Optical History

• The earliest known optical lenses were made from Quartz.

• Euclid (300 BC, known as the “Father of Geometry”) discovered the geometrical side of light. Hero of Alexandria (10 AD - 70 AD) focused more on the rays of light which led to “Fermet’s Principle of Least Time”. Pierre de Fermat (over a thousand years later, (1607-1665) is most known for “Fermet’s Principle” which states that the path taken by a ray between two given points is the path that can be traversed in the least time.

• William Herschel (1800) discovered infrared radiation (IR), up until then visible light was the only known light on the electromagnetic spectrum. This discovery occurred while studying the temperature of light based on it’s color as it passed through a prism. He realized that the heat of light increased as it passed beyond RED. He termed these non-visible light rays as “calorific”. The very next year, Johann Ritter discovered light rays beyond VIOLET, or Ultraviolet (UV) Rays. Ritter termed these light rays as “Chemical Rays” because they caused certain chemical reactions.

• In 1865 John Clerk Maxwell proposed the Electromagnetic Wave Theory as well as the first durable color photograph in 1861. His work on the Electromagnetic Wave Theory let to the proof of Radio Waves. He stated that if we took 3 Black & White photos of the same picture where taken with RED, GREEN, & BLUE filters and then projected onto a screen with similar filters the result would be an image of the picture with true color.

• William Röntgen discovered X-Rays in 1895.

• Paul Villard discovered Gamma Radiation in the 1900s.

Unit Conversion

The ABO exam, as well as the NCLE, will present problems in different formats. The questions are designed to give as close of representation to real life experience as possible. Questions may be asked using different units and it is important to make sure that they are converted correctly to produce the answer they are looking for and to make sure that any formulas used are used correctly.

The units of conversion include;

Meters

Centimeters

Millimeters

Inches

It is important to know how to convert backwards and forwards.

Meters:

How many meters are in a millimeter? (1 mm = 0.001 meters) vs How many millimeters are in a meter? (1 m= 1000 mms)

How many meters are in a centimeter? (1 cm = 0.01 m) vs How many centimeters are in a meter? (1 m = 100 cms)

How many meters are in an inch? (1 inch = 0.0254 m) vs How many inches are in a meter? (1 m = 39.37 inches)

Example Questions: (answers below)

1. How many millimeters are in 7.50 meters?

2. How many meters are in 42 cms?

3. How many inches are in 12 meters?

4. How many meters are in 12 inches?

Millimeters:

How many millimeters are in a centimeter? (1 cm = 10 mm) vs How many centimeters are in a millimeter? (1 mm = 0.1 cm)

How many millimeters are in an inch? (1 inch = 25.4 mm) vs How many inches are in a mm? (1 mm = 0.03937 inches)

Example Questions: (answers below)

5. How many centimeters are in 95 mms?

6. How many inches are in 210 mms?

7. How many mms are in 15 inches?

Centimeters:

How many centimeters are in an inch? (1 inch = 2.54 cm) vs How many inches are in a centimeter? (1 cm = 0.3937 inches)

Example Questions: (answers below)

8. How many centimeters are in 6.7 inches?

9. How many inches are in 85 cms?

Answers:

1. 7500 mms

2. 0.42 meters

3. 472.44 inches

4. 0.305 meters

5. 9.5 cms

6. 8.27 inches

7. 381 mms

8. 17.02 cms

9. 33.46 inches

Light

What is the speed of light in a vaccum?

299 792 458 m / s or 2.99 x 10^8

What is the speed of light in mms / s?

2.99 x 10^11 mms / s

What is the speed of light in miles per second?

186,000 miles per second

The shortest Wavelength is Violet and the wavelengths increase as it reaches RED.

ROY G BIV (Red, Orange, Yellow, Green, Blue, Indigo, Violet)

Typically measured in Nanometers (nm) are used as a unit of measure which is 1 billionth of a meter

The Wavelengths are broken into several groups:

Gamma Rays: Less than 10 picometers (one trillionth of a meter, 1×10^-12 meters)

X-Rays: 0.03 nm to 3 nms

Ultraviolet (UV) Rays:

10 nm - 400 nm is UV Radiation

UVc = 290 - 200 nm (absorbed by the o-zone)

UVb = 320 -290 nm (causes corneal burns, retinal damage, sunburns, and eventually cataracts). Absorbed by cornea and crystalline lens.

UVa = 320 - 400 nm (causes sun tan & cataracts, mainly absorbed by crystalline lens)

Visible Light = 400 - 750 nm

Infared (IR) = 700 nm to 1 mm

Microwaves: 1 m to 1 mm (300 MHz to 300 GHz)

Radio Waves: 1 mm to 100 kms (300 GHz to 3 KHz)

FDA requires sunglasses to absorb 95% UVa (5% transmits), 99% UVb (1% transmits). Green focuses upon on the retina, red is beyond the retina, blue is front of the retina. RGB.

Understanding the effect of a polarizer/analyzer also helps us deeply understand where many of the Optical formulas come from. This video by Scholars Wing shows us just how polarization of light works through a polarizer, reflected light, and additional optical equations.

