Laws of Reflection of Light: Angle of Incidence Equals Angle of Reflection

Physics · Ray Optics And Optical Instruments · NEET

There are two laws of reflection. Law 1: the angle of incidence equals the angle of reflection (i = r). Law 2: the incident ray, the reflected ray, and the normal at the point of incidence all lie in the same plane. Memory hook: "in equals out, measured from the normal" - both angles are counted from the normal line, never from the surface.
NormalIncident rayReflected rayiri = r (both measured from the normal)
Law of reflection at a plane mirror: the incident ray (blue) and reflected ray (red) make equal angles i and r with the normal (dashed), and all three lines lie in the same plane.

Your doubts, answered

Is the angle of incidence measured from the surface or from the normal?

Always from the normal, never from the mirror surface. The normal is the line drawn perpendicular (at 90 degrees) to the surface at the exact point where the ray hits. So a ray hitting a mirror 'flat' along the surface has an angle of incidence of 90 degrees, and a ray coming straight down onto a flat mirror has an angle of incidence of 0 degrees. NEET options often give you the angle with the surface to trick you - convert it by subtracting from 90 first.

Do the laws of reflection work for concave and convex mirrors too?

Yes. The laws of reflection hold at every single point of any surface, flat or curved. On a curved mirror the normal is the line joining that point to the centre of curvature C, and it points in a different direction at each point. Because the normal keeps changing along a curved mirror, parallel rays reflect in different directions and the mirror can form real or magnified images - but at each point i still equals r.

Why does the reflected ray turn by 2 theta when the mirror rotates by theta?

Keep the incident ray fixed. If you rotate the mirror by an angle theta, the normal also rotates by theta. The angle of incidence increases by theta, so by the law of reflection the angle of reflection also increases by theta. The reflected ray moves by theta on the incidence side plus theta on the reflection side, giving a total turn of 2 theta. This 2 theta rule is a favourite NEET question (the spot-on-a-scale experiment).

If a surface is rough, do the laws of reflection break?

No. The laws still hold at every tiny point. A rough surface is just many small facets facing random directions, so each facet obeys i = r but the reflected rays scatter in all directions. This is called diffuse reflection, and it is why you can see a wall from any angle. A smooth mirror gives regular reflection because all the normals point the same way.

What is the deviation of a ray reflected from a plane mirror?

The reflected ray is turned from the original direction of the incident ray by an angle of (180 - 2i) degrees, where i is the angle of incidence. For normal incidence (i = 0), the ray goes straight back, so the deviation is 180 degrees. This deviation formula is handy for problems combining two mirrors.

⚠️ The NEET trap
Reading '30 degrees' as the angle of incidence when the diagram shows the ray making 30 degrees with the mirror surface.
The angle with the surface is 30 degrees, so the angle of incidence (from the normal) is 90 - 30 = 60 degrees. The angle of reflection is also 60 degrees, and the angle between incident and reflected rays is 120 degrees.
🧠 Always convert 'angle with surface' to 'angle with normal' by subtracting from 90 before applying i = r.

Real NEET questions

2017

A beam of light from a source L is incident normally on a plane mirror fixed at a certain distance x from the source. The beam is reflected back as a spot on a scale placed just above the source L. When the mirror is rotated through a small angle theta, the spot of light is found to move through a distance y on the scale. The angle theta is given by

A · y/2x
B · y/x
C · 2x/y
D · x/y
Solution: Step 1: Use the mirror-rotation rule. When a plane mirror is rotated by an angle theta (with the incident ray fixed), the reflected ray turns through 2 theta. This comes straight from the law of reflection: rotating the mirror rotates the normal by theta, raising both i and r by theta, so the reflected ray shifts by 2 theta. Step 2: Relate the turn of the reflected ray to the movement on the scale. The scale sits at distance x from the mirror. For a small angle, arc = radius x angle, so the spot moves y = x times (2 theta). Step 3: Solve for theta. y = 2 x theta, therefore theta = y / (2x). Answer: (A).

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Frequently asked

What are the two laws of reflection of light?

Law 1: the angle of incidence equals the angle of reflection (i = r). Law 2: the incident ray, the reflected ray, and the normal at the point of incidence all lie in the same plane. Both angles are measured from the normal.

Are the angles of incidence and reflection measured from the normal or the surface?

From the normal - the line drawn at 90 degrees to the surface at the point where the ray strikes. In NEET diagrams, always convert any 'angle with the surface' by subtracting it from 90.

Do the laws of reflection apply to curved mirrors?

Yes. They hold at every point of any surface. On a curved mirror the normal is the line to the centre of curvature, so it points differently at each point, but i = r is always obeyed.

By what angle does the reflected ray turn if a mirror is rotated by theta?

The reflected ray turns by 2 theta when the incident ray is kept fixed. This 2 theta rule is tested directly in NEET (the spot-on-a-scale problem gives theta = y/2x).

What is the difference between regular and diffuse reflection?

Both obey i = r at every point. Regular reflection is from a smooth surface where all normals are parallel, giving a clear image. Diffuse reflection is from a rough surface where normals point randomly, scattering light so you see the surface but no image.