Snell's Window Calculator

How to Use This Calculator

1. Enter the refractive index (default 1.333 for fresh water) to get the critical angle and window cone.
2. Use Window Diameter tab with depth to find the physical size of Snell's window.
3. Use Above-Water FOV to check if your camera lens fits within the window.
4. Switch to Professional for Brewster's angle and chromatic dispersion across wavelengths.

Formula

Example

Frequently Asked Questions

• What is Snell's window? ▼
  Snell's window is the circular window through which an underwater observer can see the entire above-water world (180° hemisphere). It is caused by total internal reflection for light rays hitting the surface at angles greater than the critical angle θ_c = arcsin(1/n) ≈ 48.6° for fresh water.
• What is the critical angle for water? ▼
  For fresh water (n ≈ 1.333), the critical angle is arcsin(1/1.333) ≈ 48.59°. The full cone (diameter of the window) spans about 97.2°. For sea water (n ≈ 1.342), the critical angle is slightly smaller at ≈ 48.19°.
• How does depth affect Snell's window? ▼
  The angular diameter of the window is fixed (97.2° for fresh water), but the physical diameter grows with depth: D = 2 × d × tan(θ_c). At 5 m depth the window is about 11.4 m across; at 10 m it is about 22.8 m across.
• What is Brewster's angle? ▼
  Brewster's angle is the angle at which reflected light is completely polarized. For water: θ_B = arctan(1/n) ≈ 36.9°. Underwater photographers use polarizing filters to reduce surface glare at this angle.
• Why does Snell's window show chromatic dispersion? ▼
  Water has different refractive indices at different wavelengths (blue light bends more than red). Blue light (n ≈ 1.340) has a smaller critical angle than red light (n ≈ 1.331), so the window edge shows a colored fringe — blue outside, red inside.

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