Math Flashcards
Describe an Optical Cross
A mathematical representation of a lens
What are the steps for transposition?
- Add original sphere + original cylinder = new sphere
- Change the sign of the original cylinder
- Change the axis by 90 degrees (add or subtract in order to keep if between 001 and 180)
Define Cylinder
The difference in power between one meridian and another meridian 90 degrees away
What is the relationship between index of refraction and light bending?
The higher the index, the more the light bends
What is the formula for calculating the focal point of a lens?
D = n/f = 1.00/f D = Power in diopters n = index of refraction in air (1.00) f = focal length in m
When dealing with meters in optics, how many decimal places do you round to?
5!
What is the formula for calculating the power of a lens?
Total power = Front Curve + Back Curve
What is the formula for Snell’s Law?
n (sin i) = n’ (sin i’)
i = angle of incidence (measured to the normal)
n = index of refraction of material 1
i’ = angle of refraction (measured to the normal)
n = index of refraction of material 2
What is the relationship between i and i’ when passing from a low density material to a high density material?
The light bends TOWARDS the normal because the light slows down
What is the relationship between i and i’ when passing from a high density material to a low density material?
The light bends AWAY from the normal because the light speeds up
When dealing with sin/cos/tan in optics, how many decimal places do you round to?
3!
When dealing with degrees in optics, how many decimal places do you round to?
The closest whole number
Define Critical Angle
The angle of incidence when all of the light is reflected (none refracted). This is common in jewelry as this causes it to sparkle
What is the formula for Power in any Meridian?
Ftotal power = (Ftotal cylinder)sin^2(θ) + Sphere
theta is the angle, in degrees, from an axis to meridian in question
What is a shortcut for calculating Power in Any Meridian?
If θ =
30: use 1/4 cylinder power
45: use 1/2 cylinder power
60: use 3/4 cylinder power
90: use complete cylinder power (transposing)
What is the formula for Feffective/compensated?
Fe/c = (Ftrue power) / (1 ± d(Ftrue power)
What is the formula for calculating spherical equivalent?
Spherical equivalent = 1/2 Cylinder + Sphere
What is Vogel’s formula used for?
For ensuring that you are using the correct base curve for a given prescription
What is Vogel’s formula?
TRICK QUESTION - there are two versions
1) Plus Lenses
BC = Spherical Equivalent + 6.00 D
2) Minus Lenses
BC = 1/2 Spherical Equivalent + 6.00 DWhat is the definition of Base Curve?
the curve of a lens that determines the other curves on a lens therefore it is the Front Curve of a lens
Are magnification imbalances more trouble for hyperopes or myopes and why?
Hyperopes. Centre thicknesses change more with plus lenses
Define vergence
How a light ray enters a lens, goes through a lens and exits a lens
What are the 5 ray tracing rules for thin lenses?
- Any light ray that goes through OC remains undeviated
- Any light ray that originates at F emerges parallel to the axis
- Any Parallel light rays coming fro infinity will come to focus at F’
- Light rays from infinity that are off axis will focus at F’ but not along the axis
- Light rays emerging from F but not on the axis will emerge parallel to each other but not the axis.
What is the formula for Feq?
Feq = F1 + F2 - [(t/n)(F1)(F2)]
What is the formula for nominal power?
Front Curve + Back curve = Total power
What is the rule for reading prism on a lensometer when the two lenses have the same power?
Centre the RIGHT lens and without moving the platform centre the left lens horizontally and read the prism through the lensometer
When neutralizing lenses, how do you know if there should be vertical prism?
If you have different OC heights (single vision) that means you should try to find vertical prism
What is the rule for reading prism when one lens is stronger than the other, but they are the same TYPE?
Centre the lens with the strongest power at 90°. Without moving the platform centre the other lens horizontally and read the prism through the lensometer
What is the rule for reading prism when one lens is plus and the other lens is plus.
Centre the MINUS lens and without moving the platform centre the PLUS lens horizontally and read the prism through the lensometer
How do you read horizontal prism when neutralizing lenses?
Centre and dot both lenses and compare the Frame Mono PDs to the patient’s mono PDs.
Dot the patient’s PDs and place this dot in the middle of the lens stop. Read the amount of horizontal prism through the lensometer
How should you neutralize Bifocals/Trifocals?
You will have to neutralize them 2/3 times respectively.
- Measure the BVP in the distance portion normally (convex side facing you)
- Flip the glasses and measure the FVP of distance portion (for calculation only)
- Neutralize the segment by flipping the glasses and measuring the FVP
- Calculate the difference between FVP of near and distance OU. This is the power of the add.
- Fill out the form with BVP of the distance and add power.
Repeat these steps again if you are neutralizing a trifocal
What are the 3 ways to calculate prism?
- Prism Formula
- Read off the target within the lensometer
- Use the prism compensator
What is the formula for calculating prism?
∆ = (d x p)/10 ∆ = amount of prism d = difference in mm between the OC and the patient's PDs p = power (@90 for vertical prism and @180 for horizontal prism) 10 = simply used to convert d into centimeters
How do you use a prism compensator?
- Set the compensator @0 for 90 and 180 to start
- Place the lens on the lens stop and twist the knob until the mires which are not in the centre come into the centre
- The number on the dial of the compensator indicates the amount of prism
How do you calculate crossed cylinder when the two meridians are 90º apart?
Transpose the two prescriptions so they are in the same axis and add add the optical crosses together
What is the short form icon for “crossing cylinder”?
(∙) (but on it’s side) so it looks like an “eye”
How do you calculate obliquely crossed cylinder?
- Transpose both prescriptions to plus cyl
- Determine Rx A (axis closest to 0… NOT on a looping scale… 10 is closer to 0 than 179) and Rx B (the other one
- Find 𝜶 (alpha)… 𝜶 = difference between axis A and axis B
- Calculate 2𝜶
- Find resultant cylinder Rcyl =
- Find the resultant sphere
- Find the resultant axis
- Put it together the find the resultant Rx
How do you calculate Size of Blank?
Minimum = ED + 2(Horizontal Decentration) + 2 mm
size of bank.
What is Joe’s Rule?
How to calculate Size of Blank based on double decentration (horizontal and vertical).
SOB = Vertical Decentration + ED + 2(Horiz. Decent.) + 2 mm
How do you measure prism?
Measured in diopters, but rather than a sign, it is designated with Base Direction
What is Prentice’s Rule?
The formula to calculated UNWANTED prism
∆ = (d x P)/10
∆ : amount of prism (diopters - no sign)
d : distance from optical centre to pupil centre (mm)
P : power at a specific meridian in the lens
V∆ - Power @ 90
H∆ - Power @ 180
10 : constant in the formula to convert d to cm - easier math
In terms of prism, how are plus lenses made?
Made of two prisms touching base to base, OCs are where the two prisms meet
In terms of prism, how are minus lenses made?
Made of two prisms touching apex to apex, OCs are where the two apexes touch
In terms of prism, light bends towards the ______ ?
APEX
How do you calculate the total imbalance of prism?
If the images are going in the same direction, SUBTRACT prism values
If the images are going in the opposite directions, ADD prism values
What are the two ways to induce Dr. Prescribed prism?
- Decentre Rx
2. Grind prism into the lens
