A single slit first diffracts light to ensure both double slits receive coherent wavefronts
Waves - OCR A-Level Physics
- A single slit first diffracts light to ensure both double slits receive coherent wavefronts.
- Light passes through two narrow, closely spaced slits and produces an interference pattern of alternating bright and dark fringes on a distant screen.
- Bright fringes (maxima) occur where path $difference = n\lambda (constructive$ interference).
- Dark fringes (minima) occur where path $difference = (n + ½)\lambda (destructive$ interference).
- The central fringe is always a bright maximum (path $difference = 0)$.
$$\lambda = \frac{ax}{D}$$
- This equation requires D >> a (the screen must be much further away than the slit separation).
- Fringe spacing x increases if: wavelengthThe minimum distance between two points on a wave that are in phase (e.g. crest to crest). Measured in metres (m). increases, slit separation decreases, or screen distance increases.
- White light produces coloured fringes: blue (shorter λ) fringes are closer together than red (longer λ), with a white central maximum.
Worked Example [3 marks]
In a double-slit experiment, the slit separation is 0.50 mm, the screen is 1.5 m away, and the fringe spacing is 1.8 mm. Calculate the wavelengthThe minimum distance between two points on a wave that are in phase (e.g. crest to crest). Measured in metres (m). of the light.
Show Solution
1
Convert units
$a = 0.50 \times 10⁻^{3}\;\text{m}, \times = 1.8 \times 10⁻^{3}\;\text{m}, D = 1.5\;\text{m}$
[1]2
$\lambda = ax/D = (0.50 \times 10⁻^{3} \times 1.8 \times 10⁻^{3}) / 1.5$
[1]3
$\lambda = 6.0 \times 10⁻⁷\;\text{m} = 600 nm$
[1]Answer
$\lambda = 600 nm$
Common Mistake
MEDIUM
Students often: Measuring fringe spacing incorrectly. Taking the distance from the centre to the first bright fringe as x, or mixing up mm and m in units.
Instead: Fringe spacing x is the distance between adjacent bright fringes. For accuracyHow close a measurement is to the true or accepted value. High accuracy means low systematic error., measure across several fringes and divide: $x = total distance / number$ of fringe spacings. Always convert mm to m before substituting.
Instead: Fringe spacing x is the distance between adjacent bright fringes. For accuracyHow close a measurement is to the true or accepted value. High accuracy means low systematic error., measure across several fringes and divide: $x = total distance / number$ of fringe spacings. Always convert mm to m before substituting.