Reflection Formula

The Formula

\theta_i = \theta_r (angle of incidence equals angle of reflection)

When to use: Like a ball bouncing off a wall—the wave reverses direction at the boundary.

Quick Example

Seeing yourself in a mirror uses light reflection; an echo in a canyon uses sound reflection.

Notation

\theta_i is the angle of incidence, \theta_r is the angle of reflection, and both are measured in degrees (or radians) from the normal to the reflecting surface.

What This Formula Means

The change in direction of a wave at a boundary so that it returns into the original medium.

Like a ball bouncing off a wall—the wave reverses direction at the boundary.

Formal View

The law of reflection states \theta_i = \theta_r, where both angles are measured from the surface normal. The incident ray, reflected ray, and normal all lie in the same plane. For specular reflection from a plane mirror, the image is virtual, upright, and the same size as the object, located the same distance behind the mirror.

Worked Examples

Example 1

easy
A light ray hits a plane mirror at an angle of 35° to the normal. What is the angle of reflection?

Solution

  1. 1
    The given 35° is the angle of incidence because it is measured to the normal.
  2. 2
    By the law of reflection, the angle of incidence equals the angle of reflection.
  3. 3
    \theta_r = \theta_i = 35°

Answer

\theta_r = 35°
The law of reflection states that the angle of incidence equals the angle of reflection, measured from the normal to the surface. This applies to all types of waves.

Example 2

medium
A light ray strikes a mirror. The angle between the incident ray and the reflected ray is 80°. What is the angle of incidence?

Common Mistakes

  • Measuring angles from the surface instead of from the normal — the law of reflection uses angles measured from the perpendicular to the surface.
  • Thinking that only mirrors reflect light — all surfaces reflect light; mirrors just do it in an orderly (specular) way, while rough surfaces scatter it (diffuse reflection).
  • Forgetting that reflection does not change the speed or wavelength of a wave — only the direction changes.

Why This Formula Matters

Reflection explains how mirrors form images, how we see most objects (they reflect light into our eyes), how radar and sonar detect targets, and how fibre optics keep light trapped inside a cable.

Frequently Asked Questions

What is the Reflection formula?

The change in direction of a wave at a boundary so that it returns into the original medium.

How do you use the Reflection formula?

Like a ball bouncing off a wall—the wave reverses direction at the boundary.

What do the symbols mean in the Reflection formula?

\theta_i is the angle of incidence, \theta_r is the angle of reflection, and both are measured in degrees (or radians) from the normal to the reflecting surface.

Why is the Reflection formula important in Physics?

Reflection explains how mirrors form images, how we see most objects (they reflect light into our eyes), how radar and sonar detect targets, and how fibre optics keep light trapped inside a cable.

What do students get wrong about Reflection?

Angles are measured from the normal (perpendicular), not from the surface.

What should I learn before the Reflection formula?

Before studying the Reflection formula, you should understand: waves.

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Symmetry, Rotational Symmetry, and Congruence →
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Related Formulas

Refraction Formula