Cylindrical lenses are therefore used wherever it is desired to vary the magnification from one meridian to a perpendicular meridian. Cylindrical surfaces are employed in the anamorphic lenses used in some wide-screen motion-picture systems to compress the image horizontally in the camera and stretch it'
Link to CLZ
Read MoreThis post covers my notes from Chapters 12-14 in the System for Opthalmic Dispensing. It includes the basics of lens diagrams, the refractive index, prisms, spherical lenses, cylindrical lenses, lens form, transposition, base curves, and vertex distance.
First up, some conventions used when people diagram light and lenses:
Light always moves left to right: '
The distance light travels before it reaches the lens ('in front of the lens,' shown to the left of the lens) is expressed in negative numbers. The distance light travels after it leaves the lens ('behind the lens,' shown to the right of the lens) is expressed in positive numbers.
(Side note: When we talk about light, we diagram it as if it moved like particles in a straight line; later in the sun section, we talk about light moving in waves. Which is correct? Both, according to quantum mechanics, which states that electrons, or particles of light, have wave-particle duality, functioning like both waves and particles. But anyway. Moving on.)
Know the idea, skip the math: refraction and the refractive index
In the diagram above, light is traveling through air at an angle i, the angle of incidence, from left to right, and strikes a material. Some light is reflected off the surface of the material and travels away at angle r, the angle of reflection. But some light passes through the material, traveling more slowly, and this change in speed refracts or bends the beam of light so that it travels through the material at angle i', the angle of refraction. Remember: reflection means bouncing, refraction means bending. (After the light leaves the material, it travels at its original angle again.)
It is possible to quantify the amount any given material will bend light. The measurement is called the index of refraction. Here on planet Earth, we opticians don't worry about the speed of light in a vacuum and other such variables; we measure everything against the speed of light in air (approximately 186,000 miles per second), so we are technically using a relative refractive index. It goes like this:
The relative refractive index of a material = (the speed of light in air) ÷ (the speed of light through the material).
The higher the refractive index, the more it bends light. Think about what this means for lenses: if one material has a high index, it bends light farther, so less material is needed to bend light a required amount, so the lens can be made thinner. High-index lenses are thinner lenses. Some common refractive indexes to know include:
Don't worry about memorizing those indexes now, though. (Do that later.) For now, get the idea down. The higher the index, the thinner the lens.
Introduction to prisms: making basic lenses
Prisms are The Big Idea in optics. Prisms bend light from apex to base. Note how, in this prism, one side is flat or plano, so the light does not bend until it hits the angled surface. Also note that the angle a prism bends light is equal to the angle of its apex. I don't always diagram it correctly, but I try.
You can think of lenses like stacked prisms. Although it's an oversimplification, it's a useful one.
A positive or plus lens is convex, like two prisms stacked base to base. It converges rays onto a focal point behind the lens. A negative or minus lens is concave, like two prisms stacked apex to apex. It diverges rays and has a theoretical focal point in front of the lens. A lens with no refracting power is called plano. Here's a demonstration from wikipedia, because real lenses have curves:
Focal length (actually secondary focal length, but oddly, no one cares about the primary one) is the distance from the focal point to the lens. It is measured (again, oddly) in meters. Look at the diagrams above again. A plus lens is easy enough; the focal point is clear and, according to the diagramming conventions that started this post, because the focal point is behind the lens it is measured in positive numbers. A negative lens is a bit trickier; the focal point is theoretical and, by those same conventions, since it is in front of the lens it will be measured in negative numbers.
There's a reason we care about focal length, and that is because it is related to focal power ' how strong the lens is, how far it displaces light, how much it can correct vision. Cool! That relationship goes like this:
Focal power = 1 ÷ focal length, or
F = 1/f
The unit for measuring focal power is called a diopter. A plano surface with no refracting power is 0.00 D. A plus lens is, appropriately enough, measured in positive diopters (say, +1.25 D), and a minus lens in negative diopters (like -4.00 D). The farther the focal power is from zero, the stronger the lens is.
Example 1: The focal length of a lens is 20 cm. How many diopters of power does the lens have?
F = 1 / f
F = 1 / 0.2m ('remember focal length is is meters, so convert the centimeters)
F = +5.00 D
Example 2: A lens has power -2.50 D. What is its focal length?