Review:

1. What is the speed of light in a vacuum in meters per second?

2. Which color has the shortest wavelength?

   a. Blue

   b. Red

   c. Violet

   d. Orange

   e. Green

3. UV rays fall in what range?

   a. 10 nm to 400 nm

   b. 400 to 750 nm

   c. 750 nm to 1 mm

   d. 1 mm to 100 kms

   e. less than 1 picometer

4. Which of the following has the shortest wavelengths?

   a. Polarized Light

   b. Visible Light

   c. UVa

   d. UVc

   e. Infrared

5. What is the speed of light in miles per second?
   

Answers:

1. 2.99 x 10^8 meters per second

2. Violet

3. a

4. d

5. 186,000 miles per second

 Prism, Refraction, & Reflection

As light moves from one medium to another, it will change speed. This change in speed will change the direction of the passing light ray, and this process is known as refraction. For example, as light travels through air into another medium such as water the speed of the light will move slower. This change in direction and speed is how we are able to create optical lenses. Light will either be reflected off a surface, refracted through a surface, or be absorbed (total internal reflection ie critical angle, which we will talk about later in more depth).

The speed of light in a medium is dependent on the medium itself and the index of that medium. The index of refraction tells us how quickly light will bend through a given material. The higher the index of refraction, the slower light moves through that medium which in turn bends light quicker. The quicker light bends through a material the less of that material is needed to converge light to a focal point. This is why high index lenses (higher indexes of refraction) are thinner than lenses with the same focusing power but lower indexes of refraction.

The index of refraction is notated as “n” in many optical formulas. For example a lens with a power of -6.00 diopters with an index of refraction of 1.67 will be thinner than a -6.00 diopter lens with an index of refraction of 1.49.

Prism

As light enters into a prism it is deviated towards the BASE.

Viewing objects through a prism moves the object towards the APEX.

Dispersion

When white light travels through a prism the colors are broken apart. The colors are broken apart because shorter wavelength colors such as purple slow more than red ones. Here is a quick video on Dispersion.

https://www.khanacademy.org/science/physics/geometric-optics/reflection-refraction/v/dispersion

 Lens Materials. ABBE Values, & Index of Refraction

Memorize this chart, it will not only help you with test questions but help dispense the correct material for a patient.

• Remember that the higher the ABBE Value the less chromatic aberrations in a lens.

• The Higher the Index of Refraction, the less material is needed in a lens to refract light so the thinner it will be.

ANSI Standards

The ANSI standards below are from 2015 and are subject to change. The guides are based off of ANSI Z80.1-2015.

SV & MF Lenses

This section tells us that a lens that has a Dioptic power up to plus or minus 6.50 can only be off by 0.13 Diopters. For example, a lens with an RX of -3.00 (between +6.50 and -6.50) that came in as -3.25 is not within ANSI standards. The tolerable range for a -3.00 lens would be -2.87 to -3.13 Diopters. Anything outside of this range would not qualify as passing ANSI standards.

If an RX is great than 6.50 Diopters of power then the tolerance switches to a percentage. Any difference greater than 2% of the dioptic power does not pass ANSI standards.

PRISM

Segment

Progressive Lens Designs

Please pay careful attention to the differences located in the Sohere power ranges, tolerance as well as the CYL power ranges and tolerances associated.

Ranges and tolerances for the AXIS and the ADD power are the same as in the SV/MF lenses.

Again, please pay attention to the differences in ranges and tolerances here compared to SV/MF lens designs. Horizontal Prism Imbalance changes in Range and in tolerance.

More Tolerances

 Pythagorean Theorem

Quick math review on some geometry, pythagorean theorem.

In a right triangle the square of the hypotenuse of a right triangle is equal to the sum of the square root of the other two sides.

c^2 = b^2 + a ^2 or c = sqrtt of (b^2 + a^2) where c = the hypotenuse (longest side).

Example)

What is the hypotenuse of a triangle with one side at 1.5 meters and the other at 2 meters?

c = sqrt (1.5^2 + 2^2) = sqrt (2.25 + 4) = sqrt (6.25) = 2.5

LaramyK Reference: https://opticianworks.com/glossary-of-optical-related-terms/

Accomadation:

Change in shape of the lens to focus on objects at different focal lengths.

Aphakia :

Lens of the eye has been removed (usually do to cataracts).

Ametropia:

Refractive error in the eye (could be myopia, hyperopia)

Amblyopia:

Typically begins in infancy and with one eye affected where one eye fails to achieve visual acuity even with glasses or contact lenses. Also known as “Lazy Eye”.

Amsler Grid:

Grid of horizontal and vertical lines used to detect visual defects. Usually from the retina/macula (eg macular degeneration)

Aniseikonia:

Ocular condition where there is a perceived difference in the size of images. Can be caused from anisometropia, or antimetropia.

Anisometropia:

When both eyes have unequal refractive power. Generally, of 2.00 or more diopters.

