Light Waves in 2D SPH4U

Wave fronts To represent waves in two dimensions, we draw the wave fronts: lines connecting the crests of the waves. Wave fronts are always perpendicular to the rays showing the direction of propagation.

Huygen’s Principle When determining how a wave will propagate (where to draw the next wave front), we often refer to Huygen’s Principle: “Every point on a wave front can be considered as a point source of tiny wavelets that spread out in front of the wave at the same speed as the wave. The surface envelope tangent to these wavelets is the new wave front.”

Huygen’s Principle

Transmission When a wave passes into another medium (transmission), the wave will change speed. Since the frequency of the wave’s arrival does not change, the wavelength and therefore the spacing of the wave fronts changes.

Refraction If the wave fronts are at an angle with the boundary, the wave will refract.

Reflection At any boundary, some light will be reflected.

Reflection At any boundary, some light will be reflected. The reflected wave can interfere with the incident wave. mirror

Interference The Principle of Superposition: “The net displacement at any position is the sum of the displacements of all waves at that position.”

Interference If the waves are in phase (both positive displacement or both negative displacement) the interference will be constructive., increasing the amplitude of the resultant wave.

Interference If the waves are out of phase (one with positive displacement and the other with negative displacement) the interference will be destructive.

The Interference of Two Point Sources One of the most commonly studied interference patterns is that produced by two point sources. Nodal lines (actually hyperbolic) occur where the waves of the sources are out of phase.

Two Slits The pattern produced by light emerging from two slits in a screen is similar. . . .

Diffraction . . . but not identical, as light passing through a slit (or past any boundary) will diffract.

Diffraction Diffraction is the bending effect observed when a wave passes through a slit or by an obstacle.

Diffraction The most noticeable diffraction occurs when: wavelength slit width

Diffraction and Interference Diffraction will also result in interference effects. We will study the mathematics associated with this tomorrow.

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