F = 1 / f
-2.5 = 1/f
f = 1/-2.5
f = -.4 meters = -40 cm ('this is a minus lens, so the focal point is in front of the lens and the distance to it is measured in negative numbers)
From the ocular anatomy section, we know that in farsighted eyes, light takes too long to converge, coming to a focus too far behind the retina. Therefore, a plus lens that converges light farther inward can correct this condition. (Plus lens = like base-to-base prisms = converging rays = corrects farsightedness.) We also know that in nearsighted eyes, light converges too soon, coming to a focus in front of the retina. Therefore, a minus lens that diverges light farther outward can correct this condition. (Minus lens = like apex-to-apex prisms = diverging rays = corrects nearsightedness.)
Bring your protractor: correcting astigmatism with cylindrical lenses
All the lenses we have seen so far are called spherical lenses. They have a single point focus: in plus lenses behind and in minus lenses in front of the lens. But to correct astigmatism, which we know from the ocular anatomy section makes light focus at multiple points within the eye, we need something different.
Instead of have a single point focus like a spherical lens, a cylindrical lens focuses its power along a line. The power of this cylindrical lens is measured in diopters, just like spherical lenses are. Its line of focus can be positioned anywhere on the lens as long as it runs through the optical center. Think about a protractor, where lines called meridians bisect the center of a circle:
If a cylinder can be positioned anywhere on the lens, then we need some way to communicate where on the lens it should be placed. This measurement of placement is called the axis and, just like high school geometry class, it is measured in degrees. To make a cylinder lens, you need two measurements: the cylinder power and the axis, a measure of placement.
Let's look at a diagram. I drew it in Paint. It's terrible.
Imagine that the light purple bit is a cylinder cut in half and placed across a circular plano lens. It is placed along a 30 degree axis meridian. However, here's the important thing to remember: Because a cylinder is uniformly thick along its axis, it has no curve to refract light and has 0% of its power. The cylinder is at 100% power at the meridian 90 degrees off from its axis, sometimes called the power meridian: in this diagram it is 30 + 90 or 120 degrees. Internalize that: axis meridian = no power; axis meridian + 90 degrees = 100% power.
In the meridians between the cylinder's axis meridian and power meridian, the cylinder has proportionally increasing power. Let's say this cylinder has +4.00 diopters of power:
Now you can see that halfway between the axis meridian (0% power or 0.00D) and the power meridian (100% power or +4.00D), the lens has half its power, or +2.00D. The same holds true for any other meridian: one-quarter of the way between the axis meridian and the power meridian, the lens has one-quarter of its power, +1.00D.
Example 3: A cylindrical lens has -6.00 diopters of power and sits at axis 90 degrees. What is its power at the zero degree meridian? What is its power at the 45 degree meridian?
The cylinder sits at axis 90. So it has zero power at the 90th meridian.
The cylinder will have 100% power 90 degrees from its axis, at zero or 180 degrees. So its power at the zero meridian is -6.00.
The cylinder will have 50% of its power halfway between its axis meridian and power meridian. Halfway between 90 and zero degrees is 45 degrees. So at 45 degrees the cylinder will have -6.00 D / 2, or -3.00 D.
The ABO will probably only give you problems like this at easy meridians that have easy calculations ' 0, 45, 90, 135 degrees, maaaybe some at 30, 60, 120, 150 degrees, because they don't allow the use of calculators.
Because astigmatism is independent of nearsightedness and farsightedness, a patient could have both at the same time, and so need correction of both in the same lens. When you combine a spherical lens and a cylindrical lens, it is called, appropriately enough, a spherocylindrical lens. If you are asked to work out the power meridians of such a lens, here are your steps:
Example 4: A spherocylindrical lens has sphere power -1.00 D and cylinder power of +6.00 D at axis 45. What is its power at the 45 degree meridian? The 90 degree meridian? The 135 degree meridian?
First, work out your cylinder powers:
The cylinder sits at axis 45, so it has zero power at the 45 degree meridian.
It will have 100% of its power 90 degrees away from its axis, at 45+90 or 135 degrees, so it has +6.00 D power at the 135 degree meridian.
Halfway between the two meridians, at 45+90/2 or 90 degrees, it will have 50% of its power, so at the 90 degree meridian it has +6/2 or +3.00 D of power.
Next, remember that a spherical lens has the same power throughout the lens. So at all those meridians, the sphere has power -1.00D.
Finally, add the powers at each meridian.
