Sunscreen Dialog: Absorbance

So now that we’ve discussed what UV is, we need to discuss how the ingredients in sunscreens filter out the radiation in the ultraviolet range. So let’s look at those line graphs that people show when they talk about sunscreens

So I have been looking up sunscreens and I see all these line graphs that are supposed to explain how sunscreens work. I don’t understand them.

Chiquita, let me tell you: I understand completely, and agree. Did you take physics?

No, did you?

Obviously not. I took Melville.

There were no sunscreens in Moby Dick. What gives you the right to write about this, you misleading, uneducated wretch?

Well, number one, it's interesting to me, and I read about it all the time. Now that I believe myself to be able to understand what other people are talking about in regards to UV filters, well, I feel like everything made sense. It's amazing.

One would certainly get a better explaination of this from a physicist, but for them, that would be work. For me, this is pure joy.

You've made your passion and lack of credentials clear. Can we get started?

Sure, let’s look at this chart:

What does SPF Mean.jpg

Yeah, I don’t have any idea what that is supposed to mean.

Okay, let’s start with the X axis: it is the easiest part. these are the measured wavelengths.

Sunscreen UVA.jpg

You see that for this test, the filter X was measured from 290 nanometers (UVB) to 400 nanometers (UVA I).

On the Y axis, we see it is measuring absorbance, and there are these numbers:

Sunscreen High Protection.jpg

Yea, I don’t understand that. How much is 0.2 absorbance? 0.2 what?

I love this part.

The value of absorbance (called “A”) is a reflection of the amount of radiation received by a material, divided by the amount transmitted by the material. Absorbance isn’t measured in units: it says we gave this material X amount of radiation, and Y amount got through.

Specifically, absorbance is:

What does sunscreen mean 1.jpg

Or, in words, Absorbance is the common logarithm of the amount of radiation recieved by a substance divided by the amount of radiation that got through the substance.

If one has the Absorbance of a material, one also has the Transmittance of a material, which is the amount of radiation that was not absorbed.

This is an annotated chart from the Wikipedia page on Absorbance.

Absorbance: −log10(Φet/Φei) Absorbs how much of the wavelength? Transmittance: Φet/Φei How much of the wavelength gets through?
0 0% 1 100%
0.1 21% 0.79 21%
0.25 44% 0.56 56%
0.5 78% 0.32 32%
0.75 82% 0.18 18%
0.9 87% 0.13 13%
1 90% 0.1 10%
2 99% 0.01 1%
3 99.90% 0.001 0.10%

Using this knowledge, we can better understand the protection indicated in the chart above. Let’s look again:

safest sunscreen.jpg

Understanding the concept of absorbance was, for me, key to understanding the significance of given SPF numbers and broad spectrum claims.

Do tell.

So SPF is, of course, an in Vivo test, done on actual people. However, like absorbance, it is a logarithmic expression.

SPF is tested the same way across the globe, and measures the amount of UV filtered to bring about the result, as in:

  1. Say a person normally burns after 10 minutes without sunscreen
  2. Say that person burned with the sunscreen after 20 minutes. Then, the sunscreen protected the person for twice as long

This is to say, half of the UV was filtered. In negating the effect of half of the UV, the person's protection is twice as strong.

Makes sense?

I think so, but can you explain one more time?

Yep, in the above example, the person was shielded from twice the amount of UV because the sunscreen absorbed half of the UV. Let’s look at in the form of some equations, because I’m feeling a bit high and mighty that I’ve retained the skills taught to me in pre-algebra. It’s worth noting this isn’t exactly specific enough, as the actual SPF equation is more complicated. However, this makes for a simple explaination:

SPF Calculation.jpg

SPF = Protected Burn Time (PBT) / Unprotected Burn Time (UBT)

If Unprotected Burn Time (UBT) = 10 & Protected Burn Time (PBT)= 20

SPF = 20 / 10

SPF = 2

Thus, the SPF also indicates the percentage of total UVB absorbed by a sunscreen:

Sunscreen Absorbance.jpg

% of UVB Absorbed by the sunscreen = 100 (100 is the 100% of UVB with which the sunscreen interacts) - (100 / SPF)

If SPF = 2

% UVB Absorbed = 100 - (100 / 2)

% UVB absorbed = 100 - 50

% UVB absorbed = 50

Got it.

