Key Equations
Interference & Diffraction — AQA A-Level Physics
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Young's double slit equation
$$w = \frac{\lambda D}{s}$$
- Where:
- $w$ = fringe spacing (m)
- $\lambda$ = wavelength (m)
- $D$ = slit-to-screen distance (m)
- $s$ = slit separation (m)
D is typically several metres, s is typically in mm, w is typically in mm or cm.
Slit spacing from lines per metre
$$d = \frac{1}{N}$$
- Where:
- $d$ = slit spacing (m)
- $N$ = number of slits per metre (\(m^{-1}\))
If N is given in lines per mm, convert to lines per m by multiplying by 1000.
Diffraction grating equation
$$d \sin \theta = n\lambda$$
- Where:
- $d$ = slit spacing (m)
- $\theta$ = angle of diffraction (degrees)
- $n$ = order of maximum (integer)
- $\lambda$ = wavelength (m)
theta is measured from the normal (central beam). Maximum order when sin theta = 1.
Maximum visible order
$$n_{\text{max}} = \frac{d}{\lambda}$$
- Where:
- $n_{\text{max}}$ = highest visible order
- $d$ = slit spacing (m)
- $\lambda$ = wavelength (m)
Round down to nearest integer. Comes from setting sin theta = 1 in d sin theta = n lambda.
Intensity-amplitude relationship
$$I \propto A^{2}$$
- Where:
- $I$ = intensity (W \(m^{-2}\))
- $A$ = amplitude (m)
Used when comparing intensity at maxima and minima of interference patterns.