At meridian 45, this lens has 0 D from the cylinder plus -1.00 D from the sphere: -1.00 D.
At meridian 90, this lens has +3.00D from the cylinder plus -1.00D from the sphere: +2.00D.
At meridian 135, this lens has +6.00D from the cylinder plus -1.00D from the sphere: +5.00D
Any lens that has multiple curves on its surface, like a spherocylinder lens does, can also be called a toric lens.
Reading the prescription
There is a standard form for eye doctors to express a patient's prescription. In a simplified form, it looks like this:
In the first column, OD stands for oculus dexter, or right eye (think 'dextrous' or 'good with your hands': most people are right-handed). OS stands for oculus sinister, or left eye (think about the old superstitions about left-handed people: being left-handed was bad, 'sinister'). Sometimes you may see OU or oculus uterque, meaning both eyes.
Sphere and cylinder powers are usually expressed in quarter diopters. If there is no sphere correction, the doctor will write PL for plano in the sphere column. If there is no cylinder correction, the doctor will leave the cylinder and axis columns blank or write DS, for 'diopters sphere (only).' Remember that you cannot have a cylinder power without a cylinder axis, and vice-versa.
When prescriptions are expressed informally, with no chart, the sphere and cylinder corrections are written normally but an 'x' precedes the axis. The right eye prescription is always written above the left eye. It is best practice to include placeholding zeros so that every number is three digits long. (0.75 instead of .75, +3.00 instead of +3)
+2.50 -1.25 x035
+2.75 DS
I don't see a 20/20 on there anywhere'
The classic Snellen eye chart measures visual acuity, your capability of sight:
Visual acuity using the Snellen eye chart essentially compares the ability of each eye individually to see the chart at twenty feet with the distance a normal or average human eye could read the chart.* 20/200 vision, represented by the top E on the chart, means your eye can see at twenty feet what a normal or average eye could see at 200 feet. 20/20 vision, represented by the eighth line on the chart, means your eye can see at twenty feet what a normal or average eye could see at twenty feet. 20/15 vision, represented by the ninth line on the chart, means your eye can see at twenty feet what a normal or average eye could see at fifteen feet (better than normal). If an eye cannot be corrected (with glasses or contacts) to better than 20/200 visual acuity, that eye is legally blind.
But visual acuity just answers the yes/no question of whether you need visual correction of any kind. The prescription describes exactly what type of correction is necessary.
(*Um, actually, there's specific mathematical definitions happening, not just comparing with 'a normal or average human eye.' Visual acuity according to Snellen = the distance the test is made / the distance at which the smallest letter read subtends a visual angle of five minutes. This is a bit more detail than most people need about visual acuity, but if you want to learn it, go to the ABO Study Spot here and follow the Visual Acuity link. All the detail about subtended angles you could ever wish for!)
Theory is just theoretical: total power and lens form
So far we have seen lenses in easy-to-imagine forms: pure convex or concave shapes. But actually, the most common form of a lens is the meniscus lens. Meniscus lenses have a convex front surface and a concave back surface. They can be either plus or minus.
This diagram shows several different types of lenses: the biconvex, with two convex sides, which has a subtype the equiconvex, with two equally convex sides; the plano-convex, with one convex and one plano side; the positive meniscus, with the front side more convex than the back side is concave; the biconcave, with two concave sides, which has a subtype the equiconcave, with two equally concave sides; the plano-concave, with one plano and one concave side; and the negative meniscus, with the back side more concave than the front side is convex. Almost every lens now made for a set of glasses is a meniscus lens. But even knowing that fact, you can still oversimplify your mental picture of a plus lens into a pure convex lens and your mental picture of a minus lens into a pure concave lens, since the basic theory stays the same.
The total power of any lens, including a meniscus lens, is found by adding the power of the front surface to the power of the back surface.
In spherocylinder lenses, the cylindrical portion can be 'added to the front' or 'subtracted from the back' of the spherical lens. When it is 'subtracted from the back,' the lens is in minus cylinder form and will be written on the prescription with negative numbers. When it is 'added to the front,' the lens is in plus cylinder form and will be written on the prescription with positive numbers. There is one more way of writing a prescription for spherocylindrical lenses, called crossed-cylinder form, but it's pretty much historical at this point; I wouldn't bother to learn it unless it interests you.
So putting these ideas together, sometimes you get questions like this:
Example 5: If lens has front power +6.00 and back powers of -8.00 at the 90th meridian and -6.00 at the 180th meridian, what form does the lens have and what is its total power?
