SCIENCE · INVESTIGATE AND EXPLAIN

Predict reflection from the local surface normal

A ray represents a direction of light propagation, perpendicular to a wavefront in the simple isotropic media used here. It is not a narrow physical object whose width determines light intensity. Geometric optics follows rays when wavelength-scale interference and diffraction can be neglected; those wave effects require a different model later.

Learning outcome: Compare normal tilts 0°, +5° and −5° at the same incident setting. Check both normal-relative angles and the outgoing page-relative angle. Explain how several differently tilted patches would produce diffuse reflection.

Starting recap

Define normal angles and signed object/image distances. Distinguish actual ray intersections from backward extensions, and keep the focal/critical boundaries explicit rather than forcing a finite answer.

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Try

An incoming ray at 40° from downward vertical strikes a horizontal surface whose normal is upward. Its reflection is 40° from upward vertical. Tilting the normal 5° toward +x makes the incidence angle relative to that normal 45° and the outgoing direction 50° from upward vertical.

Open the experiment

Predict

When the normal tilts by 5°, does the reflected direction change by 5° or 10° if the incoming ray is fixed?

Your prediction and reason

Experiment

Compare normal tilts 0°, +5° and −5° at the same incident setting. Check both normal-relative angles and the outgoing page-relative angle. Explain how several differently tilted patches would produce diffuse reflection.

Use the local normal to predict reflected direction

Worked teaching model · synthetic values · A single ray reaches the origin from above-left. Unit incoming direction (sinα,−cosα); upward local normal (sinβ,cosβ). Specular reflection r=d−2(d·n)n. Normals vary on rough surfaces but the same local law still holds. Ray directions, not wave intensity.

Incident ray angle from downward vertical: 40 degrees Surface normal tilt from +y toward +x: 0 degrees

Reset keeps your prediction, captures and practice history.

Physical ray direction follows its listed first coordinate to last coordinate. Dashed lines are not extra propagating rays. Display scale changes between settings; within the diagram both axes use the same scale.

Ray segments and construction lines — coordinates in diagram units
Segment	Coordinates in listed direction	Type
Incoming physical ray	(-0.64279, 0.76604) → (0, 0)	Physical ray
Reflected physical ray	(0, 0) → (0.64279, 0.76604)	Physical ray
Local normal	(0, 0) → (0, 1)	Extension / construction
Reflecting surface	(-1, 0) → (1, 0)	Extension / construction

Calculated evidence ledger — synthetic teaching model
Quantity	Value	Unit
Incidence angle from local normal	40	degrees
Reflection angle from local normal	40	degrees
Outgoing angle from +y toward +x	40	degrees

Accessible plot coordinates

Primary plotted points

Reflection angles are measured from the local normal, not from the surface or page edge.

The incoming and outgoing unit vectors have equal magnitude and equal normal angles. Rotating a plane mirror by β rotates its reflected direction by 2β for a fixed incident ray within this geometry. Diffuse reflection changes the normal from patch to patch, not the local law.

Reflection angles are measured from the local normal, not from the surface or page edge.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Establish the model and evidence

A ray represents a direction of light propagation, perpendicular to a wavefront in the simple isotropic media used here. It is not a narrow physical object whose width determines light intensity. A coherent monochromatic laser beam is one common idealized example that can be represented by a ray, but no actual laser activity is requested. Geometric optics follows rays when wavelength-scale interference and diffraction can be neglected; those wave effects require a different model later.

The law of reflection compares angles from the local normal, the line perpendicular to the surface at the reflection point. Incident and reflected angles are equal. Measuring from the surface instead uses complementary angles; measuring from a page edge can be wrong if the mirror tilts. State the reference before inserting any numerical angle.

The activity holds the incoming direction fixed while tilting the surface normal. A change in mirror orientation changes both the normal and the outgoing direction. In this geometry rotating the normal by 5° rotates the reflected direction by 10°. That factor of two is a consequence of preserving equal angles on opposite sides of the normal, not a change in the incoming beam.

Smooth-surface specular reflection shares nearly one normal across the illuminated region. A rough surface has varying local normals and sends different rays in different directions, producing diffuse reflection. Each small patch still obeys the same local law. The model draws one patch, not the distribution of roughness or reflected intensity. No laser, bright-beam or sunlight experiment is requested.

Worked evidence

Predict and investigate

When the normal tilts by 5°, does the reflected direction change by 5° or 10° if the incoming ray is fixed?

Transfer to changed conditions

At fixed incoming direction, a plane mirror rotates by 3°. Predict the change in reflected direction and state what must be held fixed.

Compare the worked transfer

The reflected direction changes by 6° in this planar specular geometry. The incident ray direction and the same reflection plane are held fixed; rotating the source as well would be a different comparison.

Explain the boundary

Why does diffuse reflection not violate the law of reflection?

Sources and authorship

Physical relationship reference. Current AP Physics 2 framework, checked 30 October 2026. Original text, rays and computed/synthetic records, not completed optical measurements. All investigations are virtual: no lasers, intense-light viewing, sunlight focusing, flames or eye tests are requested. Any real practical work needs qualified supervision and independent safety review.

Clause-level source/action reconciliation checked 31 October 2026 against the linked current framework and Fall 2026 clarification. Added packets are original virtual comparisons; no new practical or learner-completion claim.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Why does diffuse reflection not violate the law of reflection?

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Reconcile motional emf, magnetic drag and mechanical work Next: Locate a virtual image without sending light behind a mirror

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