State that for reflection, the angle of incidence is equal to the angle of reflection; recall and use this relationship

3.2.1 Reflection of Light

Key Concept

When light hits a smooth surface, it bounces back. The law of reflection states that the angle of incidence (\$\thetai\$) is equal to the angle of reflection (\$\thetar\$).

\$\displaystyle \thetai = \thetar\$

Both angles are measured from the normal (an imaginary line perpendicular to the surface).

Illustration of the Law (no image, but imagine it!)

Incident RayNormalReflected Ray
↗️⬇️↘️
\$\theta_i\$\$\theta_r\$

Analogies to Remember

  • 🔄 Mirror‑ball dance: Imagine a ball bouncing off a smooth floor. The angle it hits the floor equals the angle it leaves.

  • 🔭 Laser pointer: Point a laser at a shiny surface; the spot will move in a straight line, reflecting at the same angle.

  • 🚗 Road reflection: When a car’s headlights hit a wet road, the light reflects at the same angle, creating a bright spot.

Practice Problems

  1. A ray of light strikes a mirror at an angle of \$30^\circ\$ to the normal. What is the angle of the reflected ray?

    Answer: \$30^\circ\$ (since \$\thetai = \thetar\$).

  2. If a ray is incident at \$45^\circ\$ to the surface (not the normal), what is the angle of incidence and reflection?

    First, find angle to normal: \$90^\circ - 45^\circ = 45^\circ\$. Therefore, \$\thetai = \thetar = 45^\circ\$.

  3. A light ray hits a polished metal surface at \$10^\circ\$ to the normal. Sketch the path and label the angles.

    Draw the incident ray, the normal, and the reflected ray, labeling both angles as \$10^\circ\$.

Exam Tips

  • 📌 Remember the definition of the normal: It’s always perpendicular to the surface.

  • 📌 Check units: Angles are in degrees.

  • 📌 Use diagrams: Even a quick sketch can help you see that \$\thetai = \thetar\$.

  • 📌 Practice converting angles: If given the angle to the surface, subtract from \$90^\circ\$ to find the angle to the normal.

  • 📌 Look for “incident” and “reflected” in the question: These words signal the reflection law.