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Diopter Formula

The eye is a simple focusing lens. Light rays from an object to the lens become refracted on the lens and create a correct vision on the retina.

What is a Diopter?

Diopter refers to the refractive (light bending) capacity of a lens. It also relates to the amount of curvature in the lens. As the diopter increases, the lens becomes thicker and the curvature greater. As the curvature increases, light rays are redirected to fill a greater portion of the viewer's retina which makes the object appear larger.

Optical Power

The optical power of a lens, expressed in units of diopters, is defined as the reciprocal of the focal distance expressed in meters. The greater the optical power, the shorter the focal distance. The power of a lens may be measured by its focal length, but we usually use diopters.

Focal Length

Focal length is the distance from the center of lens to the object being viewed. This is also known as the "working distance" of the lens. It is important to remember that as magnification increases, the focal length decreases.

The formula for calculating focal length:

                            1 Meter 
Focal Length  =   Diopter value

Examples:

A lens with a power of 1 Diopter will have a focal length of....

1/1 = 1 meter

A lens with a power of .50 Diopter will have a focal length of....

1/.50 = 2 meters

A lens with a power of 2 Diopters will have a focal length of....

1/2 = .50 meters

The top of the equation is a constant and must always be equal to 1 meter. In this example, the answer will be represented in meters. No sign is used in the diopter value, since the focal length of a plus lens is the same as the focal length of a minus lens with the same power.

It is also possible to calculate the diopter value if given the focal length, by using the inverse of the focal length formula. This formula can be used to verify the answer obtained when calculating Focal Length. In this formula, the variable and the constant must be represented in the same unit of measure in order for the answer to be correct without conversion:

Examples:

A lens with a focal length of 1 meter would have a power of...

1/1 meter = 1.00 Diopters

A lens with a focal length of 2 meters would have a power of...

1/2 meters = .50 Diopters

A lens with a focal length of half a meter (0.5) would have a power of...

1/.5 = 2.00 Diopters

The above formulas can be used on both minus and plus (concave and convex) lens calculations. However, remember that the final diopter values should be written in either (+) or (-) form.

Based on the above information, it is safe to assume that a power stronger than 1.00 diopter will have a focal length of less than 1 meter, and a power weaker than 1.00 diopter will have a focal length longer than 1 meter.

Conversions

If the focal length is requested in meters, no further steps are needed. If the focal length is requested in a unit if measure other than meters, a conversion must be done. For example:

1 Meter (M) = 1000 millimeters (mm)
100 centimeters (cm)
10 decimeters (dm)
39.37 inches (in.)

Lens Cross

The power of a lens can be shown on a Lens Cross. The major meridians are the original axis and 90 degrees away from the original axis. In a sphere, the power is the same in all meridians. With a sphero-cylindrical lens, no cylinder power (0%) is present in the lens at the original axis, and cylinder power (100%) is present in the lens 90 degrees away from the original axis. At the original axis, the lens power equals the sphere. 90 degrees away from the original axis, the lens power equals the sphere plus the cylinder (added algebraically).

Example of a +2.00 sphere:

At 90 degrees:   +2.00 (+) 0.00 = +2.00
At 180 degrees: +2.00 (+) 0.00 = +2.00

Example of –1.75 –1.00 x 180:

At 90 degrees:  -1.75 (+) –1.00 = -2.75
At 180 degrees:  -1.75 (+) 0.00 = -1.75

Example of  +4.25 –1.00 x 45:

At 45 degrees:  + 4.25 (+) 0.00 = + 4.25
At 135 degrees:  + 4.25 (+) –1.00 = + 3.25

Since there is no (0%) cylinder power at 45 degrees, the lens power in that meridian equals the sphere. Since there is 100% of the cylinder power present at 135 degrees, 100% the cylinder power is algebraically added to the sphere, making the total power in that meridian +3.25.

Transposition

Plus Cylinder Form: +1.50 +.75 x 180
Minus Cylinder Form: +2.25 -.75 x 90

An Rx can be written in plus cylinder or minus cylinder form. This simply means the sign of the cylinder, regardless of the sign of the sphere. The form usually depends on the type of equipment that was used for the exam. Since most lenses are manufactured in minus cylinder form, it may be necessary to convert from one form to the other. Transposition is a method to convert to either form without altering the actual lens power, and is only done with sphero-cylindrical lenses. The rules of transposition are:

1. Algebraically add the sphere and cylinder, resulting in the new sphere.

2. Change the sign of the cylinder from minus to plus or plus to minus.

3. Change the original axis 90 degrees (must fall between 0 and 180). If the original axis is less than 90, add 90 degrees. If the original axis is more than 90, subtract 90 degrees.

In order to confirm the accuracy of your lens power transpositions, draw the lens cross (above). The powers in each meridian should match accordingly.