Antimetropia:

Similar to anisometropia but one eye is hyperopic while the other is myopic. Can lead to diplopia (double vision)

Asthenopia:

Eye fatigue/strain. Symptoms such as fatigue, pain in or around the eyes, blurred vision, headache, and occasional double vision

Astigmatism:

The cornea is oblong shaped (like a football), causing light rays to focus on multiple points on the retina. Corrected using a Cylinder lens.

Bench Alignment:

Setting/adjusting eyeglasses into a neutral form providing the optician a starting point to adjust the frames.

1. Screws are tight

2. Crossing (One lens has more retro/panto tilt than the other)

3. Co-Planar

4. Skewed Bridge (If bridge is not aligned then lenses will have more rotation than other lenses)

5. Face Form (Frame Wrap 3 Types)

   • Positive (Ideal or some wrap around patient’s head). Use when Frame PD is greater than Patient PD.

   • Negative (wraps away from patient or bridge is closer to face than lenses) Use when Patient PD is greater than Frame PD.

   • Neutral (no wrap, perfectly flat). Patient’s PD = Frame PD

6. Frame Tilt (Panto/Retro)

7. Temples Parallel (Flat Temple Touch Test with Frames Upside down on flat surface and temples are parallel).

8. Open Temple Angles (The angle of temples when the frames are open) & Closed Temple Angles

9. Nosepads

Cataracts:

Clouding of the Crystalline Lens.

Co-Planar Alignment:

Frames form a straight line when viewed from above, or one eye is not closer to the face than the other.

Diplopia:

Seeing “ghost images” or double vision. Seeing two separate or overlapping images of the same object when you should only be seeing one.

Distometer:

Measure vertex distance of a pair of glasses.

Emmetropic Eye (Emmetropia):

Perfect Eye, Normal Vision no refractive errors.

ESO:

Turning inward or Nasally

Exo:

Outward or temporally

Exocrine Glands:

Glands that secrete a substance onto an epithelium layer by way of a duct.

Frontal angle –

The angle of the pads when viewed from the front of the frame. The tops of the pads should be slightly closer together than the bottoms of the pad following the contours of the nose as it gets wider from top to bottom.

Hyperopia:

Far-sightedess, the eye is too short causing light rays to converge at a point behind the retina. This refractive error causes objects up close to become blurry and objects further away are clear. Corrected with plus power lenses.

Inferior:

Below something

Iseikonic Lenses:

Lenses used to correct for aniseikonia

Ishihara Test:

Test used to detect color blindness.

Jaeger Chart:

Chart used to test near visual acuity (ie reading). Text size from 0.37 mm to 2.5 mm.

Lateral:

From the sides

Low Vision Aids:

Different than normal glasses, these tools are used to correct vision where glasses cannot achieve 20/20. Patients with low-vision would have, at best, 20/70 to 20/160 with corrective glasses.

Medial:

Middle

Myopia:

Near Sightedness, the eye is longer than normal and light rays land before the retina instead of on the retina causing a refractive error. Corrected with minus power lenses, patient with myopia can see up close (near) but have trouble with objects at a distance.

Nystagmus:

Condition where the eyes make repetitive, uncontrolled movements.

Pantascopic:

Tilting top of frames/lenses away from patient (increasing vertex distance) and tilting bottom of frames/lenses toward the patient (decreasing vertex distance). A frame that is adjusted with 10 degrees of pantoscopic tilt is in the correct position. Adding pantoscopic tilt gives the perception that the lens has been LOWERED (lowers optical center). If the eyes are above the optical center you can add panto tilt.

Phoria

“Tendency” for the eye to turn away from it’s normal position.

Photophobia:

Light discomfort or sensitivity. Eyes tend to turn away from light.

Photopic:

Vision at higher light levels

Presbyopia:

Generally starting at age 40, the loss of accommodation begins as the crystalline lens looses it’s ability to focus on near objects. Corrected using reading glasses or segments with additional power (ADD POWER) on the lens.

Polarization:

Process of filtering beams of light into a singular plane. Unpolarized light is a light wave that is oscillating in more than one plane. A polarizer (polarized lenses for sunglasses) filters all but one plane.

Rectus:

The Latin word meaning “Straight”

Retroscopic:

Opposite of pantoscopic tilt where the top portion of the frames/lenses is tilting towards the patient (decreased vertex distance) and the bottom of the frames/lenses is moved away from the patients face (increased vertex distance). Increasing the retroscopic tilt gives the impression that the lenses are being RAISED (increasing height of optical center). It is generally not recommended to add retro but if the eyes are slightly below the optical center this adjustment can be made if there is no other way to adjust the OC height.

Scotoma:

A Partial alteration in the field of vision surrounded by a field of normal vision (ie blind spot)

Scotopic Vision

Vision at low light levels (Rods)

Snellen Chart:

Visual Acuity Test

Splay angle:

The angle of the pads when viewed from the top of the frame. The front edges of the pads should be closer together than the back edges.

Stereopsis:

Ability to see depth.

Superior:

Above Something, upwards, or the top.

Titmus Test:

Used to detect stereopsis.

