Reflection Formula

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

The Formula

θi=θr\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

θi\theta_i is the angle of incidence, θr\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 θi=θr\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°35° to the normal. What is the angle of reflection?

Answer

θr=35°\theta_r = 35°

First step

1
The given 35°35° is the angle of incidence because it is measured to the normal.

Full solution

  1. 2
    By the law of reflection, the angle of incidence equals the angle of reflection.
  2. 3
    θr=θi=35°\theta_r = \theta_i = 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°80°. What is the angle of incidence?

Example 3

medium
Two plane mirrors meet at 90°90°. A ray strikes the first mirror at 25°25° to the normal. After reflecting off both mirrors, by what total angle has the ray's direction been deflected?

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. - Fix this by naming the system, checking "Am I describing a repeating disturbance using wavelength, frequency, amplitude, speed, medium, or superposition?", and attaching units or direction to the final statement.
  • 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). - Fix this by naming the system, checking "Am I describing a repeating disturbance using wavelength, frequency, amplitude, speed, medium, or superposition?", and attaching units or direction to the final statement.
  • Forgetting that reflection does not change the speed or wavelength of a wave — only the direction changes. - Fix this by naming the system, checking "Am I describing a repeating disturbance using wavelength, frequency, amplitude, speed, medium, or superposition?", and attaching units or direction to the final statement.
  • Using reflection from a keyword alone - Signal words like wave, frequency, wavelength only point to a possible model; the system must match too.

Why This Formula Matters

Reflection helps students connect sound, light, water waves, strings, and communication signals. The same wave habits explain music, optics, earthquakes, radio, and interference patterns.

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?

θi\theta_i is the angle of incidence, θr\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 helps students connect sound, light, water waves, strings, and communication signals. The same wave habits explain music, optics, earthquakes, radio, and interference patterns.

What do students get wrong about Reflection?

Students often know a formula related to reflection but skip the recognition step: Am I describing a repeating disturbance using wavelength, frequency, amplitude, speed, medium, or superposition? That leads to a correct-looking substitution attached to the wrong physical model.

What should I learn before the Reflection formula?

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

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Refraction Formula