Laws of reflection

Shine a torch beam at a slant onto a flat mirror in a darkened room, and the reflected beam bounces off at exactly the same slant on the other side, never more, never less. That predictable bounce is not a coincidence — it is governed by two precise rules called the laws of reflection, and they hold for every mirror you will ever meet, flat or curved. This article is part of the CBSE Class 8 chapter Light: Mirrors and Lenses. We name the rays and lines involved — incident ray, reflected ray, normal, point of incidence — state the two laws of reflection including the exact relationship $i = r$ , see how a torch-and-protractor classroom activity confirms them, and work through angle problems of the kind your exam will ask, including the common trap of measuring from the mirror surface instead of the normal.

The core insight

At every point where light strikes any mirror, the angle of incidence always equals the angle of reflection, and the incident ray, the normal, and the reflected ray all lie in one flat plane.

The core idea

When a ray of light strikes a mirror and bounces back, geometry gives precise names to every ray and line involved.

The incident ray is the ray of light travelling towards the mirror, before it strikes the surface.
The point of incidence is the exact point on the mirror where the incident ray strikes it.
The normal is an imaginary line drawn perpendicular to the mirror's surface at the point of incidence — it is not a ray of light, only a reference line used to measure angles.
The reflected ray is the ray of light that bounces away from the mirror after striking it.
The angle of incidence ( $i$ ) is measured between the incident ray and the normal, and the angle of reflection ( $r$ ) is measured between the reflected ray and the normal.

Both angles are always measured from the normal, never from the mirror's surface itself — this single habit separates a correct answer from a wrong one in almost every exam question on this topic. With these terms in hand, the two laws of reflection can be stated precisely. First, the angle of incidence equals the angle of reflection:

i = r

where: $i$ is the angle of incidence and $r$ is the angle of reflection, both measured in degrees from the normal at the point of incidence. Second, the incident ray, the normal, and the reflected ray all lie in the same plane — you could draw all three flat on a single sheet of paper without any of them needing to twist out of that flat surface. Neither law involves any calculation beyond this equality; they are geometric facts about how light bounces, verified by measurement rather than derived from a deeper formula at this level.

Figure

A ray diagram showing an incident ray striking a mirror at the point of incidence with the normal drawn perpendicular to the surface and the reflected ray leaving at an equal angle on the other side of the normal

Why it works

The laws of reflection are stated as facts confirmed by careful measurement, not results derived from an earlier formula — that is exactly why the CBSE Class 8 syllabus introduces them through an activity rather than an equation-chasing proof. Set up a plane mirror flat on a sheet of paper. Shine a torch beam at it along a known incident ray, mark the point of incidence, and mark where the reflected ray falls on the paper. Use a protractor to draw the normal — the perpendicular to the mirror at that point — and measure the angle on each side of it. Repeat the experiment at several different incident angles, and every single time the angle of incidence and the angle of reflection come out equal. Repeat it while checking whether the two rays and the normal ever leave the flat sheet of paper, and they never do. That repeatable outcome, checked again and again, is the entire justification for the two laws. The laws are also universal across mirror shapes. A plane mirror, a concave mirror, and a convex mirror all obey $i = r$ at every single point of incidence. What differs between them is only the direction the normal points at different points on a curved surface, because the surface itself is curved rather than flat. That changing normal direction is what makes a concave mirror converge a bundle of parallel rays to a single focus, and a convex mirror spread them apart — but at each individual point where a ray strikes any of these surfaces, the local law is exactly the same one: angle of incidence equals angle of reflection, measured from the local normal at that point.

Worked example

Question: A ray of light strikes a plane mirror, making an angle of incidence of $35°$ with the normal. Find the angle of reflection, and the angle the reflected ray makes with the mirror's surface itself.

Step 1. Apply the first law of reflection directly: the angle of reflection equals the angle of incidence, so $r = i = 35°$ .

Step 2. Recall that the normal is perpendicular to the mirror's surface, so the normal makes a $90°$ angle with the surface at the point of incidence.

Step 3. Find the angle between the reflected ray and the surface by subtracting the angle of reflection (measured from the normal) from $90°$ : $90° - 35° = 55°$ .

Step 4. State both answers together. The angle of reflection is 35°, and the reflected ray makes a 55° angle with the mirror's surface.

Competitive stretch

Now reverse the question. A student measures her incident ray as making a $50°$ angle with the mirror's surface (not the normal), and measures her reflected ray making a $30°$ angle with the normal. First convert her incident angle to one measured from the normal: $90° - 50° = 40°$ . By the first law, the angle of reflection should also equal $40°$ , but she recorded $30°$ — the two numbers do not match, so she has very likely made a measurement error, and the correct reflected angle should have been $40°$ , not $30°$ . This is exactly the kind of surface-versus-normal mix-up examiners like to test.

Common traps

Measuring the angle of incidence or reflection from the mirror's surface instead of from the normal — the laws always use angles measured from the normal.
Forgetting to draw the normal as its own perpendicular reference line — it is not the mirror's surface, and it is not a ray of light.
Assuming the laws of reflection apply only to flat, plane mirrors — they apply equally to concave and convex mirrors at every point of incidence.
Treating "angle of incidence equals angle of reflection" as an approximation — it is an exact equality, confirmed repeatedly by activity and measurement, not a rule of thumb.

Ask the tutor: want to try a few more torch-and-mirror angle problems, including ones that mix surface angles and normal angles in the same question?

Why is the normal always drawn perpendicular to the mirror, instead of at some other convenient angle?

The normal is defined that way on purpose, so that angles of incidence and reflection have one fixed, unambiguous reference line at every point, no matter how the mirror is tilted or shaped. If angles were measured from the mirror's surface instead, a curved mirror would need a different zero-line at every point, and the simple statement $i = r$ would not hold. Perpendicular to the surface at the point of incidence is the only choice that keeps the law this clean.

Do the laws of reflection change for a concave or convex mirror, since they curve?

No — the laws themselves never change. At any single point on a concave or convex mirror, you can still draw a normal perpendicular to the surface right at that point, and the incident and reflected rays there still obey $i = r$ exactly. What changes on a curved mirror is simply that the normal points in a different direction at different points on the surface, because the surface itself curves. That changing normal direction is what makes a whole bundle of parallel rays converge or spread out, but the local law at each point of incidence is identical to a plane mirror's.

If I only know the angle a ray makes with the mirror surface, how do I find the angle of incidence?

Subtract it from 90 degrees, since the normal is always perpendicular to the surface. So a ray making a 50 degree angle with the surface has an angle of incidence of 90 minus 50, which is 40 degrees from the normal, and the reflected ray leaves at that same 40 degrees from the normal, which works out to a 50 degree angle from the surface on the other side. This surface-to-normal conversion is one of the most commonly tested steps in this topic, so it is worth practising until it is automatic.