As opticians and vision professionals, understanding the intricate relationship between lens power and meridians is crucial for providing optimal visual solutions for our patients.

**By the end of this article, you will have a firm grasp of the principles governing lens power, enabling you to make informed decisions and deliver exceptional eyewear experiences.**

## Power of a Lens in Various Meridians and Power in the 180° and 090° Meridians

As we demonstrated, the power of a cylindrical lens changes along its various meridians as the axis of the cylinder changes. It is possible to determine the power of a lens in any meridian. For our purposes, we are primarily concerned with finding the powers of a lens along the 090° and 180° meridians when the given prescription axis is at either 090°, 180°, or 045°. Of course, the axis of a prescription lens may fall anywhere between 0° and 179°, but for the purposes of succeeding on your exam, it is most important to know the three axes mentioned above.

The figure above shows the powers in various meridians of a – 4.00 cylinder with the axis positioned along the 180° meridian. The chart below summarizes the percentage of cylinder power along the various meridians.

Degrees Away from Cylinder Axis |
% of Cylinder Power in Effect |

0 | 0 |

30 | 25 |

45 | 50 |

60 | 75 |

90 | 100 |

When the cylinder axis is at 180° or 090°:

Rx |
Power in 180° |
Power in 90° |

+ 1.00 -0.50 x 180 | + 1.00 | + 0.50 |

– 2.00 – 0.75 x 180 | – 2.00 | – 2.75 |

+ 3.00 -0.25 x 180 | + 3.00 | + 2.75 |

+ 2.25 + 2.25 x 090 | + 4.50 | + 2.25 |

+ 2.00 – 0.75 x 090 | + 1.25 | + 2.00 |

+ 0.50 – 1.00 x 090 | – 0.50 | + 0.50 |

The first number of a prescription indicates its spherical component, the second number indicates the power of the cylinder, while the third number indicates the meridian along which the cylinder axis lies. Therefore, the first number is also equal to the power of the lens along the axis of the cylinder. The first number in the first example in the chart above is + 1.00. Since the axis is at 180°, the power of that lens in the 180° meridian is equal to + 1.00.

To determine the power of the lens ninety degrees away from the cylinder axis, simply algebraically add the sphere power to the cylindrical power. In this same example, we add + 1.00 – 0.50 = + 0.50 and ninety degrees away from the axis puts us at 090°.

When the cylinder axis is at 045° or 135°:

When the cylinder axis of a given prescription is at 45° or 135°, and you need to find the power of that lens either in the 090° or 180° meridian, cut the cylinder in half and add it to the sphere.

Rx |
Power in 180° |
Power in 90° |

+ 3.00 – 1.00 x 45 | + 2.50 | + 2.50 |

– 6.00 + 1.50 x 45 | – 5.25 | – 5.25 |

– 0.75 + 1.50 x 135 | Plano | Plano |

Degrees Away from Cylinder Axis | % of Cylinder Power in Effect |
---|---|

0 | 0% |

30 | 25% |

45 | 50% |

60 | 75% |

90 | 100% |

**Lens Power and Meridians: The Basics – Critical for ABO**

The power of a lens is not uniform across its various meridians. Instead, it changes depending on the orientation of the cylinder within the lens. This phenomenon is known as the “power of a lens in various meridians.” To understand this concept, we need to familiarize ourselves with the key terms and principles involved.

**Meridians and Cylinder Axis**

A meridian is a line that runs from the top to the bottom of a lens, perpendicular to the horizontal axis. The cylinder axis, on the other hand, refers to the direction in which the cylinder component of a lens is oriented. This axis can fall anywhere between 0° and 180°, with the most common orientations being 090°, 180°, and 045°.

**Cylinder Power and Sphere Power**

The power of a lens is composed of two elements: the sphere power and the cylinder power. The sphere power represents the overall refractive power of the lens, while the cylinder power addresses any astigmatic correction needed. These two components work together to provide the necessary vision correction for the patient.

**Power in the 180° and 090° Meridians**

When the cylinder axis is positioned at 180° or 090°, the power of the lens in these meridians can be easily determined by applying a simple formula.

**When the Cylinder Axis is at 180°**

In a lens with the cylinder axis at 180°, the power in the 180° meridian is equal to the sphere power, while the power in the 090° meridian is the sum of the sphere power and the cylinder power.

For example, in the prescription “+1.00 -0.50 x 180”, the power in the 180° meridian is +1.00, and the power in the 90° meridian is +0.50 (the sphere power of +1.00 plus the cylinder power of -0.50).

**When the Cylinder Axis is at 090°**

When the cylinder axis is at 090°, the power in the 090° meridian is equal to the sphere power, and the power in the 180° meridian is the sum of the sphere power and the cylinder power.

For instance, in the prescription “-2.00 -0.75 x 090”, the power in the 090° meridian is -2.00, and the power in the 180° meridian is -2.75 (the sphere power of -2.00 plus the cylinder power of -0.75).

**Calculating Power in Oblique Meridians**

While the 180° and 090° meridians are relatively straightforward, determining the power in oblique meridians (those that fall between 0° and 180° and are not on the % of Cylinder Power in Effect table) requires a more nuanced approach. This is where the “Powers in Oblique Meridians Formula” is needed.

**The Powers in Oblique Meridians Formula**

The formula states that the total dioptric power (Dt) is equal to the sine of the angle (a) between the meridian in question and the cylinder axis, squared, multiplied by the cylinder power (Dc), plus the sphere power (Ds). Mathematically, this can be expressed as:

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

By applying this formula, you can calculate the power at any meridian, regardless of the cylinder axis orientation.

When calculating, it’s critical to enter the formula into your calculator properly. Be sure your calculator is set to “degree” vs. “radian.” During calculations, do not round until the very end (the examples shown below show only to the ten thousands, but keep all the numbers displayed on your calculator).

**Practical Applications and Examples**

Let’s explore a few practical examples to solidify our understanding of calculating lens power in various meridians.

**Example 1: -3.00 -0.75 x 052**

To find the power in the 180° meridian, we plug the values into the formula:

Dt = (sin 128)^2 x -0.75 + -3.00 =

Dt = (0.7880)^2 x -0.75 + -3.00 =

Dt = (0.6209) x -0.75 + -3.00 =

Dt = -0.47 + -3.00 = -3.47 D

**Example 2: -2.00 @ 019 and -3.00 @ 109**

To find the power in the horizontal meridian (180°), we need to determine the prescription:

-2.00 -1.00 x 019

Then, transpose it to confirm:

-3.00 +1.00 x 109

Now, the values are ready to be plugged into the formula:

Dt = (sin 161)^2 x -1.00 + -2.00 =

Dt = (0.3255)^2 x -1.00 + -2.00 =

Dt = (0.1059) x -1.00 + -2.00 =

Dt = -1.11 + -2.00 = -3.11 D

**Example 3: -4.50 -1.25 x 066**

To find the power in the vertical meridian (090°), we use the formula:

Dt = (sin 24)^2 x -1.25 + -4.50 =

Dt = (0.4067)^2 x -1.25 + -4.50 =

Dt = (0.1654) x -1.25 + -4.50 =

Dt = -0.2068 + -4.50 = -4.71 D

**OTI Key Pointers: **

Mastering the intricacies of lens power and meridians is a crucial aspect of being a skilled optician. By understanding the principles governing the 180° and 090° meridians, as well as the Powers in Oblique Meridians Formula, you can confidently navigate the world of ophthalmic lenses and provide your patients with the most accurate and tailored visual solutions.

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