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“OPTICS” of Optical Glass

Optical glass is (among other parameters) characterized by certain optical parameters; this was briefly discussed in the tutorial before. Among those, the refractive index and the Abbe number are probably the most prominent and best known ones. In this brief tutorial, “optics” of glass will be discussed further.

Optics can be defined (one of many definitions) as describing the behavior of light incident on and/or penetrating a medium, in this case glass.

Light shall for this tutorial here be restricted to that fraction of the electromagnetic spectrum, which is detectable by the human eye, so approximately the spectral range of 400nm to 750nm.

The reason to allow this simplification is, that in many common applications, the human eye is used as the primary detector of an image as well as because “standard” films - B&W as well as Color - are sensitized to primarily work within that spectral range.

Talking earlier about refractive index and dispersion includes already the understanding, that light can and does interact with glass – it can be reflected, transmitted, diffracted, etc. - the path of light is altered as soon as light enters a medium.

Regarding the interaction of light with a medium – for the purpose of this tutorial and of practical photography, we need to make the following limitations and state:

Light means only that small part of the electromagnetic spectrum, which approximately covers the wavelengths range from 400nm to 700nm (slightly extended into IR up to 850/900nm to cover IR films and image formation as well) 

Light can either mean the entire 400-700nm range, then it is called “white” light – light, consisting of all wavelengths in the spectral range as defined before or

 Light is restricted to only a small range of wavelengths by means of optical filters – devices, which transmit only a narrow range of wavelengths

 To understand the optics of optical instruments and equipment, we need to deal with several important situations where the path of light is altered like

Light is reflected at the border between air and glass – there are two possible scenarios – one is that light is propagating through air and hits a glass surface, which reflects it and the other is that light is propagating within glass and hits the glass-air surface and is reflected back into the glass

Light hits the glass surface but enters the glass medium and therefore the path of the light rays are altered

Light exists glass again and continues to travel through air

To be complete, as some optical systems contain(-ed) liquid elements – light is entering/exiting a liquid

 Before we start with anything else, we need to establish a law, which sounds very obvious, but as we will see later, when we talk about light as electromagnetic wave, it is not so blinkingly obvious.

This law is the Law of rectilinear propagation. Sounds horrible, right? Well, in laymen’s terms it means, that under “normal” circumstances, light travels straight from one point to another. What “normal” means – well, if you switch on a lamp and walk a few feet away, the light will travel in a direct, straight path from the bulb to you and not make a detour via the sofa or the bookcase. You laugh – well, in physics, there might be circumstances, where this light might want to travel on a bent curve or around a corner…but let us stick for the time being to the fact – light travels straight from A to B.

 I will try to keep the explanations as simple and short as possible, but sometimes, they need to be more detailed, so let’s start!

 “Light” means that small part of the electromagnetic spectrum….”Light” means “white” light….

 As mentioned before, light is a small part of the entire electromagnetic spectrum, which spans a huge range of wavelengths from cosmic rays to Ultrasound.  Technically from wavelength zero to infinity – within this span, a tiny range is called “light” – traditionally only the range which can be detected by the human eye, but the ranges below and above the visible range are usually added to the word “light” so that this definition covers the range of UV to IR. Some authors define “light” as electromagnetic radiation in the frequency range from 3.84x10¹⁴ Hertz to 7.69x10¹⁴ Hz.

 The electromagnetic spectrum (from “Optics”, E.Hecht, A.Zajak – as most of the figures and diagrams)

Let me make it very clear – “white” light does not exist as a defined wavelength.

Red, to take an example, is pretty well defined and limited to a certain very narrow range of wavelengths and one can take a single wavelength, as example 632nm and call this red, same with the colors green (546nm) or blue (486nm) but white light is the result of the combination of all wavelengths of the visible part of the electromagnetic spectrum and cannot be represented by one single wavelength.  

In the tutorial before, I mentioned that “dispersion” is one of the important parameters to characterize optical glass, this means, that if we use “white light”, then we have to take this term “dispersion” into account – as white light is the sum of all wavelengths within the visible spectrum, once this light starts interacting with glass, it will not remain “together” - white – anymore, it will be more or less separated, depending on the kind of interaction with glass and the type of glass.

