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# Waves in 2 dimensions

Waves in 2-dimensions

Glencoe Physics, Chapter 14.

Throw a stone into water: observe the circular crests and troughs

Waves propagate in 2 dimensions:

along the X-axis, and Y-axis, simultaneously.

a wavefront represents the crest of a wave in 2 dimensions

2-dimensional waves always travel perpendicular to their wavefronts

wave’s direction is represented by a ray

Here, water waves, or light waves, hit a curved surface

The wavefronts reflect to a point, called the focus.

## Refraction of 2-D waves

Refraction is the change in direction of wave propagation due to a change in its transmission medium.

Often seen with light.

Seen with water waves, when they move from deep water into shallow water.

Here light waves refrac as they move from one medium into another (from air into diamond)

In this simplified case, the light waves (or water waves) are all parallel to each other.

Here we see the same thing, but now the rays of light are more realistic.

They emanate from a source, so they are circular, not parallel.

Yet when the rays hit the water, they are approximately parallel, so the result is the same.

Snell’s law at PhysicsClassroom.com

Water waves can be refracted

Animation: Wiley Refraction

Animation GCSE Light and water refraction

Here we see water waves changing direction, as they enter shallower waters.

From a presentation by Luo Yanjie.

From a presentation by Luo Yanjie.

Details on the cause of refraction (PhysicsClassroom.Com)

## Learning Standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework

HS-PS4-1. Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling within various media. Recognize that electromagnetic waves can travel through empty space (without a medium) as compared to mechanical waves that require a medium

SAT subject test in Physics: Waves and optics

• General wave properties, such as wave speed, frequency, wavelength, superposition, standing wave diffraction, and Doppler effect
• Reflection and refraction, such as Snell’s law and changes in wavelength and speed
• Ray optics, such as image formation using pinholes, mirrors, and lenses
• Physical optics, such as single-slit diffraction, double-slit interference, polarization, and color