Laws of reflection

Look into a still pond, a polished spoon, or the bathroom mirror and you are trusting a rule so exact that opticians and periscope-builders alike lean on it without a second thought: light bouncing off a smooth surface always leaves at the same angle it arrived, measured from a line perpendicular to that surface. This pair of statements — the laws of reflection — opens the "Light" chapter, and every later idea in ICSE Class 9 Physics (plane mirrors, image formation, curved mirrors) is built directly on top of it. Get the geometry of the normal, incident ray, and reflected ray fixed here, and the rest of the optics chapter becomes bookkeeping. Get it wrong — say by measuring angles from the mirror surface instead of the normal — and every diagram after this one goes crooked. This section fixes the two laws precisely, shows how they combine into a simple deviation formula useful for mirror problems, and works through the angle arithmetic examiners actually test.

The core insight

When light reflects off any smooth surface, the angle of incidence always equals the angle of reflection ( $i = r$ , both measured from the normal), and the incident ray, reflected ray, and normal all lie in one flat plane.

The core idea

The normal is the reference line, never the mirror. At the exact point where a ray strikes a reflecting surface (the point of incidence), draw a line perpendicular to the surface — this is the normal. It is redrawn fresh at every new point of incidence; it is not a permanent mark on the mirror. The incident ray is the ray arriving at the surface, the reflected ray is the ray leaving it, and both angles — angle of incidence $i$ and angle of reflection $r$ — are measured between each ray and the normal, never between the ray and the mirror surface itself.

The two laws, stated precisely. First, the angle of incidence equals the angle of reflection:

i = r

where: $i$ is the angle of incidence (between the incident ray and the normal) and $r$ is the angle of reflection (between the reflected ray and the normal), both measured in degrees on the same side convention. Second, the incident ray, the normal at the point of incidence, and the reflected ray all lie in the same flat plane — none of the three twists out sideways into a different plane. Both laws hold for every angle of incidence, including the special case $i = 0°$ , where the ray falls straight along the normal and simply reflects back along its own path with $r = 0°$ too.

The laws hold for any smooth surface. Plane mirrors, curved mirrors, polished metal, even still water — any surface smooth enough not to scatter light diffusely obeys $i = r$ at every point. A curved mirror is really a stitched-together family of tiny flat elements, each with its own normal, and the law applies locally at each one.

Figure

A ray of light hitting a flat mirror with the normal drawn perpendicular to the mirror at the point of incidence and the incident and reflected rays making equal angles i and r on either side of the normal

Why it works

The laws of reflection are an experimental fact about how smooth surfaces redirect light, verified directly rather than derived from a deeper formula at this level — so this section shows the reasoning that connects $i = r$ to a second, exam-useful quantity: the angle of deviation, the total turn a ray makes on reflection. Knowing this link explains why mirror problems so often ask for the angle between the incident and reflected rays rather than $i$ or $r$ alone, and it follows in three short steps from the first law and basic angle facts about straight lines.

Step 1. Take a ray striking a mirror with angle of incidence $i$ . By the first law, the angle of reflection is also $i$ (since $r = i$ ). The incident ray and the reflected ray, together with the mirror surface, form two angles with the mirror: the incident ray makes an angle of $(90° - i)$ with the mirror surface, and so does the reflected ray, since both are measured as $90°$ minus the angle from the normal.

Step 2. The angle of deviation, $D$ , is defined as the total angle through which the ray has turned — the angle between the original direction of the incident ray (extended straight through the mirror) and the actual direction of the reflected ray. Because the incident ray, the normal, and the reflected ray lie in one plane (the second law), this deviation can be read straight off the same flat diagram used to mark $i$ and $r$ .

Step 3. The reflected ray sits at angle $r$ from the normal on the far side, and the extended incident ray sits at angle $i$ from the normal on the near side; together with the straight normal line, the incident ray, its extension, and the reflected ray span $180°$ across the mirror, so $D = 180° - i - r$ . Substituting $r = i$ from the first law gives the compact result

D = 180° - 2i

where: $D$ is the angle of deviation and $i$ is the angle of incidence. This single formula packages both laws into one number: it only exists because $i = r$ (law one) and because the whole picture is planar (law two), so a deviation question is really an $i = r$ question in disguise.

