1. What is Grating Dispersion?

Grating dispersion (D) describes how much the diffraction angle changes with wavelength for a diffraction grating. It's a crucial parameter in spectroscopy and optical design, determining the wavelength resolution of grating-based instruments.

2. How Does the Calculator Work?

The calculator uses the grating dispersion equation:

Where:

• \( D \) — Angular dispersion (rad/m)
• \( m \) — Diffraction order (integer)
• \( d \) — Grating spacing (m)
• \( θ \) — Diffraction angle (degrees)

Explanation: The equation shows that dispersion increases with higher diffraction orders and decreases with larger grating spacing and larger diffraction angles.

3. Importance of Grating Dispersion

Details: Higher dispersion allows better wavelength separation in spectroscopic applications, but may reduce light throughput. Optimal dispersion depends on the specific application requirements.

4. Using the Calculator

Tips: Enter diffraction order (typically ±1, ±2, etc.), grating spacing in meters (often in micron range), and diffraction angle in degrees (-90 to +90).

5. Frequently Asked Questions (FAQ)

Q1: What's typical grating spacing?
A: Common gratings have 300-2400 lines/mm, corresponding to d=3.33×10⁻⁶ to 0.417×10⁻⁶ m.

Q2: How does angle affect dispersion?
A: Dispersion increases as θ approaches 90° (where cosθ approaches 0), but practical angles are typically <70°.

Q3: What's the difference between angular and linear dispersion?
A: Angular dispersion (D) is in rad/m, while linear dispersion includes the focal length of the focusing optics (typically in mm/nm).

Q4: Does wavelength affect dispersion?
A: Indirectly, since θ depends on λ through the grating equation. This calculator gives dispersion at a specific θ.

Q5: What about blazed gratings?
A: Blaze angle affects efficiency but not the fundamental dispersion relationship shown here.