Tropia:

“Definite” turning of the eye from it’s normal position.

Tunics of the Eye:

3 Tunics - Fibrous Tunic (scleral, cornea), Vascular Tunic (choroid, cilliary body, & iris), & Nervous Tunic (retina, macula)

Vertex Distance:

Distance between the glasses lenses and the patient’s cornea. Increasing distance will increase the perceived plus power of the lens, decreasing it will the perceived power more minus. Most doctors will refract their patients at a vertex distance of 12 mm.

Vertical angle:

The angle of the pads when viewed from the side of the frame. Since most frames will have some amount of pantoscopic tilt, the bottoms of the pads should be slightly closer to the frame front than the tops.

the Prescription/RX

A lens is made up of two prisms connected either base to base (plus lenses) or apex to apex (minus lenses). A minus lens will diverge light, and a plus lens will converge light onto the retina.

The Rx is measured in dioptic power, usually in quarter diopters starting at 0.00 and going in a positive or minus direction. The minus or plus power indicates if light needs to be either converged or diverged so that it lands directly on the retina. Additional refractive errors including astigmatism or presbyopia will mean the RX will need additional powers to be added to the lens to refract all light onto the retina.

An RX for Glasses contains several parts:

Sphere (SPH): Spherical power of a lens.

Cylinder (CYL): This is an additional power curve added to the lens to correct for astigmatism.

Axis: The degree of axis tells us where the CYL curve must be placed to correct refract light onto the retina.

ADD: Additional plus power added to the lenses to correct for presbyopia.

PRISM: This is added to the lenses to reduce diplopia.

PRISM Direction: This tells us where the BASE of the Prism lens is in relation to the pupil.

An RX for Contact Lenses may have the above corrections but sizing information is important because these lenses fit directly onto the eye.

Base Curve (BC): How steep the curve of a lens is.

Diameter: The size of the lenses.

Brand/Type: There are several manufacturers of contact lenses that all offer different materials for contact lenses, wear time, and care instructions.

Transpose an RX

Transposing an RX is done in 3 steps:

1. Add the Cylinder power to the Spherical power which gives you your new Spherical power.

2. Change the sign of the cylinder (do not drop the power), this gives you your new cylinder power.

3. Add or subtract 90 degrees from the axis. (remember the rx must be between 0 & 180 degrees). This gives you your new axis.

Example

-1.00 -1.00 090

Step one says to add the Sphere power and the CYL power. -1.00 + -1.00 = -2.00 (this is your new sphere power)

Step two says to change the sign of the CYL power. -1.00 is now +1.00

Step three says to add or subtract 90 degrees to the axis. 090 + 090 = 180

So your new RX is written as -2.00 +1.00 180.

You can check your work by transposing the new RX again. The answer should be the originally transposed RX. Let’s work through it.

Step one: -2.00 + +1.00 = -1.00

Step two: +1.00 is now -1.00

Step three: 180 - 090 = 090

So your new rx is -1.00 -1.00 090.

The Optical Cross

The optical cross shows the power of a lens in different meridians, mainly 090 degrees apart from each other. This is power, not necessarily prescription. You can put a prescription into an optical cross or you can understand the prescription of a lens from an optical cross. For example a spherical lens with a power of -5.00 will have the same power in all meridians and will look like this on an optical cross. Because there is no change in power at any point in this lens it is safe to say that there is no CYL power on this lens.

When you compare a spherical lens to a lens that has Cylinder power (to correct for astigmatism) you will see that a cylinder lens will have two different powers and thicknesses 090 degrees apart from each other. The lenses thinnest point will be 090 degrees away from it’s thickest point and will look like this on an optical cross. Let’s use this power, -4.00 -1.00 045 as an example. The difference in power 090 away from each other gives the CYL power of the lens. In the example here you see a difference of -1.00 when you go from -4.00@045 to -5.00 @135 and you see a +1.00 CYL power when you go from -5.00 @135 to -4.00 @045.

A Quote from John Seegers that may help you understand the optical cross and something great to memorize.

“The Shorter the Radius the Steeper the Curve, The Steeper the curve the higher the power, The Higher the power the thicker the lens.”

Example 1

A lens with a power of -2.50 @ 060 and a power of -1.50 090 degrees away (150) can be written onto an optical cross like this.
The power of the lens has a difference of +1.00 090 away when moving from -2.50 @060 to -1.50 @150

-2.50 to -1.50 is +1.00 (this difference is the CYL power) and can be written out as;

-2.50 +1.00 060

The power of lens has a difference of -1.00 090 away when moving from -1.50 @150 to -2.50 @060

-1.50 to -2.50 is -1.00 (this difference is the CYL power) and can be written out as;

-1.50 -1.00 150

Example 2

Let’s say you have these two powers -12.00 @045 and -6.00 @135. How would you put this into an optical cross and how would you write this out in RX form? The difference in power in either direction 6.00 diopters. It is plus 6.00 diopters when moving from -12.00 to a -6.00 and minus power when moving from -6.00 to -12.00. It can be written as

-6.00 -6.00 045 or -12.00 +6.00 135 and on an optical cross it would look like this.

