Laser Cavity Mode Spacing: Wavelength Difference Calculation
📘 Question:
The mirrors in the laser of the figure, which are separated by 9.0 cm, form an optical cavity in which standing waves of laser light can be set up. Each standing wave has an integral number n of half wavelengths in the 9.0 cm length, where n is large and the waves differ slightly in wavelength. Near λ = 607 nm, how far apart in wavelength are the standing waves (in terms of pm)?
🧮 Step-by-Step Solution:
📌 Step 1: Given Values
- Cavity length (L): 9.0 cm = 0.090 m
- Wavelength (λ): 607 nm = 607 × 10⁻⁹ m
- Speed of light (c): 3.0 × 10⁸ m/s
📐 Step 2: Frequency Spacing (Δf)
Δf = c / (2L) = 3.0 × 10⁸ / (2 × 0.090) = 1.667 × 10⁹ Hz
🔁 Step 3: Convert Δf to Δλ
Δλ = λ² × Δf / c = (607 × 10⁻⁹)² × 1.667 × 10⁹ / 3.0 × 10⁸ = 2.047 × 10⁻¹² m = 2.05 pm
✅ Final Answer: Δλ = 2.05 picometers (pm)
Conclusion: The standing wave modes in the laser cavity are separated by 2.05 pm in wavelength, demonstrating the precision and narrow spacing of optical laser modes.