Reflection, Refraction, Diffraction, and Interference

Key Concepts

Waves, including light waves, exhibit several key behaviors when they encounter different surfaces or obstacles. These behaviors include reflection, refraction, diffraction, and interference. Understanding these properties is essential for explaining many natural phenomena and technological applications.

Reflection

• Definition: Reflection occurs when a wave bounces off a surface. The angle at which the wave hits the surface (angle of incidence) is equal to the angle at which it reflects (angle of reflection).
• Laws of Reflection:
  • The incident ray, the reflected ray, and the normal (a line perpendicular to the surface at the point of incidence) all lie in the same plane.
  • Angle of incidence $\theta_i$ = Angle of reflection $\theta_r$.
• Curved Surfaces: Curved mirrors, like concave and convex mirrors, can form images by reflecting light. The nature of the image (real or virtual, upright or inverted) depends on the curvature and position of the object.

Refraction

• Definition: Refraction is the bending of waves as they pass from one medium to another, due to a change in speed.
• Snell's Law: The relationship between the angles and the refractive indices of the two media is given by: $$\frac{\sin \theta_1}{\sin \theta_2} = \frac{v_1}{v_2} = \frac{n_2}{n_1}$$ where $\theta_1$ and $\theta_2$ are the angles of incidence and refraction, $v_1$ and $v_2$ are the wave speeds in the respective media, and $n_1$ and $n_2$ are the refractive indices.
• Applications: Lenses use refraction to focus light, forming images in devices like cameras and glasses.

Diffraction

• Definition: Diffraction is the spreading of waves around obstacles or through openings. The extent of diffraction increases with longer wavelengths and smaller openings.
• Examples: You can hear someone speaking around a corner due to sound wave diffraction.

Interference

• Definition: Interference occurs when two or more waves overlap, resulting in a new wave pattern.
• Types of Interference:
  • Constructive Interference: When waves combine to make a wave with larger amplitude.
  • Destructive Interference: When waves combine to make a wave with smaller (or zero) amplitude.
• Applications: Noise-cancelling headphones use destructive interference to reduce unwanted sounds.

Examples

Example 1: Reflection

A light ray strikes a mirror at an angle of 30° to the normal. What is the angle of reflection?

Solution: According to the law of reflection, the angle of reflection is equal to the angle of incidence. Therefore, the angle of reflection is 30°.

Example 2: Refraction

A light ray passes from air (refractive index = 1.0) into water (refractive index = 1.33) at an angle of 45° to the normal. Calculate the angle of refraction.