Because the back surface of this lens has more than one curve, you know that the cylinder is on that surface. Therefore the lens is in minus cylinder form.
Now add each meridian separately.
At the 90th meridian, the lens has +6.00 front power plus -8.00 back power = -2.00 total power
At the 180th meridian, the lens has +6.00 front power plus -6.00 back power = 0.00 total power
Now take what you know about cylinders. The cylinder should be in minus form, expressed in negative numbers. So its axis will be at the higher meridian, 180 degrees, 0.00 total power. Because the power here is zero, you know that the spherical element of the prescription is also zero. Ninety degrees away, at the 90th meridian, the cylinder should have 100% of its power. The total power is -2.00, and we just decided that there is no sphere power in this prescription, so all of that power is cylinder power. The cylinder is at axis 180 with power -2.00.
In prescription form, your answer is
PL -2.00 x180
Example 6: If a lens has front power +7.00 at the 90th meridian and +8.00 at the 180th meridian, and a back power of -6.00, what is the lens form and power?
Because the front surface of this lens is more than one curve, you know that the cylinder is on that surface. Therefore the lens is in plus cylinder form.
Now add each meridian separately.
At the 90th meridian, the lens has +7.00 front power and -6.00 back power = +1.00 total power
At the 180th meridian, the lens has +9.00 front power and -6.00 back power = +3.00 total power
Now take what you know about cylinders. The cylinder should be in plus form, expressed in positive numbers. So its axis will be at the lower meridian, 90 degrees, +1.00 power. Because the power of a cylinder at its axis is 0, you know all of that +1.00 power is spherical power. Ninety degrees away, at the 180th meridian, the cylinder should have 100% of its power. The total power here is +3.00 ' but you know +1.00 of that is sphere power, so take the sphere power away and your remaining cylinder power is +2.00. The cylinder is at axis 90 with power +2.00.
In prescription form, your answer is
+1.00 +2.00 x090
You should always order a doctor's prescription exactly as written, but sometimes it is useful to be able to change or transpose a prescription from plus to minus cylinder form. You might do this when the limits of a material are expressed only in diopters of minus cylinder and you need to know if you can make a prescription expressed in plus cylinder in that material. To transpose a prescription, first add the sphere and cylinder powers together; this becomes your new cylinder. Next, change the sign of the cylinder; this becomes your new cylinder. Last, change your axis by 90 degrees.
Example 7: Transpose +1.00 +2.00 x090 into minus cylinder form.
Sph+cyl=new sph: +1.00 + +2.00 = +3.00
Change cyl sign: -2.00
For more information, please visit Meniscus Cylindrical lenses manufacturer.
Add or subtract 90 degrees from axis: 90 ' 90 = 0 degrees ('or 180 degrees; same thing)
New scrip: +3.00 -2.00 x000
I used the prescription from Example 6. Notice how the new prescription has the same total powers as the old one ' +3.00 at the cylinder axis, 180 degrees, and +1.00 at the meridian where the cylinder is at 100% power, 90 degrees.
And sometimes it is useful to be able to determine the purely spherical equivalent of a spherocylindrical lens. Such an equivalent will not correct vision like the real prescription will, but when you're imagining how thick a lens will be, think this:
Approximate spherical equivalent = sphere + cylinder/2
Base curves
The base curve of a lens is just that: its basic curve, upon which the lens power is based. For spherical lenses, it's the front sphere curve. For plus cylinder lenses, it's the weaker or flatter of the two front curves. For minus cylinder lenses, it's the front sphere curve again. Knowing the base curve allows you to do some complicated-looking problems:
Example 8: A lens has power +3.00 -2.00 x180 and will be ground in plus cylinder form. What curves will this lens have on its front and back surfaces at 90 and 180 meridians if the base curve is +6.00?
