🌈 Physical Optics & Wave Spectroscopy
Diffraction Grating & Spectroscopy Calculator
Compute diffraction angles ($\theta_m = \arcsin(m\lambda/d)$), maximum observable diffraction orders ($m_{\max}$), slit groove spacing ($d$), and angular spectral dispersion.
🔴 He-Ne Red (632.8 nm, 600 l/mm)
🟢 Green Laser (532 nm, 600 l/mm)
🔵 Blue Diode (450 nm, 600 l/mm)
🟡 Sodium D (1200 l/mm)
Grating & Light Inputs
nm (Nanometers)
lines / mm
1st Order Diffraction Angle (θ₁)
θ₁ = 22.31°
Slit Spacing ($d$)
1.667 μm
Angular Dispersion
0.037 °/nm
Order 2 Angle ($\theta_2$)
49.41°
💡 Grating Formula:
$$\sin\theta_1 = \frac{1 \times 632.8\text{ nm}}{1666.7\text{ nm}} = 0.3797 \implies \theta_1 = \arcsin(0.3797) = 22.31^\circ$$
The Mathematics of Diffraction Gratings
Periodic slit structures produce constructive interference maxima when path differences equal integer wavelengths:
- Grating Equation: $$d \sin\theta_m = m \lambda \implies \theta_m = \arcsin\left(\frac{m\lambda}{d}\right)$$
- Slit Spacing: $$d = \frac{1\text{ mm}}{N} = \frac{10^{-3}\text{ m}}{N}$$
- Maximum Possible Order: $$m_{\max} = \left\lfloor \frac{d}{\lambda} \right\rfloor \quad (\text{since } \sin\theta \le 1)$$
- Angular Dispersion: $$D = \frac{d\theta}{d\lambda} = \frac{m}{d \cos\theta}$$