So now we can look at the following chart and understand:

Unprotected Burn Time Protected burn time UVB Protection offered Equiv. UVB Absorbance SPF
10 20 x2 50% 2
10 40 x4 75% 4
10 80 x8 87.50% 8
10 10 x15 93.36% 15
10 300 x30 96.68% 30
10 400 x40 97.79 40
10 500 x50 98.11 50
10 600 x60 98.34 60
10 1200 x120 99.17 120

However, this testing is different than the absorbance test mentioned above. As I noted above, UV is a spectrum, and different filters have different absorbance spectra. So, the SPF testing may indicate that 93% of UVB is being absorbed by the sunscreen, but this does not mean that 93% of all UVB wavelengths are absorbed. It’s likely that 99% of some wavelengths are absorbed. and only 50% of some other wavelengths are absorbed. Thus, an SPF is perhaps better thought of as the mean absorbance of the sunscreen in the UVB spectrum, not a monolithic block across all wavelengths of UVB.

So how do I know whether or not this makes a good sunscreen?

Well, maybe it will be interesting to you have access to the chart measuring a product’s absorbance, but we have SPF and Broad Spectrum as a means of telling consumers they are protected. Those are much easier to understand than these charts.

So, what's the point?

The point is the best way to determine the protection offered by a product is the SPF and UVA protection factor indicated on the label.

However, this is not to say that understanding these charts is not helpful: it is from an absorbance spectra that SPF is determined. Understanding what they means allows one to understand the specific protection offered by a sunscreen product against each wavelength of radiation.

Hold on, before we go, just quickly, when you say absorbance, that only refers to chemical filters, right? Because they absorb UV?

That’s a great question. No. Absorbance is the relationship between the amount radiation emitted versus the amount received, so the absorbance is indicative of the amount of radiation reflected, bounced off, “absorbed,” broken down, or whatever.

Additionally, the claim that chemical filters absorb UV and mineral reflect them is a kind reductive claim: it doesn’t tell the full story, as mineral filters actually chemically convert some wavelengths to heat, and some chemical filters reflect some wavelengths like mineral screens are said to, so while that is a useful “big picture” way of explaining the difference, it isn’t exactly fully true.

So, which filters have the highest absorbance?

That isn’t really the question. Absorbance doesn’t mean anything without knowledge of a wavelength’s frequency.

“Broad Spectrum” filters, which cover the whole spectrum of UV, will have a higher mean absorbance across the UV spectrum, but that doesn’t mean they offer the most protection for any particular wavelength. Zinc is a good example of this: it has a remarkably consistent level of absorbance across the whole UV spectrum. However, it’s absorbance of any particular wavelength is quite low. This is why you’ll see 20% zinc oxide sunscreens which have an spf of lower than 30. Thus, one can understand that zinc has a very consistent, moderate level level of absorbance across the UV spectrum.

Interesting. Can you show me the absorbance chart for zinc?

Sort of: there are lots of ‘zincs’ that are commercially available: many are coated and have different particle sizes. This is the extinction of one kind of zinc in comparison with Tinosorb S (adapted from a chart by BASF.

Zinc oxide sunscreen.jpg

So while Zinc is very consistent, it isn’t as efficient a filter: one needs to add more of it to a formula to get high protection.

Got it, but that chart has E, not A, on the Y axis. What is E?

I was just reading about this – it's cool. E, or extinction, is a more specific way of expressing absorbance. We can use E(1,1) to get the value for A, if we want to. At least, the math I am doing adds up. We can't use a value for A to get a value for E, because E sets forth some specific conditions that don't exist with an Absorbance measurement.

If one sees "E(1,1)," one should understand that a researcher took a 1% solution of the filter being measured, and sent radiation through 1 centimeter of it. E meausres the amount of radiation at a specific wavelength that was extinguished from the origin point to the end.



Therefore, E(1,1) divided by 100 tells you the percentage of UV that got through the system.

We already know that A = log10(the percent of UV that got through the system)

So, A = log10(E(1,1) / l00)


E is, for me, more convenient, because it gives you the percentage absorbed more transparently: it's the number on the Y axis divided by 100.

Yeah, it's a lot easier because you don't need to put the log in your calculator. Why don't they use it instead of A to determine a sunscreen's absorbance??

Well, it wouldn't work to determine a sunscreen's performance. It refers to the amount of energy extinguished by a 1cm patch of a 1% solution of a thing. Sunscreen tests use 2mg / cm2 of skin.

Ah, yes, you are right. So E(1,1) isn't helpful for that.

Yeah, I know right. The log of it all.

Well, this has been fascinating.

I know right? Physics is fun when it is about sunscreen.