Questions: Law of Reflection and Angle Relationships

Question 1

A flat mirror is tilted by 15° from its original position. A laser beam that was previously hitting it at 40° from the normal now hits the tilted mirror. By how much does the reflected beam's direction change?

• A. 15°, because the mirror tilted by 15°
• B. 30°, because the reflected beam rotates by twice the mirror tilt angle
• C. 55°, because you add the tilt to the original angle
• D. 7.5°, because the rotation is halved by the symmetry of reflection

Answer: (B)

When a mirror tilts by α, the normal rotates by α. This shifts the angle of incidence by α and the angle of reflection by α — a total beam deflection of 2α. Here α = 15°, so the reflected beam rotates by 30°. This factor-of-two is not obvious but follows directly from the geometry: both the incidence and reflection angles change by α when the normal moves by α. Laser galvanometers exploit this to sweep beams over wide angles with small mechanical movements.

Question 2

Why must angles of incidence and reflection be measured from the normal to the surface, rather than from the surface itself?

• A. It is just a convention with no physical significance
• B. Measuring from the surface gives angles that depend on the light's wavelength
• C. The normal is perpendicular to the surface at the exact contact point, making the angle measurement invariant to surface orientation and applicable to curved surfaces
• D. Measuring from the surface gives larger numbers that are easier to work with

Answer: (C)

The normal is defined locally at the point of incidence, perpendicular to the surface there. This makes the measurement independent of how the surface is globally oriented — whether the mirror is vertical, tilted, or curved. For a curved mirror, the normal direction changes across the surface, but the law θᵢ = θᵣ (from the normal) applies at every point. Measuring from the surface would give the complementary angle and would make the law appear inconsistent across tilted or curved geometries.

Question 3

A rough white wall illuminated by a spotlight obeys the law of reflection at every point on its surface, even though light scatters in all directions.

• T. True
• F. False

Answer: True

Diffuse reflection is not a violation of the law of reflection — it is the law applied to a surface with many different local normal directions. Each microscopic patch of the rough wall has its own local normal pointing in a different direction, and each patch reflects incident light at angle θᵣ = θᵢ from its own local normal. The statistical distribution of normal orientations across the surface sends reflected rays in all directions. The law holds perfectly at every point; the diffuse appearance is the aggregate of many correctly-reflected rays.

Question 4

The angle of incidence in the law of reflection is measured from the reflecting surface, not from the normal.

• T. True
• F. False

Answer: False

This is the most common geometric error in applying the law of reflection. Both the angle of incidence and the angle of reflection are measured from the normal — the line perpendicular to the surface at the point of contact. The angle between the incident ray and the surface is the complement of the angle of incidence. If the incident ray makes a 30° angle with the surface, the angle of incidence is 60° (from the normal), and the reflected ray also makes 60° with the normal (30° with the surface).

Question 5

A flat mirror is tilted by angle α from its original position. Explain why the reflected beam rotates by 2α rather than α.

Model answer: When the mirror tilts by α, the normal to the mirror also rotates by α. The incoming ray direction is unchanged. Because the angle of incidence is measured from the normal, the incidence angle changes by α when the normal shifts. By the law of reflection, the angle of reflection also shifts by α on the other side of the new normal. The total change in the reflected ray's direction is α (from the incidence side) + α (from the reflection side) = 2α. The factor of two arises because the law of reflection creates a symmetric response — both angles adjust by the same amount when the normal moves.

This 2α rule has practical engineering applications: a small mirror movement produces a large beam deflection, allowing fine mechanical movements to sweep light across large angles. Optical scanners, laser rangefinders, and galvanometer mirrors all rely on this geometric amplification.