Worked example

A ray of light strikes a plane mirror such that the angle between the incident ray and the mirror surface is $35°$ (the same setup as the standard glancing-angle problem for this topic). Find the angle of deviation of the ray.

Step 1. Convert the glancing angle to the angle of incidence. Since the normal is perpendicular to the mirror, $i = 90° - 35° = 55°$ .

Step 2. Apply the first law of reflection. Since $i = r$ always, $r = 55°$ as well — this matches the earlier result that the reflected ray also leaves at $55°$ from the normal, or equivalently $35°$ from the mirror surface.

Step 3. Apply the deviation formula. Using $D = 180° - 2i$ with $i = 55°$ ,

D = 180° - 2(55°) = 180° - 110° = 70°

Answer: the ray of light is deviated by $70°$ on reflection — this is the angle you would actually measure with a protractor between the incoming ray's original direction and the outgoing reflected ray.

Competitive stretch

Two plane mirrors are inclined at an angle $\theta = 60°$ , arranged like an open book (the geometry behind a simple periscope or kaleidoscope). A classic result — provable by applying the deviation formula at each mirror and adding the triangle angle sums — is that the total deviation after reflecting off both mirrors depends only on the angle between the mirrors, not on the incidence angle at the first one:

D_{\text{total}} = 2\theta

With $\theta = 60°$ , $D_{\text{total}} = 2(60°) = 120°$ : no matter what angle a ray enters the first mirror at, after bouncing off both mirrors it emerges turned through exactly $120°$ from its original direction. This is why kaleidoscope and periscope mirror angles are chosen deliberately — the turning angle is fixed by the mirror geometry alone.

Common traps

Measuring $i$ or $r$ from the mirror surface instead of from the normal — always measure from the normal; the glancing angle and the angle of incidence are complements ( $i = 90° - \text{glancing angle}$ ), not the same thing.
Forgetting that $i = r$ holds even at $i = 0°$ : light along the normal reflects straight back on itself, with $r = 0°$ too.
Treating the normal as a fixed line drawn once on the mirror — it must be redrawn perpendicular to the surface at each new point of incidence.
Mixing up the angle of deviation $D$ with the angle of incidence or reflection — $D = 180° - 2i$ is the total turn of the ray, always a different number from $i$ or $r$ unless $i = 90°$ .

Ask the tutor: Want to practise converting between glancing angles and angles of incidence, or work through a few more deviation-angle problems step by step? Ask the AI tutor for extra examples on the laws of reflection.

Why do we always measure angles from the normal and not from the mirror itself?

Because the normal gives a fixed, unambiguous reference direction at each point, while the mirror surface can be curved or tilted differently at different points. Measuring from the normal keeps the law $i = r$ true for every kind of reflecting surface — flat or curved — using the exact same rule. If you measured from the surface instead, the numbers would still be related (glancing angle is just $90° - i$ ), but the clean law $i = r$ would not hold in that form, and curved-mirror geometry would become far messier.

Does the angle of deviation formula D equals 180 minus 2i apply to curved mirrors too?

Not directly in this simple form. It comes from treating the mirror surface as flat at the point of incidence, which is exactly true for a plane mirror. A curved mirror is locally flat at each point (each point has its own normal), so $D = 180° - 2i$ still applies to the ray at that one point, but the normal's direction changes from point to point across a curved surface, so you cannot use a single $i$ for the whole mirror the way you can for a plane one. Curved-mirror image formation needs its own set of rules, which build on this same $i = r$ starting point.

If i equals r always, why do mirrors ever look distorted or make images look different from the object?

The law $i = r$ describes what happens to a single ray at a single point — it is always exactly true. What creates a distorted or unusual-looking image is the shape of the mirror: a flat mirror reflects a bundle of rays from an object in a way that reconstructs the object faithfully (same size, reversed left-right), but a curved mirror bends the normal direction differently at every point, so parallel or diverging rays from the same object point get redirected to different places, producing magnified, shrunk, or flipped images. The distortion comes from geometry across the whole surface, not from any single reflection breaking the law.