SCIENCE · INVESTIGATE AND EXPLAIN

Measure reflection angles from the normal

Trace a ray at a smooth boundary and separate direction from reflected power.

Learning outcome: Draw a normal, convert surface angles to normal angles and predict a reflected direction.

Starting recap

A normal is perpendicular to a surface at the meeting point; a right angle is 90 degrees.

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Try

A ray meets a surface at 20 degrees to the surface. Is its angle of incidence 20 degrees?

Open the experiment

Predict

At 30 degrees incidence and second index 1.00, predict the reflection angle and the angle each upper ray makes with the surface.

Your prediction and reason

Experiment

Capture incident angles 30 and 60 degrees at index 1.00. Inspect the normal and reflected ray. Set angle zero, then change second index to 1.50 to inspect matched media.

Trace light at one boundary

Worked teaching model · synthetic values · Ideal smooth stationary boundary between transparent, lossless, isotropic, nonmagnetic media. First index fixed at 1.50; second index 1.00–2.00. Monochromatic frequency 5 × 10¹⁴ Hz; rounded vacuum speed 3 × 10⁸ m/s. Incident angles measured from the normal, 0–80 degrees. Rays show direction, not beam width, intensity or travel distance. No absorption, roughness, dispersion, diffraction, polarization response or evanescent-field calculation. At matched indices the reflected ray is omitted. Medium-two speed and wavelength are bulk reference properties, not a transmitted ray when total internal reflection occurs.

Incident angle from the normal: 30 degrees Second-medium refractive index: 1

Reset keeps your prediction, captures and practice history.

Angles and the transmission condition
Quantity	Value	Interpretation
Incident angle	30°	From the normal; angle from surface is 60°
Reflection angle	30°	Same angle from the normal when reflection exists
Required transmitted sine	0.750000	1.50 × sin(incident angle) / 1.00
Transmitted angle	48.590378°	transmission
Critical angle	41.810315°	Exists only when n₂ is less than n₁

Frequency, speed and bulk wavelength
Property	Medium 1	Medium 2
Refractive index	1.50	1.00
Frequency of transmitted wave, when present	5 × 10¹⁴ Hz	5 × 10¹⁴ Hz
Bulk wave speed (m/s)	2.000000e+8	3.000000e+8
Bulk wavelength at this frequency (nm)	400.000000	600.000000

Frequency is unchanged at this stationary boundary. Speed and wavelength are properties of each ideal medium at that frequency. Under total internal reflection, the medium-two values describe a hypothetical bulk wave, not a propagating transmitted ray. The model does not calculate the evanescent field or reflected/transmitted power fractions.

Compare incident angles at the selected index
Incident angle	Transmitted angle from normal	Regime
0°	0.000000°	transmission
20°	30.865882°	transmission
40°	74.618568°	transmission
45°	No real angle	total internal reflection
60°	No real angle	total internal reflection
80°	No real angle	total internal reflection

Transmitted angle 48.590 degrees from the normal.

Reflection direction, when present, makes 30 degrees with the normal. Required transmitted sine 0.750000. Critical angle 41.810315 degrees; total internal reflection requires a larger incident angle.

Observation to attach to a capture

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

Understand

Choose the reference line first

Imagine drawing the path of a narrow beam as it reaches a flat window. Draw the surface, mark the meeting point, and draw a perpendicular line there. This is the normal: a geometry reference, not another beam.

The browser places medium 1 above a horizontal boundary. The incident arrow points toward the boundary; the reflected arrow points away into medium 1. At the default 30-degree incidence, reflection is also 30 degrees from the upper normal. Each upper ray makes 60 degrees with the horizontal surface. The small arcs mark normal angles.

Change incidence to 60 degrees. Predict the reflected direction before reading its label. Its normal angle is now 60 degrees and its surface angle is 30 degrees. The normal has not moved. The dashed reflected line distinguishes the rays without relying on color.

Preserve the angle definition

Write θᵢ for incident angle and θᵣ for reflection angle, both in degrees from the normal. The reflection law is θᵣ = θᵢ. The corresponding angle from the surface is 90° − θᵢ. Adding two rays’ angles can answer a different geometry question; it does not change the definition of incidence.

At zero incidence the incoming ray follows the normal and the reflected ray retraces that path in the opposite direction. The lines overlap, so use their arrows and the ledger together. Zero incidence is not grazing incidence: grazing lies along the surface, 90 degrees from the normal, beyond this investigation’s 80-degree control limit.

Separate direction from power

Keep second index at 1.00 while exploring reflection. The first index is 1.50, and the model can show reflected and transmitted directions together. Equal drawn lengths do not mean half the light goes each way. The model does not calculate power fractions or polarization response. Direction and brightness require different evidence.

Set second index to 1.50. In this ideal nonmagnetic, lossless matched-media case, the boundary has no optical contrast: transmission continues straight and the reflected ray is omitted. An absent reflected ray is not a zero-degree reflection; there is no reflected beam in this modeled case.

The boundary is smooth. A rough surface has varying local normals; this single-normal diagram does not model diffuse scattering. It also does not model a mirror coating or absorption.

Repair a mislabeled sketch

A learner labels an arc “incident angle 20 degrees,” but draws it between the incoming line and the surface. Correct the incidence and reflection labels. Draw the normal and outgoing direction yourself on paper; no lamp or laser is needed.

Check the reflection transfer

Incidence is 90 − 20 = 70 degrees from the normal. Reflection is also 70 degrees from the normal, or 20 degrees from the surface on the other side of the normal. Both upper rays are in the incident medium. The outgoing arrow points away from the meeting point.

OpenStax: the law of reflection explains the normal-angle convention. Continue to refraction and wave properties to analyze the ray crossing the boundary.

Apply

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

Distinguish normal and surface angles. Explain why a reflected direction does not specify the reflected power fraction.

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: Separate observer motion from source motion Next: Connect refraction to wave speed and wavelength

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