Example 3

Now let’s work backwards from an optical cross into written form. Let’s say you have the following optical cross and you want to know how to write out the power.

Start with either meridian and write the power in that meridian as the sphere power and your axis at that point. For this example you see that there is -3.75 @045 so we now have two parts, the sphere power and the axis. We just need the CYL power and we are done! So far we have -3.75 _______ 045.

Next, calculate the power difference moving 090 degrees away and write that out as your CYL power. At 090 away the power is -4.25, because this power is MORE minus the CYL power is minus. There is an additional -0.50 power going from -3.75 to -4.25. You can write the -0.50 into your power so you now have -3.75 -0.50 045.

Let’s also try starting from the power at 135 degrees. We have -4.25 @135 and this can be written out as -4.25 ________ 135. When moving from -4.25 to -3.75 you are becoming LESS minus (or adding plus power) so your CYL is now in PLUS form. The power can be written out as -4.25 +0.50 135

Checking your work!

Transpose your written power to see if it matches up to the optical cross. This is a great way to double check your work. Another tip is to make sure you work from both meridians just to double check your math and power signs.

Concept of Axis from Laramy-K

https://www.youtube.com/watch?v=z6cHAQbych4

Concept of Axis from Laramy-K

https://www.youtube.com/watch?v=z6cHAQbych4

BOX Measurements

Box Measurement Definitions and Additional Verbiage to help with following formulas.

A = Width of the Lens

B = Height of the Lens

ED = Effective Diameter (longest diameter of lens)

DBL = Distance between Lenses

GC = Geometric Center of lens

DBC/GCD (Distance between GC/ Geometric Center Distance) = Distance between centers of each lens (frame PD)

Datum Line = Line that runs horizontally through the GC of the lens. Also could be called the “mounting line”

OC = Optical Center of Lens (that point on a lens through which a passing ray is not deviated). Provides best VA when line of sight is lined up with the OC. Does not take into account prescribed prism.

MRP = Major Reference Point. (The OC and MRP are the same if there is no prescribed prism).

PRP = Prism reference point or point at which the prescribed prism is located.

DRP = Distance Reference Point (should be slightly higher than the fitting cross (based on progressive lens design)

NRP = Near Reference Point, reference point for best visual acuity for near vision.

FRAME PD

The frame and the patient both have their own PD measurements. The frame PD is calculated by adding the A measurement to the Bridge Measurement.

Total Frame PD = A + DBL

To get each eye separately, divide your answer by TWO.

Frame PD = (A + DBL)/2

Another way to calculate the FRAME PD is to find the distance between the GC of each lens.

Decentration

Decentration is the difference between the FRAME PD and the PATIENT PD. When we hear decentration we are usually speaking of a lens being decentered horizontally. For vertical decentration you would take HALF of the B measurement and subtract either the OC or the SEG height. These measurements tell us how far away the OC of the lens is from the center of the frames. It is important to know this because the thickness of a lens is greatly affected by the amount of decentration.

DEC = FRAME PD - PATIENT PD

Vert DEC = OC HT - (B/2) <This is the distance of the Patient’s OC Height from the Datum Line)

For example if the patient’s PD is 61 and the frame PD is 65 the deccentration would be

DEC = 65-61 = 4 mm decentered nasally. (nasally because the patient’s pd is more narrow than the frame PD)

Example for vertical decentration, if the OC is 48 and the SEG HT is 22 then

(48/2) - 22 = 24 - 22 = 2 mm decentered below the datum line.

Minimum Blank Size (MBS)

What we are trying to find out here is what is the smallest lens that can be used that can fit into the frame that was selected. This is important because many lens designs may not have a size available that fit the patient’s frame choice.

MBS = (GCD - PD) + ED

For example if the frame we choice has a frame PD of 75, the patient’s PD is 65 and the ED is 50 then the MBS would be calculated as

MBS = (75-65) + 50 = 10 + 50 = 60 mm

Nominal Lens Formula

The nominal lens formula gives us the total power of the lens by adding the power of the front surface(s) to the power of the back surface(s).

Power = Front Surface Power + Back Surface Power or Dn = D1 + D2

Base Curve = The curve from which all other curves are measured. The Base Curve is on the front of the lens and is POSITIVE (+) in power.

*The more shallow curve on the backside of a lens is the called the “toric curve”.

• The steeper curve is called the “cross curve”

Vogel’s Rule

Used To determine base curve’s

• + Powers: Spherical Equivalent +6.00 D

• - Powers: 1/2 Spherical Equivalent +6.00 D

& Tscherning

Len’s Power & Focal Length Calculation

The power of a lens is measured in dioptic power by quarters. The power can be either PLUS or MINUS. A plus lens will converge light to focal point and a minus lens will diverge light to an imaginary focal point (focal point is located in front of the lens by tracing the diverging light rays backwards). You can find the power of a lens if you know the focal length with the formula

D (power in diopters) = 1 / f (focal length)

For example if light rays pass through a lens and they CONVERGE to a point at a point 1.50 mm from the lens your power would be;

D = 1 / 1.50 = +0.67

The power is PLUS because the light is CONVERGING. Remember the stronger a prescription is the quicker it will converge or diverge light. So, the longer the focal length the lower the power of the lens, the shorter the focal length the higher the power of the lens.

