0.4 2d and 3d wavefronts

Introduction

You have learnt about the basic principles of reflection and refraction. In this chapter, you will learn about phenomena that arise with waves in two and three dimensions: interference and diffraction.

Wavefronts

Investigation : wavefronts

The diagram shows three identical waves being emitted by three point sources. All points marked with the same letter are in phase. Join all points with the same letter.

What type of lines (straight, curved, etc) do you get? How does this compare to the line that joins the sources?

Consider three point sources of waves. If each source emits waves isotropically (i.e. the same in all directions) we will get the situation shown in as shown in [link] .

We define a wavefront as the imaginary line that joins waves that are in phase. These are indicated by the grey, vertical lines in [link] . The points that are in phase can be peaks, troughs or anything in between, it doesn't matter which points you choose as long as they are in phase.

The huygens principle

Christiaan Huygens described how to determine the path of waves through a medium.

The Huygens Principle

Each point on a wavefront acts like a point source of circular waves. The waves emitted from these point sources interfere to form another wavefront.

A simple example of the Huygens Principle is to consider the single wavefront in [link] .

Given the wavefront,

use the Huygens Principle to determine the wavefront at a later time.

1. Draw circles at various points along the given wavefront

   

2. Join the crests of each circle to get the wavefront at a later time

   

Interference

Interference occurs when two identical waves pass through the same region of space at the same time resulting in a superposition of waves. There are two types of interference which is of interest: constructive interference and destructive interference.

Constructive interference occurs when both waves have a displacement in the same direction, while destructive interference occurs when one wave has a displacement in the opposite direction to the other, thereby resulting in a cancellation. When two waves interfere destructively, the resultant absolute displacement of the medium is less than in either of the individual displacements. When total destructive interference occurs, there is no displacement of the medium. For constructive interference the displacement of the medium is greater than the individual displacements.