Later, when we talk about aberrations, the reader will remember this statement here – dispersion and the use of white light are the determining factors for most of the color related aberrations in optical systems.

 “Light” is restricted to only a small range of wavelengths….

 Taking white light, one can “filter” out a certain wavelengths range – that’s what happens when an optical filter is placed in front of a light source or an optical system. In this context, an optical filter is an optical device, which allows only a small part of the electromagnetic spectrum to pass, whereas the majority of other wavelengths are at least attenuated if not absorbed or reflected.

This selective behavior results in changing the color of light from “white” to a certain color, which is connected to the wavelengths passing through that filter.

In photography, the energy of light entering an optical filter (and subsequently the optical system) is usually rather small, therefore the amount of heat, which is produced by absorbing all other light (electromagnetic radiation) is small, so the temperature of the filter remains more or less unchanged. But there are many imaging and other applications, where the absorbed heat needs to be dissipated to avoid damage to the filter and often more important, to the optical system.

It is also quite common to use the filters mentioned before - absorption filters, in photography, and only in rare cases filters, which do primarily not absorb those wavelengths, which are not supposed to pass, but reflect them - called interference filters (their transmittance is controlled by internal interference of light between very thin multi-layers of inorganic substrates).

Those interference filters however are commonly used in most other applications, where light of a certain, well defined wavelengths range is needed – like optical microscopy, optical high resolution test equipment etc.

The main advantages of interference filters are that for a given wavelengths range, the transmittance compared to absorption filters is much higher and that IF filters can be produced with very well defined narrow spectral performance – allowing either only a very narrow range of wavelengths to pass or all wavelengths below a certain “cut-off” or all above. Depending on their functionality, they are consequently called bandpass=, shortpass or longpass filters. Main disadvantages of them are a much higher price and that they are much more sensitive to temperature, humidity as well as chemical and mechanical environmental challenges.

Interference filters have a “relative”, which is very important in photography and most imaging applications – optical coating. Acting in a similar way as in the interference filters, optical coatings are a surface treatment of optical glass. Several very thin layers of inorganic substances are deposited on a glass surface and this stack of layers interact with incoming light in such a way that more or less all light is able to enter the optical glass medium and only a tiny residual amount is reflected (an uncoated glass surface reflects about 4-5% of the incoming light) In older times, these surface layers were very sensitive to mistreatment – greasy fingers, hard cloths etc. scratched these layers easily and produced the well known cleaning marks and scratches which have a visible and detrimental effect on the image quality – usually a loss of contrast is the result of partially damaged coating. But in the last 10-15 years, the coating process became much more sophisticated and newer lenses all have protecting top layers so that a normal handling and cleaning procedure is of no negative influence anymore, not even after many years.

 Light is propagating through air and hits a surface of optical glass….

 This simple sounding event is not at all simple if looked at in detail. Not only is it of importance under which angle the light hits the glass surface but also what kind of light we are talking about.

And we must not forget that until now, we did not yet talk about how light travels through space/air. We assumed very quietly that the propagation of light is straight, meaning that light takes the shortest distance between two points to travel. And this is correct for most circumstances and is of key importance.

Often you hear the expression – Ray of Light – so it seems necessary to briefly cover this expression as well. A ray of light does practically not exist, but its concept is of importance throughout all optics. This ray of light is a mathematical device, which describes a line drawn in space corresponding to the direction of the flow of energy (as you know, light is energy…etc) or with other words, a line, drawn orthogonally (under 90degrees) to the propagating wave front (correct only for a homogeneous medium).

But this concept of rays is so useful, that in all books and publications on geometrical optics, you see rays of light drawn. It makes life in optics easier and helps to understand the various phenomena and characteristics of optical systems. 

Now back to the case study, what happens, when light hits a surface of optical glass? Let us start with talking about the incident angle of light – if light hits a surface of glass (assuming this surface is “even”), what happens to that light, depends on the angle of incidence.

If we let a ray of light hit that surface, we will see, that light is reflected and as soon as we measure the angles, we understand that there is a fixed relation between the angle of incidence and the angle of reflection – easy to state – they are equal.

 Related to this fundamental law is the fact that the incoming ray of light, the reflected ray and (also the refracted ray together with) the point where they hit the glass surface lay in one and the same plane.