For example a lens with a focal length of 0.25 mm would be stronger than a lens with a focal length of 0.50 mm.

D = 1 / 0.25 = 4 diopters

vs

D = 1 / 0.50 = 2 diopters

You can also find the focal length of a lens if you know the power. By rearranging the variable in the formula you would get f = 1 / D. Let’s say you know that the power of a lens is -3.50 and need to know the focal length. This can be calculated by;

f = 1 / -3.50 = -0.285 mm

The minus sign is important to know if the light rays are diverging or converging. In this example since the POWER of the lens is in MINUS form we already know that it is DIVERGING.

Practice Problems

1) What is the power of a lens that converges at a point 0.15 mm behind a lens?

2) What is the power of a lens that diverges light at a point 1.10 mm in front of a lens?

3) What is the focal length of a 5.00 diopter lens?

4) Light comes to a focal length 0.75 mm in front of a lens, what is the power of this lens?

Answers

1) D = 1 / f = 1 / 0.15 = +6.67 (plus because it converges)

2) D = 1 / 1.10 = - 0.91 (minus because it diverges light)

3) f = 1 / 5 = 0.20 mm

4) D = 1 / 0.75 = - 1.33 (minus because it comes to a focal point IN FRONT of the lens which is from diverging light).

Spherical Equivalent

The equation for spherical equivalent gives us the refractive power of the eye in SPHERICAL form by taking half the CYL power and adding it to the SPH power.

Dse = (CYL/2) + SPH

For example if you have the following RX: -1.00 -2.00 090 the spherical equivalent would be half of the CYL (-2.00 divided by 2 = -1.00) plus the SPH power (-1.00) of the lens. This would give you a total of -3.00 D of power.

Practice Problems

What are the Spherical Equivalents of the following RXs?

1) -2.00 -1.00 090

2) Plano -2.00 090

3) +1.50 -1.50 090

4) +1.00 -2.00 090

Answers

1) -2.50

2) -1.00

3) +0.75

4) Plano (PL)

 Compounding & Cancelling Prism

It is important when working with either prescribed or unwanted prism that we notate the direction of the prism. The direction of the prism can have either a “compounding affect” or “cancelling” depending on the direction in each eye. Let’s take a look at prism direction first, then we will either compound or cancel the affects.

We will start with horizontal prism. When a PD is off, or when working on the horizontal plane (180 degrees) this will create PRISM either BASE IN or BASE OUT. Where the patient is looking through the lens will determine the direction of the lens. Remember that the OC of the lenses is apex to apex in a minus lens with the bases on the edges, and in a plus lens the optical center are positioned base to base.

A patient looking directly through the OC of the lenses will experience NO PRISMATIC effect. This is regardless if the lenses are plus power or minus power. See the two examples shown here.

Prism Direction Examples:

Example of Base IN Prism

Prism Base Out

When working on the horizontal plane if the direction is the same (BO & BO or BI & BI) for both eyes then the prism will be “Compounding”. The opposite is also true, if the directions or opposite for each eye then the result will be cancelling. A lens that has 1 D prism BO in the left and in the right eye will have 2 diopters BO prism. If a patient has 1 D BI in the left and 1 D BO in the right the effects of the prism will cancel and will result in no prismatic effect.

Please use & memorize the following chart to help remember when prismatic affects are either cancelling or compounding.

For cancelling powers the remaining power is the prismatic effect in the eye with the most dioptic power.

 30-45-60 Rule

This rule allows us to calculate powers at an axis that is not conveniently located perfectly vertical (90 degrees) or horizontally (180 degrees). This comes in handy when we need to calculate the amount of prism in oblique meridians. When you need to calculate the amount of power a lens has 90 degrees away from the current axis all you have to do is flat transposition. For example;

-7.00 -1.00 090 is the same as -8.00 +1.00 180.

At no point will the lens power go lower than -7.00 (thinnest portion of the lenses) and at no point will it go above -8.00 (thickest portion of lenses). If your math is wrong, keep this in mind to double check your work. Your power should be somewhere between the lowest and highest possible powers (90 degrees apart).

The 30-45-60 formula works on a percentage basis.

30 degrees away is 25%

45 degrees away is 50%

60 degrees away is 75%

A key point to remember is this is talking about DEGREES AWAY.

The next key point to remember is that this is the percentage of the CYL POWER, not the SPH POWER.

