Quick answers:

1. 65 degrees. The 25 is measured from the surface, so the angle of incidence from the normal is 90 - 25 = 65, and reflection equals incidence.
2. Away from the normal, and it speeds up - it is moving into a less dense medium.
3. Total internal reflection - 50 is greater than the 42-degree critical angle, so no light escapes; it all reflects back inside.

Missed one? Drop the idea you are stuck on into /explain for a plain rebuild, then fire a few fresh ray questions at /quiz to lock it in.

FAQ

Do reflection and refraction only happen to light?

No - every wave does both. Sound echoes off walls (reflection) and bends through air of different temperatures (refraction), and water waves refract as they slow in the shallows. Light is just the easiest one to draw.

Why does light not bend if it hits the surface straight on?

Because there is no leading edge to slow down first. Along the normal the whole wavefront crosses into the new material at the same instant, so it changes speed without changing direction.

What is the difference between the critical angle and the angle of incidence?

The critical angle is a fixed property of the boundary - it depends only on the two materials. The angle of incidence is whatever angle you send the ray in at, and total internal reflection only kicks in once that incidence angle climbs above the critical angle.

In short: reflection bounces a wave off a surface with the angle of incidence equal to the angle of reflection, both measured from the normal, while refraction bends it because the wave changes speed crossing into a new material - towards the normal when it slows in something denser, away when it speeds up. Draw the normal first and those two rules carry most of the marks. Stuck on a ray diagram? /explain will talk you through it.