Interference: Young's slits and diffraction gratings

Practical method

Aim

Measure the wavelength of laser light with Young's double slits and a diffraction grating, and demonstrate interference of sound from two loudspeakers.

Variables

Independent variable: slit–screen distance D
Dependent variable: fringe spacing w
Control variables: slit separation s; the same laser.

Apparatus

• Laser (class 2)
• Double slit of known separation
• Diffraction grating
• Screen and metre rule
• Two loudspeakers driven by one signal generator
• Microphone or ear for sound

Method

1. Shine the laser through the double slit onto a screen at distance D (about 1–2.5 m).
2. Measure across several fringes (for example 10) and divide to find the fringe spacing w.
3. Repeat for several values of D and plot w against D; gradient = \(\dfrac{\lambda }{s}\).
4. Replace the slits with a grating and measure the angle to each order to check λ with d sin θ = nλ.
5. For sound, connect two loudspeakers to one signal generator and walk along a line in front of them: loud and quiet regions show interference.

Sample results

Double slit s = 0.50 mm.

Analysis

w is proportional to D, with gradient 1.266 × 10⁻³. λ = s × gradient = 0.50 × 10⁻³ × 1.266 × 10⁻³ = 6.33 × 10⁻⁷ m = 633 nm, matching a helium–neon laser.

Uncertainty

Measuring across 10 fringes (±0.5 mm in 25 mm, 2%) is much better than one fringe. The slit separation is given to ±0.01 mm (2%), so λ = 633 ± 20 nm.

Errors and improvements

Risk assessment

Common mistakes

• Using the slit width instead of the slit separation.
• Measuring D to the wrong point.
• Forgetting to convert mm to m.

Worked analysis

At D = 2.00 m, w = 2.53 mm. λ = \(\dfrac{ws}{D}\) = \(\dfrac{2.53 \times 10^{-3} \times 0.50 \times 10^{-3}}{2.00}\) = 6.33 × 10⁻⁷ m.

Common misconception

Dark fringes are not places where light energy is destroyed; energy is redistributed to the bright fringes.