Interference
Two stones in a pond
- Drop two stones together and the ripples cross, making a steady criss-cross pattern.
- Some places churn; others stay almost still.
- This is interference — superposition from two sources.
What interference is
- Two coherent waves overlap to give a fixed pattern.
- Bright (constructive) where they add; dark (destructive) where they cancel.
Coherence
- Two sources are coherent if they keep a constant phase difference (same frequency).
- Two separate lamps are not coherent — their phases jump randomly, so any pattern flickers away.
Two coherent sources have:
Coherence means a constant phase difference (and so the same frequency) — needed for a steady pattern.
Two separate lamps make a steady, visible interference pattern.
No — their phase difference changes randomly, so any pattern flickers too fast to see.
Path difference
- Constructive: path difference $= n\lambda$ (a whole number of wavelengths).
- Destructive: path difference $= \left(n + \tfrac{1}{2}\right)\lambda$.
Constructive interference happens when the path difference is:
$\Delta x = n\lambda$ → crests arrive together → they add. $(n+\tfrac{1}{2})\lambda$ gives cancellation.
Destructive interference happens when the path difference is a whole number plus a ____ of a wavelength.
$\Delta x = \left(n + \tfrac{1}{2}\right)\lambda$ — a crest meets a trough, so they cancel.
Young's double slit
- One source lights two slits, so they act as coherent sources.
- Fringe spacing $x = \dfrac{\lambda D}{a}$ ($a$ = slit gap, $D$ = distance to screen).
Light of wavelength $600\ \text{nm}$ passes through slits $1.0\ \text{mm}$ apart onto a screen $2.0\ \text{m}$ away. Find the fringe spacing, in mm.
$x = \dfrac{\lambda D}{a} = \dfrac{600 \times 10^{-9} \times 2.0}{1.0 \times 10^{-3}} = 1.2 \times 10^{-3}\ \text{m} = 1.2\ \text{mm}$.
Changing the fringe spacing
- From $x = \dfrac{\lambda D}{a}$: closer fringes need bigger $a$, smaller $D$, or shorter $\lambda$.
- Bluer light gives tighter fringes than red.
Select all the changes that make the fringes closer together.
From $x = \dfrac{\lambda D}{a}$: smaller $x$ needs a bigger $a$, a smaller $D$, or a shorter $\lambda$.
You've got it
- interference needs coherent sources (constant phase difference)
- constructive: $\Delta x = n\lambda$; destructive: $\Delta x = \left(n+\tfrac{1}{2}\right)\lambda$
- double-slit fringe spacing $x = \dfrac{\lambda D}{a}$