First, figure out a way to keep track of what you're being asked, in a graphical power cross or like so:
(at the 90th meridian) front surface + back surface = total power
(at the 180th meridian) front surface + back surface = total power
Next, start filling in what information you know. You can figure out the total power of the lens from the prescription. At the cylinder axis of 180 degrees there is no cylinder power, only sphere power, so the total power at 180 degrees is just the spherical power: +3.00. The full power of the cylinder is in effect 90 degrees away at the 90 degree meridian, so the power there is +3.00 + -2.00 = +1.00. Now we have:
(at the 90th meridian) front surface + back surface = +1.00
(at the 180th meridian) front surface + back surface = +3.00
Then, fill in your base curve. You know that for a plus cylinder lens, the base curve is the weaker/flatter of two front curves. The weaker meridian of this lens is the 90th, and you know from the problem your base curve is +6.00. Now you know:
(at the 90th meridian) +6.00 + back surface = +1.00
(at the 180th meridian) front surface + back surface = +3.00
From here on out, you do some algebra for the back surface, and you realize that the back surface doesn't have a cylinder so it will be the same at both meridians:
(at the 90th meridian) +6.00 + -5.00 = +1.00
(at the 180th meridian) front surface + -5.00 = +3.00
And you finish by filling in the last bit of math.
(at the 90th meridian) +6.00 + -5.00 = +1.00
(at the 180th meridian) +8.00 + -5.00 = +3.00
There is an instrument called a lens clock or lens measure that measures the curves of a given lens. It works by finding the 'sagittal depth,' or the depth of the surface curve, s in the following picture:
However, curves measured this way are not always accurate. For one, most are calibrated for the refractive index of crown glass and are not as accurate with other materials. And with high prescriptions, often the form of the lens isn't really a pure cylinder or spherocylinder, because they get very thick ' but more on that in a later post.
Opticians often worry about base curves more than they need to. According to this book, the only times to specify a base curve are 1) replacing one lens out of a pair, or 2) ordering an identical second pair of glasses with an identical prescription. You do not need to specify a base curve to match an old prescription, to get a thinner lens (trying to do that will increase optical aberrations), to avoid ghost images (instead, add an anti-reflective coating), or to avoid long eyelashes (pick a different frame).
Otherwise, manufacturers and laboratories choose best form base curve, or the base curve that will usually work best with the given prescription in order to minimize optical difficulties called aberrations. I wouldn't be surprised if the ABO asked about best form base curve, but I still honestly have no idea how to get the correct answer and for that I apologize. My book gives the Vogel formula with approximate best form guidelines
Plus lenses: best form base curve = (spherical equivalent) + 6
Minus lenses: best form base curve = (spherical equivalent)/2 + 6
but these guidelines are completely contradicted by the chart of approximate guidelines given in the Open Optix course:
So I really have no idea here. If you have a great resource about base curves, send it my way! I would love to understand better.
Regardless of the best form-ness of best form base curves, those with myopia will notice errors and differences in base curves before those with hyperopia do.
Example 9: A lens has power -5.25 -0.50 x180. Another lens has power +1.00 +1.00 x045. According to the Vogel formula, what base curves should be used for these lenses?
Let's start with the first lens.
Find its spherical equivalent: sph + cyl/2.
-5.25 + (-0.50/2) = -5.25 + -0.25 = -5.50
Next, apply the Vogel formula for minus lenses: (sph equiv)/2 + 6
-5.50/2 + 6 = -2.25 + 6 = +3.75 base curve
Now for the second lens.
Find its spherical equivalent: sph + cyl/2.
+1.00 + (+1.00/2) = +1.00 + 0.50 = +1.50
Next, apply the Vogel formula for plus lenses: (sph equiv) + 6
+1.50 + 6 = +7.50 base curve
Example 10: A lens has power -5.25 -0.50 x180. Another lens has power +1.00 +1.00 x045. According to the Open Optix chart, what base curves should be used for these lenses?
Let's start with the first lens. Find its base curve on the chart.
A lens with -5.25 sphere should have a +2.00 base curve
Now for the second lens. Find its base curve on the chart.
A lens with +1.00 sphere should have a +6.00 base curve
Example 11: A lens has power -5.25 -0.50 x180. Another lens has power +1.00 +1.00 x045. What base curves should be used for these lenses [no method specified]?
Compare examples 9 and 10. If you know how to answer this question, please let me know. I ended up memorizing the Open Optix chart for the ABO, because I know that guide was created by currently working opticians with lab experience, but I have no idea if my base curve questions were marked correct or not.
One reason contact and glasses prescriptions are different: vertex distance
Besides the unique aspects of contact prescriptions (like prescribing a particular brand, wear schedule, and diameter to fit the patient's habits and eyes), one reason prescriptions for glasses and contacts are different is this: there's a distance between back surface of a glasses lens and the front of your eye, called vertex distance. Remember that power and position are closely linked: F = 1 / f. (Focal power equals one over focal length in meters.)
