Angle-Dependent Blue Shift
How the effective design wavelength shifts with angle of incidence (blue shift).
Effective λ at 45° = 472.3 nm
Blue shift at 45° = 77.7 nm
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Quarter-wave point of one lossless, non-dispersive film lit from air: λ₀ cos θ_film, the same for s and p. For a multilayer, an effective index (slightly different for s and p) gives a first-order estimate.
- Macleod H. A. (2010). Thin-Film Optical Filters, 4th ed., ch. 2 (phase thickness 2πNd cos θ/λ) and ch. 9 (tilted coatings). CRC Press. doi:10.1201/9781420073034