So, using the example above

-7.00 -1.00 090 if we wanted to find the power of the lens 45 degrees away from this either at 135 or at 45 degrees we would take 50% of the CYL power. -1.00 times 0.50 = -0.50 diopters. This power is then added to the CYL power to give you the power of the lens 45 degrees away. -7.00 + -0.50 = -7.50 @45 or -7.50 @ 135. Double check to make sure your answer is not below the lowest possible power (-7.00) or above the highest possible power (-8.00). You can also work from the transposed RX to again double check your work. -8.00 +1.00 180, what is the power 45 degrees away or at 135 or 45 degrees? +

Step 1) Take half the CYL power. +1.00 * 0.50 = +0.50

Step 2) Add this power to your sphere power. -8.00 + +0.50 = -7.50 @135 or -7.50 @045

Your answers are both the same regardless if you are working in plus cylinder form or minus cylinder form.

*** Double checking your answers only works this way @045 degrees away.

If you are trying to find the power 30 degrees away, at @060 then you must use 60 degrees away from the transposed RX to arrive at the same point and power of the lens. 60 degrees away from

-8.00 +1.00 180 is at 060 degrees. The power should be the same, let’s try it out.

What is the power of the lens 30 degrees away from this RX from above? (-7.00 -1.00 @090) Power @060

1) 25% of the CYL = -0.25

2) Add power to SPH = -7.00 + -0.25 = -7.25 @060

Double Check (must use 60 degrees away)

1) 75% of the CYL = +0,75

2) Add power to SPH = -8.00 + + 0.75 = -7.25 @060

Practice Problems)

1) What is the power of a lens 30 degrees away if the RX is -12.00 -2.50 127?

2) What is the power of a lens at 080 degrees if the RX is -2.00 -2.00 020?

3) What is the RX of a lens if the power @095 is -3.00, @125 it is -2.00?

4) What is the RX of a lens if the power is -1.00 @130 & PL @085?

Answers)

1) -12.63 @097

2) -3.50 @080

3) -3.00 + 4.00 095 or +1.00 -4.00 005

4) +1.00 -2.00 040 or -1.00 +2.00 130

 Powers in Oblique Meridians Formula

This formula is more accurate that then percentage estimates in the 30-45-60 rule, and it also helps us solve the power at every point from 0 to 180. The formula says that;

“The total dioptic power (Dt) is equal to the sin of the axis from the merdian you are trying to solve for (either 90 or 180) squared, times the CYL power (Dc) plus the Sphere power (Ds). It is written as

Dt = (sin a)^2 x Dc + Ds

For example if you have a lens at -8.00 -2.00 112 and need to know the power at 180 because the PD is off center then you need to follow a few steps. First identify all the variables that you have.

Dt = ?

a = 180 - 112 = 68

Dc = -2.00

Ds = -8.00

So, Dt = (sin 68)^2 x -2.00 + -8.00 =

(0.9272)^2 x -2.00 + -8.00 =

0..8597 x -2.00 + -8.00 =

- 1.72 + -8.00 = -9.72 @180

You can check this by working from the transposed RX just as in the oblique formulas. -10.00 +2.00 022

Dt = (sin 22)^2 x +2.00 + - 10.00 = +0.28 + -10.00 = -9.72 @180

Practice Problems)

1) -4.00 -0.75 048 what is the power at 180?

2) What is the power of lens in the horizontal meridian with a power of -2.00 @037 and -3.00 @127?

3) What is the power of a lens in the vertical meridian with a power of -2.50 -1.25 076?

Answers)

1) -4.41 @180

2) First find the RX and transpose to double check. Then calculate the power at 180.

-2.36 @180

3) -2.57 @090

Prentice’s Rule

The rule states that as the prismatic affect of a lens increases the further away the view point is from the optical center. The stronger the lens power, the more prism is induced into the lenses. The formula is written as

△ = hcm x D where

△ = Prismatic Power

hcm = movement in cm (You will be given the movement in mm so do not forget to convert!)

D = dioptic power of the lens

Example)

For example if a patient is looking through a lens that 5 mm away from the optical center in a -10.00 lens then the prism they will experience will be

△ = 5 mm x -10.00 = -50.00 (this is in mm so we must convert).

50.00 / 10 = 5.00 △

The only thing missing here is the prism direction, it is important to note if the lens is plus power or minus power as that affects the direction. The direction and power of both lenses affects the total prism power experienced in both eyes. BU/BU, BD/BD, and BI/BO all have canceling effects. BU/BD, BI/BI, and BO/BO all have compounding effects.

Examples)

A lens that is 4.00 △ BU in the left and 4.00 △ BU in the right would experience how much prism in both eyes? Since the directions are both BU the powers would cancel (subtract). 4 - 4 = 0, so there is no prismatic power experienced by the wearer.

A lens that is 2.00 △ BI in the right and 1.00 △ BO in the left also has a cancelling affect. 2 - 1 = 1 △ or Prism experienced. The direction would be BI because the remaining (majority) of the power is in the RIGHT eye with BI direction. Your final answer would be 1.00 △ BI OD

Let’s say you have the same examples from above except the power is now compounding. 4.00 △ BU in the left and 4.00 △ BD in the right, you would now add these two powers. 4 + 4 = 8.00 △ of Dioptic Power OD.