 This before mentioned law of reflection states that these angles are equal. Light hitting a surface under 57.5degress will be reflected under 57.5degrees – period. This law is very well known for a long time – Euclid mentioned it for the first time in the book “Catoptrics”.

 Law of reflection: Θ_I = Θ_R (Θ = angle of the light) 

But in most cases, not all light is reflected – part of the light is entering the glass.

 The light entering the glass has to obey another law – the law of refraction. This law tells us that the angle of the light entering the glass medium is a direct function of the entering angle and the refractive index of the medium, in our case, glass.

 Law of refraction: n₁sinΘ₁ = n₂sinΘ₂

(n₁ = refractive index of medium 1, in our case air, n₂ = refractive index of medium 2, in our case glass)

 The definition of this term, refractive index, is, that it is a value, which gives a measure of the ratio of the speed of light in vacuum compared to that in that medium. This ratio is called absolute index of refraction. In most cases, the relative index of refraction or (relative) refraction index can be used as well, which is using the ratio air vs medium instead of vacuum vs medium. The difference between these two ratios is very small but well measurable - it is 1 to 1.000293.

 As you remember from the first tutorial, the refractive index is not a constant number, it varies with the wavelength of light. And this variation, which causes a spreading out of white light into a spectrum, just to repeat, is called dispersion and increases, for transparent bodies, as the color of light changes from red through yellow to blue.

 Another law is important for us to consider and keep in mind – look at the reflection of light on an even surface – you will see that all light is always reflected in the same plane as the incoming light – you will never see that light is bounced under 30, 40 or any other angle to the side when it is reflected. Also the light, which was able to enter the glass medium, is traveling within the same plane it came from. You might say, that this is so obvious, but it is a law in optics. If this law would not exist, you would not be able to take an image of anything because all optical cameras are based on the fact that incident, reflected and refracted ray are all traveling in the same plane. (Think about this for a second and imagine what would happen if this would not be the case….!!) 

Here how it looks in the graphical mode:

I have mentioned before that light takes the shortest possible route between two points. This can be expressed more professionally by stating that light, traveling from point S to point , traverses this route having the smallest optical path length – here we got another law, it is called Fermat’s principle (well, the original definition was rather a definition of the least time to travel, but needed some modifications to avoid serious shortcomings).

Despite the fact that the light ray does not propagate in a straight line, it still takes the shortest possible route from S to P considering the refractive indices of the medium on the S side and the P side – assumed air and glass.

 This is another very important fundamental law in optics and imaging – images constructed by light are therefore predictable and calculable…without it, you can imagine what would happen.

You might now ask what happens if light is not entering glass (air/glass surface), but exiting (glass/air surface) – well the same laws apply. This means, that the light rays are obeying again the law of refraction (and reflection) but in the opposite way as the refractive index of air is lower than the one of glass. If light travels now back from P to S, it uses the same path as the one traveling from S to P.

 One special case needs to be mentioned – there exists an angle, which is called Critical Angle. Normally, light hitting the glass/air surface exits the medium glass and continues traveling in air – but this is not the case if the angle θ is reaching a certain value, which depends on the refractive index of the medium. For glass with a refractive index of n=1.50, this angle is 41.81degrees. If the angle becomes larger than this value, light cannot exit the glass medium anymore and is reflected back in the glass. This critical angle is also called angle of total internal reflection.

I want to spare you the theoretical reason but want to make you aware of the perhaps most important application of this total internal reflection – to use it in s.c. Prisms to let the light make a ( as example) 90degree turn.

We have touched now some fundamental laws and facts, which are

1. Law of rectilinear propagation of light
2. Law of reflection
3. Law of refraction
4. Refractive index
5. Dispersion
6. Reversibility of the optical path
7. Fermat’s principle
8. Critical angle and total internal reflection

 We could think that we are well prepared now to start understanding the formation of an image by an optical device such as a lens or a mirror.

But to understand the formation of images, we need to deal with the fact, that light is not properly characterized by using rays of light ( silently assuming that light is consisting of “light particles”, photons, which are traveling and nothing else – as we learned before, light is an electromagnetic wave and this means we need to cover in the next tutorial this fact in greater detail – light as a wave, propagation of light as propagation of a wave front and related topics.

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