Optical Path Length Calculator
OPL = nL and group delay n_g L/c along the refracted ray, L = N·d/cos θ_t, for a custom medium or a catalog glass.
Optical Path Length nL
1.500 cm
18750.0 waves at λ; geometric path L = 1.000 cm
Phase Delay OPL/c
50.03 ps
n = 1.50000; internal angle θ_t = 0.000°
Group Delay n_g L/c
50.03 ps
n_g = 1.50000: the transit time of a pulse
Extra Delay vs Vacuum
16.68 ps
(n_g − 1)L/c; OPD vs vacuum (n − 1)L = 0.5000 cm
sin θ = n sin θ_t, L = N d / cos θ_t, OPL = nL, τ_φ = OPL/c, τ_g = n_g L/c, n_g = n − λ dn/dλ
The ray path inside a plane-parallel slab entered from air; reflections between the faces are ignored. The phase index sets fringe counts and interference; the group index sets when a pulse arrives.
Model and references
Exact. The equations are exact within the stated assumptions, or are a standard's tabulated values. The results are as good as the inputs. About the tiers
Exact ray path through a homogeneous plane-parallel slab entered from air, with multiple reflections between the faces ignored; glass indices from the Sellmeier formulas within their stated wavelength ranges.
- Hecht E. (2017). Optics, 5th ed., chs. 4 and 7. Pearson.
- Saleh B. E. A., Teich M. C. (2007). Fundamentals of Photonics, 2nd ed., ch. 5. Wiley.