Finding the reflected angle is straightforward, based on a fundamental principle of physics: the Law of Reflection.
The Law of Reflection Explained
According to the Law of Reflection, the angle of reflection equals the angle of incidence. This is often written mathematically as θr = θi.
- θr represents the angle of reflection.
- θi represents the angle of incidence.
These angles are specifically measured relative to the perpendicular to the surface at the exact point where the incoming light ray (or any wave) strikes the surface. This perpendicular line is commonly referred to as the "normal" line.
Think of the normal as an imaginary line drawn at a perfect 90-degree angle to the surface where the reflection occurs. Both the angle of incidence (between the incoming ray and the normal) and the angle of reflection (between the outgoing reflected ray and the normal) are measured from this line.
How to Determine the Reflected Angle
To find the reflected angle (θr) for a light ray or wave bouncing off a surface:
- Identify the point of incidence: This is where the incoming ray strikes the surface.
- Draw the "normal" line: Draw an imaginary line perpendicular (at 90 degrees) to the surface at the point of incidence.
- Measure the angle of incidence (θi): This is the angle between the incoming ray and the normal line.
- Apply the Law of Reflection: The reflected angle (θr) will be exactly equal to the angle of incidence (θi).
Therefore, if you know or can measure the angle at which a ray hits a surface relative to the normal, you automatically know the angle at which it will reflect, measured from that same normal line.
For instance, if a light ray hits a mirror at an angle of 30 degrees relative to the normal, it will reflect off the mirror at an angle of 30 degrees relative to the normal.
This fundamental principle holds true for various types of waves, including light, sound, and water waves, when they encounter a boundary. While smooth surfaces show clear, mirror-like reflections, the law of reflection applies at the microscopic level even on rough surfaces.
