Diffraction grating calculator

Worked example

Find θ, the angle to the normal. Given: order of the maximum n = 1.00; wavelength λ = 5.90 × 10⁻⁷ m; grating spacing d = 2.00 × 10⁻⁶ m.

1. Write the equation
   n λ = d sin(θ)
2. Rearrange to make θ the subject
   θ = sin⁻¹(n λ / d)
3. Substitute the values
   θ = sin⁻¹(1 × (5.9 × 10⁻⁷) ÷ (2 × 10⁻⁶))
4. Calculate
   θ = 17.1575°
5. Give the answer to 3 significant figures
   θ = 17.2°

Symbols and units

Diffraction grating: rearranged

• To find order of the maximum: n = d sin(θ) / λ
• To find wavelength: λ = d sin(θ) / n
• To find grating spacing: d = n λ / sin(θ)
• To find angle to the normal: θ = sin⁻¹(n λ / d)

Exam tip

The grating spacing d is the reciprocal of the number of lines per metre. 300 lines per mm is d = 3.33 × 10⁻⁶ m.

Common questions

What is the formula for diffraction grating?

The equation is n λ = d sin(θ), where n is the order of the maximum; λ is the wavelength (m); d is the grating spacing (m); θ is the angle to the normal (°).

What units should I use for diffraction grating?

In SI units: order of the maximum in no unit (a ratio), wavelength in m, grating spacing in m, angle to the normal in °. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange n λ = d sin(θ)?

Rearranging gives these forms: to find order of the maximum: n = d sin(θ) / λ. to find wavelength: λ = d sin(θ) / n. to find grating spacing: d = n λ / sin(θ). to find angle to the normal: θ = sin⁻¹(n λ / d).