1. Interference & Diffraction Gratings
HIGHER PHYSICS
Interference & Diffraction Gratings

2. Interference of Light 1 Young’s Slits Monochromatic source
Double narrow slit
Pattern of bright maxima & dark minima obtained on distant screen

3. Interference of Light 2
Pattern obtained from Young’s Slits is poorly defined, so fringe separation is difficult to judge.
More slits gives better defined and wider separated maxima
An array of slits – Diffraction Grating – gives clearest pattern

4. Diffraction Gratings 1 Array of slits with separation, d
Often described by ‘pitch’ – number of lines per millimetre
e.g. 400 lines per mm d
d = 1x10-3
400
= 2.5 x 10-6 m

5. Diffraction Gratings 2 Formation of maxima
Beams from adjacent slits combine to produce maxima where path difference = nλ
For 1st maximum, path difference from adjacent slits = λ
beam 1
beam 2
beam 3 λ

6. Diffraction Gratings 3 For 1st maximum, For 2nd maximum, λ = d sin θ2λ θ

7. Diffraction Gratings 4 In general, for nth maximum, nλ = d sin θ
The fringe separation, θ, can be increased by -
Increasing wavelength, λ, (i.e. blue  red)
Decrease slit separation, d, (i.e. increase pitch)

8. Small Angle ApproximationD
grating
screen x
angle θ
For fringe separation, x, and screen distance, D, where
D >> x,
sin θ  x / D.
So nλ = d x D

9. Practical Aim Apparatus
to find grating separation, d from diffraction pattern
Apparatus

10. Practical Procedure Use He-Ne laser wavelength, λ = 6.33 x 10-7 m
Measure grating – screen distance, D
Measure fringe position from central maximum, xn for nth fringe
Calculate grating separation, d, using expression
d = n λ D x

11. Practical Results λ = 6.33 x 10-7 m D = m Order of maximum, n
Fringe position, x
(m)
d = n λ D 1 2 3 4 5