Interference

Diffraction When waves pass through a narrow gap they spread out or……… The amount of diffraction depends on the size of the gap compared with the size of the wavelength Link to Diffraction animation 1 barrier and gap link to wave interference

light diffraction animation link to diffraction animation light diffraction animation

Extension: Why does a single slit produce an interference pattern? Each half of a narrow slit acts like a separate source of waves. Light from the top half will interfere with light from the lower half

NODE

Smaller slit…wider diffraction

Wave Interference

We first look at interference of sound waves LINK TO phet sound Recall the definition of path difference. The extra distance one wave has to travel to reach the observer

Recall the definition of constructive interference and destructive interference. When two waves arrive in phase (pd = nλ) you get constructive interference. When two waves arrive out of phase {pd = (n – ½) λ} you get destructive interference.

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Explain what causes the loud and quiet spots.

Why do your amplifier and speakers have black and red terminals?

Noise Canceling Headphones These work by producing a sound wave that is out of phase with the external sound reaching your ear.

Interference of Light When light shines through a double slit a similar phenomenon occurs:

Explanation

the waves arrive the waves arrive in phase This produces a big wave Link to 2 source interference / path difference This shows that: when the path difference is the waves arrive in phase This produces a big wave (constructive interference) when the path difference is the waves arrive out of phase This produces no wave (destructive interference)

Young’s Equation

L nλ θ θ x Consider the big green triangle Consider the small green triangle

Can be used for any situation Can only be used for small angles (not diffraction gratings)

L nλ θ θ x What happens to θ when λ increases? What happens to θ when d increases?

Can be used in any situation Θ means ………… n means ………… λ means ………… d means ………… Can only be used where θ is small

This is what the formula predicts …………… Longer wavelength Larger angle A larger angle between antinodes means the antinodes are ……… Further apart

L θ x L θ x

Larger slit separation This is what the formula predicts …………… Larger slit separation smaller angle

d = 0.20 mm d = 0.15 mm d = 0.10 mm

link to young's expt

Why does a longer wavelength light have an antinode at a larger angle???

link to ripple tank applet We can simplify the diagram by considering one ray from each slit. Path difference is zero Incoming light These rays meet to produce the antinode central

λ λ Remember that the light diffracts through the hole These rays go to the antinode first Incoming light θ λ λ Path difference is

λ λ A longer wavelength produces the first antinode at a greater angle These rays produce the antinode First Incoming light θ λ λ Path difference is A longer wavelength produces the first antinode at a greater angle

Path difference is λ θ Path difference is λ θ

Why does a larger slit separation produce an antinode at a smaller angle???

Bigger slit separation = smaller angle Path difference is λ θ Incoming light Bigger slit separation = smaller angle

Link to factors affecting Interference

Diffraction Grating Diffraction gratings have lots of slits very close together Typically 500 slits/mm This means 1/500 or 0.002mm apart.

Diffraction Grating Equation N is the number of slits per metre

100 slits/mm d= 0.010 mm 300 slits/mm d= 0.0033 mm 600 slits/mm d= 0.0017 mm

We have been talking about the slit separation, not slit width. Note: We have been talking about the slit separation, not slit width. In Young’s Equation, “d” is the distance between the centres of the slits. (slit separation) slit width slit separation

The width of the pattern is the same. If you move the slits closer the angle between the antinodes in the interference pattern increases. Bright fringes Closer slits The width of the pattern is the same.

If you decrease the width of each slit, you get more diffraction If you decrease the width of each slit, you get more diffraction. the angle between the antinodes is the same, but the pattern is wider. Bright fringes narrower slits

As the width of each slit is narrowed, the whole pattern is wider (ie there are more fringes, same spacing)

This time the slit width is constant This time the slit width is constant. BUT the distance, d, between the slits is varied

How could you make the “harp strings” closer together?

Diffraction Grating and White Light Central antinode white 1st antinode Full spectrum

White light passes through slit and diffracts. Diffracted beams overlap Different colours (wavelengths) have their 1st antinode at different angles Full spectrum is formed

Reflection from a CD

Interference of a CD

Interference of a CD

Beats Listen to two tuning forks with slightly different frequencies…………… Describe what you hear. use two big tuning forks, put plasticene on one OR use 2 signal generators and speakers OR use Zeitnitz oscilloscope program (free off internet)

Every second, the maxima will overlap; these are "beats" Every second, the maxima will overlap; these are "beats".  The beat frequency is f2 - f1 = 1001 - 1000 = 1 Hz.

Adding Sound Waves

The frequency of the sound heard is the average of the two frequencies The frequency of the variation in loudness (beat frequency) is the difference between the two frequencies

Listener hears average of two frequencies, 441 Hz; this average is heard to go through a   maximum loudness two times each second. This produces 2 Hz beats  

What causes Beats? Two waves of similar frequency arrive together. Sometimes they are in phase, and add to give a large amplitude. Sometimes they are out of phase, and add to give zero amplitude. The amplitude thus varies from zero to maximum periodically. Amplitude determines loudness of a sound wave, so the sound goes loud/quiet/loud…… at a frequency of |f2-f1|