4.9.6 Determining the Wavelength of Light

Question: A grating has 300 lines per mm. The first-order maximum is at 11.0° to the normal. Calculate the wavelength of the light.

1. Slit spacing d = 1 ÷ (300 × 10³) = 3.33 × 10⁻⁶ m.
2. Use nλ = d sin θ with n = 1.
3. λ = 3.33 × 10⁻⁶ × sin 11.0° = 3.33 × 10⁻⁶ × 0.1908 = 6.36 × 10⁻⁷ m.

Answer: λ ≈ 636 nm (6.36 × 10⁻⁷ m).

4.9.6 – Key Points for the Exam

• Diffraction grating: A plate with many equally spaced parallel slits that gives sharp, bright maxima.
• Order: The integer n in nλ = d sin θ, with n = 0 at the central maximum.
• Normal incidence: Light striking the grating at right angles to its surface.
• Percentage uncertainty: Absolute uncertainty divided by the measured value, multiplied by 100.

Common Mistakes

• Forgetting that lines per mm must be converted to lines per metre before finding d.
• Using small-angle approximations for a grating, where angles can be large.
• Measuring only one fringe width instead of spanning many fringes.
• Looking directly into the laser; always follow laser safety rules and use a screen.