Pharma Glass Properties - Part 3. Refractive Index

Hello everyone – this is Part 3 of an ongoing series about properties that are included on technical data sheets for pharmaceutical glass packaging.?Part 2 focused on the linear coefficient of thermal expansion – you can check it out here.

Refractive index, often represented by the symbol n, is a unitless quantity that can be defined as the ratio of the speed of light in a vacuum to the speed of a light in a medium of higher density (density is another property that appears on your data sheet – refer to my first post for more information).?You can sleep relatively soundly at night while believing the refractive index will always be >1.?Reality is a little more interesting – there are cases where the refractive index of a homogeneous medium can be less than 1 due to behavior such as resonance and absorption.?Even more strange, there is an entire class of periodically structured “metamaterials” that have a negative refractive index…but I digress.

The refractive index of materials within the visible region of the electromagnetic spectrum is largely dictated by the interaction of light with electrons in a material.?Think of a car (light) driving down a road with speed bumps (electrons within a material) as a very crude analogy.?Assuming you’re a reasonable driver looking to avoid permanent damage to the car’s suspension, your speed decreases by an amount that depends on the height and number of speed bumps (see Footnote 1).?This decrease in speed is analogous to an increasing refractive index of the material.

One of the first practical applications that you may have learned about the refractive index is its relation to bending of light.?A ray of light passing between two media will be bent at an angle that is dependent on the angle of incidence and the refractive indices of the two media.?This behavior is captured by a formula that is often called “Snell’s Law”, as shown in the figure below.?Two consequences of Snell’s Law include: 1) there is no refraction if the two media have the same refractive index and 2) there is no refraction if the incident light is perpendicular to the interface (θ? = 0°).

This leads to my first anecdote – one of our teams reported an issue with making dimensional measurements on a new 33 expansion borosilicate glass vial.?They were using an optical test bench that had only been previously used to characterize 51 expansion borosilicate glass vials.?The measurement relied on immersing the part in a clear oil.?The surfaces of the 51 expansion vial were visibly crisp and clear when immersed in this oil.?The 33 expansion vial? – not so much.?I had to smile when I heard about this, only because I knew about a classic science experiment known as the “disappearing glass rod”.?The version that I’m familiar with starts by filling a container with common vegetable oil.?You then immerse a rod of clear soda lime silicate glass ?(Type III glass in the parlance of pharma glass packaging) into the oil.?This SLS glass rod is clearly visible.?Next, you immerse a rod of clear 33 borosilicate glass into the same oil – the immersed portion of the glass rod should be difficult if not impossible to see.?The rod apparently disappears because the refractive index of 33 expansion borosilicate glass is identical to the vegetable oil, and so no light is bent to reveal the immersed surface of the rod.?The fix in this case was easy – we just had to switch the immersion oil depending on the type of glass vial that was being measured.

The next thing that you may have learned about the refractive index is that it can depend on the wavelength of light that is propagating through the medium of interest.?Going back to Snell’s Law, this means that the angle of refraction, θ?, will depend on the wavelength of light.?This also explains why a white light source is converted to a continuously variable rainbow of colors after passing through a prism, a phenomenon called optical dispersion.?The consequences of dispersion are significant when designing optical systems such as microscopes, cameras, etc. ?However, at a minimum, dispersion also means that we need to be a little more precise when quoting refractive index values for a material, which is why you will commonly see a subscript D attached to the variable n on your technical data sheet for pharmaceutical glasses.?The “D” means that the refractive index is being reported for a wavelength of 589.29 nm, corresponding to the sodium D-line (see Footnote 2).?The choice to use the sodium D-line is not an accident – it sits roughly in the middle of the visible light spectrum and therefore provides a reasonable estimate of the average refractive index for pharmaceutical glasses (see Footnote 3).

One final consequence of refractive index is its impact on reflectivity.?I previously mentioned how Snell’s Law predicts incident light that is perpendicular to an interface is not refracted.?However, this doesn’t mean the incident light is wholly unaffected – it is still reflected by an amount that is dependent on the refractive indices of the two media.?We can predict the amount of reflection for this simplified case (see Footnote 4) using the below formula.