Vertex distance can be measured with a handheld instrument called a distometer, but these days, it is more likely that a digital image-capturing system will take this measurement.
The assumed average vertex distance of a glasses prescription is 14 mm. Picking a frame that sits unusually close to the face or unusually far from the face can result in a patient noticing their vision is not totally clear, because power and position are linked. In all cases, more vertex distance equals more perceived plus power. Think about how moving a magnifying glass closer to an object (further away from your eye, more vertex distance) makes objects appear larger and more magnified (more plus power).
So for a minus lens, reducing vertex distance increases the effective power of the lens (makes it less plus/more minus), and increasing vertex distance decreases the effective power of the lens (makes it more plus/less minus). For a plus lens, reducing vertex distance reduces the effective power of the lens (makes it less plus), and increasing vertex distance increases the effective power of the lens (makes it more plus).
You probably won't do the actual calculations for vertex distance on the ABO, because they would require a calculator, unless the numbers picked were extremely easy. But here are examples anyway. Remember, vertex distance comes into play in the difference between contacts and glasses, and if the lens power is high enough for differences to be noticeable (the lens power is plus or minus 4.00 or more).
Example 12: A patient is prescribed a lens -14.00 using a vertex distance of 12 mm. What is the effective power of this lens at a 15 mm vertex distance?
First, find the original focal length of the lens.
F = 1 / f
-14 = 1 / f
f = 1/-14 = -. meters = -71.4 mm ('remember focal length is given in meters, so you have to convert)
Now subtract the additional vertex distance from the focal length:
15-12=3 mm extra vertex distance
-71.4 mm ' 3 mm = -74.4 mm
Finally, use the new focal length to find the new, effective power:
F = 1 / f
F = 1 / -. meters ('remember focal length is given in meters, so you have to convert)
F = -13.44 D (This lens is so high-powered that a three-millimeter difference in vertex distance made more than a +.5 diopter difference ' it would be very noticeable to the patient.)
Example 13: A patient is prescribed a lens +10.00 using a vertex distance of 12 mm. What is the effective power of this lens at a 15 mm vertex distance?
First, find the original focal length of the lens.
F = 1/f
10 = 1/f
f = 1/10 = .1 meters = 100mm
Now subtract the additional vertex distance from the focal length:
15-12=3 mm extra vertex distance
100 mm ' 3 mm = 97 mm
Finally, use the new focal length to find the new, effective power:
F = 1/f
F = 1/. 97 meters (converted)
F = +10.31 D (This lens is so high-powered that a three-millimeter difference in vertex distance made about a .3 diopter difference; it would probably be noticeable to the patient, as this much variance is outside of ANSI tolerance .)
Example 14: A patient is prescribed a lens +10.00 using a vertex distance of 14 mm. What is the effective power of this lens at a 10 mm vertex distance?
First, find the original focal length of the lens.
F = 1/f
10 = 1/f
f = 1/10 = .1 m = 100 mm
Now subtract the additional vertex distance from the focal length:
10-14= -4 mm less vertex distance
100 mm ' -4= 104 mm
Finally, use the new focal length to find the new, effective power:
F = 1/f
F = 1/.104 m
F = +9.62 D (This lens is so high-powered that a four-millimeter difference in vertex distance made about a .4 diopter difference; it would be noticeable to the patient.)
Additional resources:
Open Optix. Wikipedia's article on lenses.
Image sources:
My terrible Paint diagrams. 'Large convex lens' by User Fir on en.wikipedia. Licensed under CC BY-SA 3.0 via Commons . 'Concave lens' by User Fir on en.wikipedia. Licensed under CC BY-SA 3.0 via Commons . Snellen Eye Chart is public domain. Types of lenses is public domain via Wikimedia Commons. 'LensClockSF' by User:StationNT5Bmedia and User:Srleffler. Licensed under CC BY-SA 3.0 via Commons .
Disclaimer: My name is Ericka Erickson, ABOC, licensed in California as of . I do not claim any of this information is correct, except to the best of my knowledge. I studied on my own, from books and the internet, and therefore I might have misunderstood something; alternatively, I might have understood things correctly at the time I took the test but the information has now been changed or updated. I assume NO responsibility for your use of this information. I do NOT claim or guarantee that your use of this information will lead you to pass the ABO. Nothing I say represents my employer.
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