A Lens that has 2 D BI in the right and 1 D BI on the left then the resulting prism will be compounding. 2 + 1 = 3 D Prism BI OD

The other note is to make sure that you are working in the correct meridian, we will keep it simple for the following examples in either the 90 or the 180. To convert the axis from 90 to 180 all you have to do is flat transposition. For example -1.00 -1.00 090 is working in the vertical plane and you need it to be on the horizontal. The transposed RX would be -2.00 +1.00 180

Practice Problems: Notate the Power and the Direction of the Prism

1) How much prism would a patient experience if her PD is off 3 mm in each eye nasally? The RX is;

-1.00 -1.00 @180

-1.00 -1.00 @090

2) How much prism would a patient experience if the OC was placed at the frame PD (64mm) and the patient PD is 34/30? The RX is;

-4.00 -2.00 180

-3.50 -1.50 090

3) How many cms is a lens displaced if the patient is experiencing 2 diopters of prism BI on the left eye? RX is:

-12.00

-10.00

4) How much prism will a patient experience if the glasses are made at a 70 PD but the patient’s PD is 64? RX is;

-5.00

-6.50

5) How much prism will a patient experience if the OC was placed at half of the B measurement of a frame when it should of been at 20 mm for the OC.

Box: A = 55 B = 32 DBL = 18 ED = 55

RX =

+7.00

+6.75

6) How much prism will a patient experience if their PD was switched from 34/32 to 32/34 with an RX of

-600 -2.00 058

-4.50 -3.00 120

7) A patient needs 2 Diopters of prism BU OD and 2 diopters of prism BD OS. How far do the lenses need to be moved to obtain this prism?

OD: -8.00

OS: +6.00

8) Your patient is just now pickup up his eyeglasses and he does a lot of reading, he has an RX of +12.00 in both eyes and looks below the OC of his lenses 7mm to read his ipad. How much prism will he experience in these frames?

Answers:

1) 0.90 BO OS

2) 0.2 BI OS

3) 0.17 cm or 1.7 mm

4) 3.5 BI OD & 3.5 BI OS

5) 0.1 BD OD

6) 0.14 BO OD

7) 1.25 mm down OD & 1.67 mm down OS

8) No prism since both lenses are cancelling (BD OU with 8.4

Snell’s Law

Formula = n1 sinθ1 = n2 sinθ2

n1 = incident index

n2 =refracted index

θ1 = incident angle

θ2 = refracted angle

This formula can identify the index of refraction of the medium being used to refract light, or the angles used. Generally, n1 is coming from Air unless specified otherwise and can be regarding as 1.0.

The angles are in relation to the Normal line, not the 0/180 line. All angles are measured from an imaginary line drawn at 90° to the surface of the two materials. For example, if light is entering water then the normal line would look something like the following diagram, generally drawn as a dotted line. If light enters any substance with a higher refractive index, such as from air into water, it slows down. The light bends towards the normal line. The diagram shows light bending towards the normal line (slowing down) as it goes from Air (n=1.0) into water (n=1.33). If light enters any substance with a lower refractive index, such as glass to air, it speeds up or bends away from the normal line.

It is a good idea to memorize the following indexes of refraction of these materials.

Air: Approximately 1.00

Air in a Vacuum: 1.00

Water: 1.0

Diamond: 2.42

CR39: 1.49

Crown Glass: 1.52

Flint Glass: 1.66

Trivex: 1.53

Polycarbonate: 1.59

Example:

Let’s say light travels from air into an unknown substance with an IOR of 1.43 at an incident angle of 20, The angle of refraction would be calculated by;

θ2 = (n1/n2 sin θ1)* sin-1

Write out what you know so far. We know that;

θ1 (a1) = 20 degrees

n1 (air) = 1.00

n2 (new material) = 1.43

Since light is traveling from a material with a lower index of refraction to a new material with a higher index of refraction it will slow down or bend toward the normal line.

θ2 = (n1/n2 sin θ1)* sin-1 = (1/1.43 * sin20) sin-1 = 0.24* sin-1 = 14 degrees

 Vertex Power Formulas

Effective Power (De)

The effective power formula tells us how the power of the lens was effected when it was moved wither farther away or closer to the eyes.

Remember to check what you are looking for first. Ask yourself if the lens moved closer or farther away and your final answer should match that.

A lens that moves away becomes more PLUS in power.

A lens that moves toward becomes more MINUS in power.

There are two ways to write the formula based on which direction the lens moves. The sign of d changes depending on which direction the lenses are moved. A lens that moves closer to the eye makes d a positive (+) number and a lens that moves away from the eye changes d to a minus (-) sign. The formulas for effective power are;

De = Dt / (1 + d x Dt) when moving away (more plus)

or

De = Dt / (1 - d x Dt)

where;

De = Effective Power

Dt = Total power of the lens (starting power)

d = movement in METERS. (must convert to mms).

Effective power with a toric lens.

Now we will be calculating the effective power of the SPH & the CYL.

You MUST use the POWER in the major meridians, DO NOT USE THE CYL Power.

Transpose/Use the Optical Cross to get your powers.

Compensated Power (Dc)