Transcript Diffraction - Antonine Education

Diffraction
Deriving
nl = d sin q
Diffraction
• Diffraction results from the spreading out of waves
passing through a gap.
• The narrower the gap, the more the waves spread out.
• If the gap is less than one wavelength, there is no
diffraction at all.
• Wavelength is not affected by diffraction.
• Diffraction happens with all waves.
Single slit and multiple slit diffraction
have nothing to do with Young’s double
slits.
So don’t use the double slit formula.
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Single Slit Diffraction
For a wide gap, there is not much diffraction.
Sharp shadows
Light rays
Single bright
region
If the gap is made narrow, then we get to see a diffraction pattern
Bright regions
Light rays
Central bright
region
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Monochromatic
light is needed
for a clear
pattern.
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Intensity and diffraction
Intensity
The observed pattern of bright and dark fringes can be explained by the
superposition of secondary wavelets.
The intensity is greatest in the middle.
The bright fringes either side are much less intense.
The further we move away from the centre, the dimmer they are.
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Equation
Bright regions
Light rays
Central bright
region
Wavelength (m)
Angle of spread.
sin q 
Wavelength of light are in
nano-metres (nm).
l
a
If a is less than l, sin
q > 1. That simply
will not do.
Width of gap (m)
Convert to m.
1 nm = 1 × 10-9 m
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A further equation
From the diagram we can see:
D tan q 
W
2
D
Red light
W
q
For very small angles, tan q = sin q
Since:
sin q 
l
a
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we can write:
l
W
D 
a 2
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Rearranging:
Dl
W 2
a
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Linking with Double Slits
Fringe spacing
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ws
l
D
Width of the central bright fringe
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W 2
Dl
a
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Resolution
Consider two objects very close together:
Easily resolved
Just resolved
Not resolved
This was first worked out by John William Strutt, 3rd Lord Rayliegh.
It is often called Rayliegh’s criterion
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Diffraction Grating
• There are two kinds of diffraction grating:
– Transmission (where the light goes through);
– Reflection (where the light is reflected).
• The diffraction grating has the advantage over
the double slit method of measuring wavelength
in that:
– the maxima are more sharply defined
– the beam passes through more slits than two, so the
intensity is brighter
– the angles are larger so that they can be measured
with greater precision.
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How does diffraction work?
Monochromatic
light,
wavelength l
1
d
N
These rays go to the first
bright fringe.
d
q
Monochromatic light is shone onto a
transmission grating which has N lines
per metre.
The slit spacing is given by:
1
d
N
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Bright spots appear only when there
is constructive interference, i.e.
when light from A is in phase with B.
That happens when they are one
whole wavelength apart.
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Deriving the equation
Let’s look in close up:
Monochromatic
light,
wavelength l
d
1
N
AC = 1 l
AB = d
AC = d sin q
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A
C
d
q
q
B
So we can write:
1l  d sin q
This is true for any of the
bright spots, 1, 2, 3, …n
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Therefore:
nl  d sin q
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Be careful!
The diffraction grating is often given as lines per millimetre.
You will have to convert to lines per metre.
750 lines per mm = 750 × 103 lines per metre.
d = 1.33 × 10-6 m.
In some gratings, the situation is even worse – they write N in lines per inch! (US–
sourced gratings in particular.
10000 lines per inch = 393 per millimetre.
The maximum order of diffraction possible is limited by sin q < 1. If you find that n =
3.8, then the maximum orders possible is 3, NOT 4.
Wavelengths are in nanometres (nm)
1 nm = 1 × 10-9 m
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Patterns of Diffraction
If the wavelength is reduced, we
observe that the angle of each
order is reduced.
If we have white light, we will see
several coloured lines for each
order.
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