Assuming refractive index values of 1 and 1.5 for air and glass, respectively, we would predict a reflection of ~4% for light passing through the air/glass interface.?In reality, the various compositions of glass containers that are known to be generally suitable for containing parenteral drugs have refractive indices ranging from about 1.46 (fused silica) up to 1.49 (the various flavors of borosilicate glasses and aluminosilicate glass at the higher end).?The difference between these two extremes equates to an absolute difference in reflectivity of about 0.5%.? The takeaway message is that any automated process for inspecting vials of sufficiently different refractive index may need to adjust the recipe to account for these differences in reflectivity.

There’s one more item that I wanted to briefly address.?The prior discussion was mostly framed within the context of glass containers, but glass-derived particulate can also be present in drug products as a contaminant (see Footnote 5).?Previous studies have demonstrated that refractive index differences between particulate and the surrounding liquid medium can become important, particularly when inspecting for translucent, subvisible particulate such as glass and proteinaceous material.?As reference points, the refractive index of water at 25°C is ~1.33 (this will increase with increasing solute concentration) and condensed protein particulate has a refractive index of ~1.4.?Validated test methods can in principle be developed to accommodate these refractive index effects, although the availability of suitable calibration standards may impose limitations.?For example, borosilicate glass microsphere standards are available in a variety of mean particle sizes (± a relatively narrow tolerance) for this purpose, although I caution you to carefully evaluate material properties of the standards.?I’m aware of at least one series of borosilicate glass standards having a refractive of 1.56, which is well above the refractive index of standard Type I borosilicate glasses used in parenteral packaging (see Footnote 6).?Further drug characteristics such as turbidity and viscosity can further impact the sensitivity and accuracy of particulate detection.

I imagine there are a number of people in the visual inspection community who could contribute to this discussion, and so please feel free to comment below if you have further thoughts or experiences that you would like to share.?I’d be very curious to learn more about how optical properties such as the refractive index are leveraged in your work.

Footnotes

1.?A complete discussion of the relationship between glass composition and the number/height of “speed bumps” is beyond the scope of this post.?In brief, increasing the number of speed bumps generally relies on stuffing the glass structure with other cations that raise the average electronic density of the material.?Increasing the height (the polarizability) can be accomplished with cations that are generally large in size relative to their charge – examples include barium and lead.?For those of you in the know, I’m ignoring the role of bridging vs. non-bridging oxygens on refractive index – I have to the cut this off somewhere.

2.?Let’s clean up some sloppy terminology.?It’s convention to casually toss around the term sodium D-line, but in reality it should be the sodium D-lines (plural).? Energetically excited sodium vapor actually emits light at two closely spaced wavelengths of similar intensity at 588.9950 nm and 589.5924 nm, also referred to as the sodium doublet.?For simplicity, we average this doublet to a single wavelength of 589.29 nm and just refer to a single sodium D-line.?You might be wondering why it’s specifically called a “D” line.?Sodium isn’t the only element that has characteristic wavelengths associated with absorption/emission (it’s the whole basis for techniques such as inductively coupled plasma optical emission spectroscopy).?A German physicist named Joseph von Fraunhofer observed dark features (lines) in the emission spectrum of the Sun. The dark line occurred wherever a specific wavelength of light was being absorbed by a particular element within the outer region of the Sun.? Each one of these major features was assigned a letter – A, B, C, D, and so on.?The sodium doublet just happened to match up with the letter D.

3.?I’m being careful here by pointing out that it’s a reasonable estimate for pharmaceutical glasses, which are examples of what are called “low dispersion” glasses – i.e., glasses in which the refractive index has a relatively low dependence on wavelength.?Relatively high dispersion glasses also exist.?Things get interesting when optical glass elements having different dispersion behavior are used in combination to cancel out chromatic aberration effects.

?4. The full form of the Fresnel equations for reflection are more complex, taking into account the polarization state and incident angles of the light being reflected.?The idea here is just to communicate the basic message that refractive index differences relate to the reflection of light.

5. I’m thinking specifically here of glass particulate from a mechanical event such as abrasion.?Refer to one of my earlier posts for more info on this and other sources of glass-derived particulate in parenteral drug products.

6.?In this case, the borosilicate glass composition is specified as 0.2K?O-0.2FexOy-0.3Na?O-1.2MgO-22.5CaO-14.5Al?O3-8.6B?O?-52.5SiO? (weight%) – clearly different from conventional Type I borosilicate glass compositions.?This highlights the generally vague practices that we use in naming glass compositions.?What does it mean for something to be a “borosilicate glass”, an “aluminosilicate glass”, etc,??There are no hard rules here, unfortunately.