Demonstrating two-source interference

Two-source interference occurs when waves from two coherent sources combine. We will explore this phenomenon with different types of waves.

Coherent sources have the same frequency and a fixed phase relationship, which is essential for sustained interference.

Water waves:

• Use two dippers driven by the same oscillator (vibrator) to create waves.
• This setup ensures the waves from the two dippers are coherent.

Sound waves:

• Connect two loudspeakers to the same audio oscillator.
• This setup ensures the sound waves from the loudspeakers are coherent.

Young's double slit experiment

This experiment uses a single laser source to demonstrate two-source interference:

1. Laser light passes through two narrow slits, causing diffraction.
2. The slits act as two coherent point sources of light.
3. An interference pattern of alternating light and dark fringes appears on a screen.

• Maximas (bright fringes) - Observed where the waves from the two slits are in phase and they superpose constructively.
• Minimas (dark fringes) - Observed where the waves from the two slits are out of phase and they superpose destructively.

Where n = 0,1,2,3,4...

Fringe spacing

The spacing of the fringes is dependent on the wavelength of light, distance between the slits and the screen, and the slit spacing:

$\text{w = }\frac{\lambda\text{ D}}{\text{s}}$

Where:

• w = fringe spacing (m)
• $\lambda$ = wavelength (m)
• D = distance from slits to screen (m)
• s = distance between slits (m)

Worked example - Calculating fringe spacing

Calculate the fringe spacing when a double slit experiment is performed using light of wavelength 650 nm, with the slits placed 1 m away from the screen and the distance between the slits being 0.25 mm.

Step 1: Convert mm to m

To convert from mm to m, divide by 1,000

0.25 mm = 2.5 x 10^-4 m

Step 2: Formula

$\text{w = }\frac{\lambda\text{ D}}{\text{s}}$

Step 3: Substitution and correct evaluation

$\text{w = }\frac{650 \times 10^{-9} \times 1}{0.25 \times 10^{-3}} = \frac{650}{0.25 \times 10^{-6}} = 2.6 \text{ mm}$