1. Interference of waves

2. Wavefronts and direction of propagation
The crests/troughs of a wave are sometimes called wavefronts.
The shape of a wave is determined by its wavefronts.
The direction of propagation of the wave is perpendicular to wavefronts
Direction of wave
Wavefront

3. Phase
Particles moving in the same motion all the time are in phase. Particles moving oppositely all the time are in opposite phase. If particles are not always moving in the same direction, they are out of phase. F A B C D E G H
wave propagation

4. Phase difference
Phase difference is expressed in wavelength. The distance between two points in phase is a whole number of wavelength (nλ). The distance between two points in opposite phase is an odd number of half wavelength ((2n+1) λ /2).

5. Two waves are in phase
Two waves are out of phase
Two waves are in opposite phase

6. Interference
When two waves meet in the same medium, the vibration intensifies at some places and weakens at others. This phenomenon is called interference.
If the vibration is larger than individual waves, the interference is called constructive interference (superposition). If the vibration is smaller than individual waves, it is destructive interference (superposition).

7. Wave interference
constructive interference
destructive interference
Simply align the waves in time and add the displacements.
If the displacements are of the same sign, the wave is reinforced and grows bigger – constructive interference.
If the displacements are of opposite sign, the wave is diminished and becomes smaller – destructive interference.

8. Interference patterns
nodal lines
antinodal lines P Q S1 S2
Any point on the antinodal lines the path difference is a whole number of the wavelength, eg: S1P-S2P=7.5 λ – 6.5 λ =λ
Any point on the nodal lines the path difference is an odd number of the half wavelength, eg: S1Q-S2Q=6 λ – 7.5 λ =1.5λ

9. Young’s double slit experiment device

10. Young’s double slit experiment
When light passes through a slit it is diffracted, acting as a light source. When the light passes through a pair of slits (carefully placed the right distance from the original slit), it is diffracted. The slits behaved as if they were also individual sources of light. The light interferes and forms patterns on the screen.

11. Young’s double slit experiment
The interference patterns consist of a series of evenly spaced dark and bright lines called fringes. The bright fringes are caused by constructive interference , while the dark fringes are the result of destructive interference. First conducted in 1801, this experiment established the wave nature of light. Young's double slit experiment is a typical experiment to show the diffraction and interference of light.

12. Double slit experimentθ
Screen L S2
The path difference from two sources at point P is:
pd =S2P-S1P= dsinθ
When dsinθ = nλ, P is on a bright fringe.
When θ is small, sin θ =tan θ =x/L,
For monochromatic light, dx/L = nλ gives the position of bright fringe.
The spacing of fringes is given by x = λL/d

13. Example
Describe and explain how the spacing of an interference pattern is affected by
The wavelength of a wave.
The distance from the screen.
The separation of the sources.
Ans: the spacing is determined by x = λL/d.
The spacing is proportional to wavelength λ. When λ increases, the spacing increases;
The spacing is proportional to the distance. When L increases, the spacing increases;
The spacing is inversely proportional to the separation, when d increases, x decreases.

15. Multiple source interference
Diffraction grating: a series of many fine parallel slits, evenly spaced on a piece of glass or plastic. Slit spacing d is given by the number (N) per metre: d = 1/N.
Interference patterns similar to double slit pattern. Main differences:
The slits are very thin so light is diffracted through a wide angle.
Slits are so closely spaced so the bright fringes are widely spread.
There are large number of slits, so fringes are bright.

16. Interference pattern formulax d θ L
Screen
generally: dsinθ =nλ (n =0, 1, 2, …)
When L >>x,

17. eg: Light from a red laser (wavelength 6
eg: Light from a red laser (wavelength 6.70x10-7m) is shone on a diffraction grating. The light forms a pattern showing nine bright fringes spread across a distance of 4.0cm. When the laser is replaced with a green laser, the interference pattern shows nine fringes spread out over a distance of 3.2cm. Calculate the wavelength of the green laser.

18. Ans:
spacing: so ie:

19. Interference of white light
Antinodal lines for different wavelengths (frequencies) of same order spread out except the zero order. The red light bends more than violet light. The diffraction grating produces a series of spectra on both sides of a central white line.

20. Interference of waves
Rippletank Demo