3.3 Reflection, Refraction, and Diffraction of Waves

3.3 Reflection, Refraction, and Diffraction of Waves

Reflection:

When a wave encounters a boundary or obstacle, it may bounce back into the medium from which it came. This phenomenon is known as reflection. The angle of incidence (the angle between the incident wave and the normal to the surface) is equal to the angle of reflection.

Refraction:

Refraction occurs when a wave passes from one medium into another, causing a change in its speed and direction. This bending of the wave is due to the difference in wave speed in the two media. The relationship between the angles of incidence and refraction is given by Snell's law:
sin(θ1)/sin(θ2) = v1/v2

where:
- θ1 and θ2 are the angles of incidence and refraction, respectively,
- v1 and v2 are the wave speeds in the first and second media, respectively.

Diffraction:

Diffraction is the bending of waves around obstacles and the spreading of waves as they pass through small openings. The extent of diffraction depends on the wavelength of the wave and the size of the obstacle or opening. Longer wavelengths diffract more than shorter wavelengths.

Example Problem:

Light waves pass from air into water. If the speed of light in air is 3 × 10^8 m/s and the speed of light in water is 2.25 × 10^8 m/s, what is the angle of refraction if the angle of incidence is 30 degrees?

Solution:

Using Snell's law:
sin(30°)/sin(θ2) = 3 × 10^8 m/s / 2.25 × 10^8 m/s
sin(θ2) = 0.75 × 0.5 = 0.375
θ2 = arcsin(0.375) ≈ 22°
The angle of refraction is approximately 22 degrees.