Questions: Reflection and the Law of Reflection

Question 1

A student measures a light ray hitting a mirror at 60° from the surface and concludes the reflected ray makes 60° with the surface on the other side. What error has the student made?

• A. The reflected ray should be on the same side as the incident ray
• B. Angles must be measured from the normal (perpendicular to the surface). If the ray is 60° from the surface, it is 30° from the normal — so the reflected ray is 30° from the normal, not 60°
• C. The law of reflection only applies when angles are measured from the surface, so the student is correct
• D. The error is that the ray's angle changes upon reflection because the mirror absorbs some energy

Answer: (B)

The law of reflection measures angles from the normal — an imaginary line perpendicular to the surface at the point of contact — not from the surface itself. A ray 60° from the surface is 30° from the normal (since 90° − 60° = 30°). The reflected ray is therefore 30° from the normal, which equals 60° from the surface. In this specific case the numbers agree, but for other angles they won't, and the conceptual error (measuring from the surface) is still wrong in principle and breaks the consistency with Snell's law for refraction.

Question 2

Why does a flat mirror produce an image that appears to be located behind the mirror, at the same distance as the object in front?

• A. Mirrors are slightly curved, causing all reflected rays to appear to converge behind the mirror
• B. Light slows in the glass of the mirror and appears to originate from further away
• C. Applying θᵢ = θᵣ to every ray from an object point produces diverging reflected rays whose backward extensions all meet at a point symmetrically behind the mirror
• D. The mirror's silver coating emits light that appears to come from behind the surface

Answer: (C)

This is a direct geometric consequence of the law of reflection applied to all rays. Each ray from an object point hits the mirror at a different angle, reflects at the equal angle, and diverges. Tracing these reflected rays backward (as your eye does when it sees them), they all converge at a single point as far behind the mirror as the object is in front. No special properties of glass or coatings are needed — only the geometry of equal angles.

Question 3

The law of reflection (θᵢ = θᵣ) applies specifically to light reflecting from polished surfaces and does not extend to sound, water waves, or other wave types.

• T. True
• F. False

Answer: False

The law of reflection is universal for all wave types reflecting from smooth surfaces. Sound echoing from a flat wall, a water ripple bouncing from a barrier, seismic waves reflecting from geological boundaries — all obey θᵢ = θᵣ. The geometry of wavefront reflection is the same regardless of what is waving. The law derives from the wave nature of the phenomenon, not from properties specific to light.

Question 4

Measuring angles from the normal rather than from the surface is an arbitrary convention that could equally well be done the other way.

• T. True
• F. False

Answer: False

The normal provides a stable, orientation-independent reference that simplifies the geometry. When a surface is tilted, angles measured from the surface change with the tilt, producing different numbers for the same physical interaction. The normal always provides a perpendicular baseline that cleanly separates incident and reflected rays. More importantly, the same normal convention is used in Snell's law for refraction — angles of incidence and refraction are both measured from the normal — making all of geometric optics internally consistent. The choice is principled, not arbitrary.

Question 5

Explain why concave and convex mirrors focus or diverge light differently from flat mirrors, even though the law of reflection is the same at every point on all three surfaces.

Model answer: The law of reflection applies locally: at each point on any mirror, θᵢ = θᵣ measured from the local normal. On a flat mirror, all normals point in the same direction, so all reflected rays remain parallel (or diverge uniformly from a point). On a curved mirror, the normal direction rotates from point to point along the surface. Different rays from the same source hit different parts of the curve at different angles from their respective local normals and are redirected in different directions. For a concave mirror, this geometry causes the reflected rays to converge (focus); for a convex mirror, to diverge further.

The key insight is 'same law, different normals, different outcomes.' The law itself is universal; surface curvature determines how the normals are oriented, which determines the redirection of each ray. Understanding this makes curved mirror optics a direct extension of flat mirror geometry, not a separate phenomenon.