Interference & Diffraction

Path difference, coherence, Young's double slit, single slit diffraction, diffraction gratings and the required practical.

Spec Points Covered
  • State the conditions for constructive and destructive interference in terms of path differenceThe difference in distance travelled by two waves from their sources to a given point. Determines whether constructive or destructive interference occurs..
  • Define coherenceTwo wave sources are coherent if they have the same frequency and a constant phase relationship. and explain why it is needed for a stable interference pattern.
  • Apply the Young's double slit equation $w = \lambda D / s$.
  • Describe the diffraction patterns from single slits, double slits and diffraction gratings.
  • Apply the diffraction gratingAn optical component with many equally spaced parallel slits that produces sharp interference maxima at specific angles. equation d sin $\theta = n \lambda$.
  • Calculate the maximum observable order from a diffraction gratingAn optical component with many equally spaced parallel slits that produces sharp interference maxima at specific angles..
  • Describe the required practical for Young's double slit and diffraction gratings.
  • State laser safety precautions.
Notes
01 Coherent sources have the same frequency and a constant phase difference Coherence 3.3.2.1 → 02 Path difference determines whether interference is constructive or destructive Path difference 3.3.2.1 → 03 Worked example: counting quiet spots from two speakers 3.3.2.1 → 04 Young's double slit produces equally spaced bright and dark fringes 3.3.2.1 → 05 The fringe spacing equation: w = lambda D / s $w = \frac{\lambda D}{s}$ 3.3.2.1 → 06 Diffraction is the spreading of waves through a gap or around an obstacle Diffraction 3.3.2.2 → 07 Single slit diffraction has a wide, bright central maximum 3.3.2.2 → 08 A diffraction grating produces sharp, bright maxima $d \sin \theta = n\lambda$ 3.3.2.2 → 09 The maximum visible order is limited by sin theta = 1 $n_{\text{max}} = \frac{d}{\lambda}$ 3.3.2.2 → 10 Deriving the grating equation from path difference and trigonometry 3.3.2.2 → 11 Applications of diffraction gratings 3.3.2.2 → 12 Lasers are coherent and monochromatic -- with safety rules 3.3.2.1 → 13 Required practical: Young's double slit and diffraction gratings 3.3.2.1 → 14 Historical development: from Newton's corpuscles to wave-particle duality 3.3.2.1 →
Σ Key Equations Full Reference →
On Data Sheet
Not on Data Sheet
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.
Q Retrieval Practice All 13 Questions →
Q1. State the two conditions for coherenceTwo wave sources are coherent if they have the same frequency and a constant phase relationship..
Same frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). and a constant phase differenceThe fraction of a cycle by which one wave leads or lags behind another, measured in degrees or radians..
Q2. Define path differenceThe difference in distance travelled by two waves from their sources to a given point. Determines whether constructive or destructive interference occurs..
The difference in distance travelled by two waves from their sources to the point where they meet.
Q3. State the condition for constructive interference in terms of path differenceThe difference in distance travelled by two waves from their sources to a given point. Determines whether constructive or destructive interference occurs..
Path difference = n lambda (a whole number of wavelengths), where n = 0, 1, 2, 3...
Q4. State the condition for destructive interference in terms of path difference.
Path difference = (n + 1/2) lambda (an odd number of half wavelengths), where n = 0, 1, 2, 3...
Q5. Write the Young's double slit fringe spacing equation and define all terms.
w = lambda D / s. w = fringe spacing (m), lambda = wavelengthThe minimum distance between two points on a wave that are in phase (e.g. crest to crest). Measured in metres (m). (m), D = slit-to-screen distance (m), s = slit separation (m).