1. Refraction of light c n = v
In dense media such as water or glass, light travels slower than in thin media such as air or vacuum. This causes the phenomenon of refraction, which includes the phenomenon of the “broken stick”.
The velocity (c) of light in vacuum is km/second, the highest speed possible in our universe.
If the velocity of light in a medium is v, then the “refractive index” (n) of that medium is given by:
Transition from air to water v c n =
The refractive idex of matter thus is always greater than 1, for example:
Air: n =
Water: n = 1.33
Glass: n = 1.52
The refractive index of matter bears relevance to the functionality of security features, such as pearl luster ink, optically variable ink and transparent overlays.

2. Refraction and reflection of light
Transition from “thin” to “dense” matter i r
air
water
Refraction also makes a light beam “break” when it transits from a thin to a dense medium under an angle with the interface between both media. Here a laser beam enters a vessel of water under an angle i to become refracted under an angle r. The laser beam has been visualized by blowing smoke in its path in air and by adding some milk to the water.
Willebrord Snel in 1621 discovered the law of refraction, which formulated the relation between the refractive indices of both media n1 (e.g. of air) and n2 (e.g. of water) and the angle of entrance i and refraction r:
n1 sin ( i ) = n2 sin ( r )

3. Refraction and reflection of light
Transition from “thin” to “dense” matter i r
air
water
The phenomenon is sometimes compared to the change of direction that a marching column of soldiers would undergo when it transits from a paved street to loose sand under an angle with the interface between both media: paved street and sand.
The soldier that first enters the sand, is slowed down while the soldier next to him still proceeds faster on the paved street. The result is illustrated in the next slide.

4. Analogy of the marching column of soldiers
Refraction and reflection of light
Transition from “thin” to “dense” matter
air
water n
velocity 1
velocity 2 =
paved street: fast
loose sand: slow
Analogy of the marching column of soldiers

5. Reflection and refractive index (n)
reflection low
reflection high
n = high
n = low
water n = 1,33
magnesium fluoride n = 1,38
diamond n = 2,3
titanium dioxide n = 2,7
The higher the refractive index,
the stronger the reflection and the refraction.

6. Specular reflection of transparent matter25 .
diamond 20
titanium dioxide 15
TiO
flint glass 2
Perpendicular reflection (%)
zirconia 10
crown glass
ZrO 2
water 5
air 1
1,2
1,4
1,6
1,8 2
2,2
2,4
2,6
2,8 3
Refractive index of matter

7. Colour shift and refractive index of single thin interference films
The next slides show that thin interference films with a low refractive index, such as a soap film, display a considerable colour shift with the angle of observation. However, because of that low refractive index, their reflection is low.
Interference Security Image Structures (ISIS) must have a sufficient reflection and therefore single thin film devices must be based on a high refractive index material.
Titanium dioxide (n = 2.7) is the basis of pearl luster ink. Pearl luster inks have a significant reflection, but, because of their high refractive index, their color shift is negligible.
Pearl luster ink is an interference based ink, but calling it iridescent is highly overdone.

8. Interference colours in thin films
Soap film

9. Interference colours in thin films
Newton rings in an air film between two glasses
Newton rings in an oil film on a wet road

10. Spectral response of soap film in air
Thickness = 300 nm n = 1.34
Low reflection because of low refractive index

11. Pearl luster ink structure
TiO n = 2,7
Substrate: mica flakes
Medium: transparent ink

12. Spectral response of TiO2-film in ink medium
Thickness = 145 nm n = 2.7, nmedium = 1.5
High reflection because of high refractive index

13. Spectral response of TiO2 films on mica in air

14. Pearl luster ink on
5, 10 and 20 euro notes

15. Pearl luster ink on Swiss notes
Diffuse reflection (outside the gloss)
Reflection (in the gloss)

16. Pearl lustre ink in transparent window
Papua New Guinea
100 kina note
with G-switch® feature.
The feature shifts between purple in glossy reflection and green against a light background, but displays no appreciable color shift with angle of reflection.
No polarization effects are present.
This is typical of pearl lustre ink.
Black background W
purple
-purple
White printed background

17. Microphotos of pearl lustre ink
transmission
1 div = 10 µm
1 div = 10 µm
reflection

18. Spectral response of TiO2 films on mica in air
0,5
50 nm
0,4
0,3
A 50 nm titan dioxide film has a virtually neutral spectral response. It provides an efficient half-mirror that can replace aluminum to form a semi-transparent overlay. These are called “high-index” overlays.
Reflection
0,2
0,1
400
450
500
550
600
650
700
Wavelength (nm)

19. Transparent (high-index) overlay film
Replace aluminium by a high refractive index substance such as titan dioxide or zinc selenide.
OVD Kinegram Corp, Switzerland

20. Colour shift and refractive index of Optically Variable Ink (OVI)
The next slides show that the large color shift of OVI is based on the low refractive index of magnesium fluoride (n = 1.38). On itself, this would render the thin film a reflection about as low as that of water (n = 1.33).
However, by adding a reflective aluminum layer and a semi-reflective chromium layer, the structure becomes a highly efficient iridescent reflector, often called a Fabry-Perot interference filter or Fabry-Perot etalon.
The thickness of the magnesium fluoride layer defines the particular color shift of the thin film. In order to make the OVI flakes independent of orientation on printing, the thin film structure has been made symmetric.

21. Optically Variable Ink (OVI)
Cr nm
MgF (variable thickness)
n = 1,38
Low refractive index
Al nm
MgF (variable thickness)
n = 1,38
Cr nm
Medium: transparent ink

22. Optically Variable Ink (OVI)
based on wave-resonance in an etalon interferometer θ
Reflection
wavelength
transmission
reflection 0%
100%
mirror 1
low reflectivity t
spacer n
high reflectivity
mirror 2
Transmission
An etalon consists of a transparent plate with two reflecting surfaces. Its transmission as a function of wavelength exhibits peaks of large transmission corresponding to resonances of the etalon.
The transmission spectrum is a function of the refractive index n, the spacer thickness t and angle of incidence θ.

23. Optically Variable Ink (OVI)
Measured reflection of an etalon consisting of 30 nm Al, 500 nm MgF2 and 5 nm Cr

24. Optically
Variable
Ink
(OVI)
Swiss passport,
detail 14 x 19 mm

25. Spectral response of OVI (schematic)
magenta to green
← shift of response to shorter wavelengths with angle of observation

26. Spectral response of OVI (schematic)
magenta to green
← shift of response to shorter wavelengths with angle of observation
green to magenta

27. End of presentation