Section 3.1: Prismatic Effects & Prentice's Rule

Section 3.1: Prismatic Effects & Prentice's Rule

An understanding of prismatic effects is fundamental to the practice of opticianry. Spectacle lenses are not merely devices that focus light; they are also optical systems that can redirect light. When a patient looks through any point of a lens other than its optical center, they experience a prismatic effect. In this section, we will explore the physics of prisms, define the prism diopter, introduce Prentice's Rule, and examine how decentration induces prismatic effects in plus and minus lenses.

Optical Prisms and Light Refraction

An optical prism is a transparent, wedge-shaped optical medium with non-parallel surfaces. The thickest part of the prism is called the base, while the thinnest part is called the apex.

When light passes through a prism, it is refracted (bent) according to Snell's Law. Because the surfaces are not parallel, light is bent toward the base of the prism. However, when an observer looks through a prism, they perceive the light as coming from a different direction. Because our visual system projects light rays straight back, the virtual image seen by the patient is shifted toward the apex of the prism.

This behavior is a crucial concept for the National Opticianry Competency Exam (NOCE):

• Light rays bend toward the base.
• Visual images shift toward the apex.

In clinical practice, prisms are prescribed to manage binocular vision disorders, such as strabismus (misaligned eyes) and phorias (tendencies for the eyes to misalign), by shifting the image to align with the eye's resting position, thereby preventing diplopia (double vision) and asthenopia (eyestrain).

The Prism Diopter (Δ)

The unit of measurement for prismatic power is the prism diopter, denoted by the Greek letter delta (Δ). One prism diopter is defined as the power of a prism that displaces a ray of light by 1 centimeter at a distance of 1 meter from the prism.

The relationship can be expressed by the formula: $\text{Prismatic Power } (\Delta) = \frac{\text{Displacement (cm)}}{\text{Distance (m)}}$

Example Table of Lateral Displacement

Base Directions and Patient Orientation

To specify how a prism should be placed in front of an eye, opticians use four standard base directions:

1. Base In (BI): The base of the prism points nasally (toward the patient's nose).
2. Base Out (BO): The base of the prism points temporally (toward the patient's temple).
3. Base Up (BU): The base of the prism points superiorly (toward the patient's forehead).
4. Base Down (BD): The base of the prism points inferiorly (toward the patient's chin).

Prism direction is always described relative to the patient's face, not the optician's perspective. For example, a "Base In" prism for the right eye points to the left, while a "Base In" prism for the left eye points to the right.

Prentice's Rule

The optical center of a lens is the point where light passes through without bending. When a patient looks away from the optical center, the lens acts as a prism. The amount of induced prism depends on the power of the lens and the distance from the optical center. This relationship is quantified by Prentice's Rule:

$P = c \times D$

Where:

• $P$ is the induced prismatic power in prism diopters (Δ).
• $c$ is the decentration distance (the distance from the optical center to the pupil) in centimeters (cm).
• $D$ is the dioptric power of the lens in the meridian of decentration.

Decentration Unit Conversion

Lenses are measured in millimeters, but Prentice's Rule requires the decentration distance to be in centimeters. To convert millimeters to centimeters, divide by 10: $c\text (cm) = \frac{\text{Decentration (mm)}}{10}$ Failing to perform this conversion is the most common mathematical error made on the NOCE. For example, a decentration of 4 mm must be expressed as 0.4 cm in the formula.

Induced Prism in Plus and Minus Lenses

To determine the base direction of induced prism, we must examine the geometric shapes of plus and minus lenses:

• Plus Lenses: Thicker in the center and thinner at the edges. A plus lens can be modeled as two prisms joined base-to-base.
• Minus Lenses: Thicker at the edges and thinner in the center. A minus lens can be modeled as two prisms joined apex-to-apex.

Plus Lens: Base-to-Base

Because the bases meet at the optical center, moving away from the optical center in a plus lens means moving toward the bases. Therefore, the induced prism base direction is in the same direction as the decentration.

• Decentering a plus lens out induces Base Out (BO).
• Decentering a plus lens in induces Base In (BI).
• Decentering a plus lens up induces Base Up (BU).
• Decentering a plus lens down induces Base Down (BD).

Minus Lens: Apex-to-Apex

Because the apices meet at the optical center, moving away from the optical center in a minus lens means moving toward the bases, which are at the outer edges. Therefore, the induced prism base direction is in the opposite direction of the decentration.

• Decentering a minus lens out induces Base In (BI).
• Decentering a minus lens in induces Base Out (BO).
• Decentering a minus lens up induces Base Down (BD).
• Decentering a minus lens down induces Base Up (BU).

Summary of Induced Prism Directions

Calculation Examples

Example 1: Spherical Plus Lens

A patient is fitted with a $+6.00$ D spherical lens in the right eye. The optical center is positioned 3 mm temporal (out) relative to the pupil. Calculate the induced prism.

1. Convert decentration to centimeters: $c = 3\text{ mm} / 10 = 0.3\text{ cm}$.
2. Apply Prentice's Rule: $P = 0.3\text{ cm} \times 6.00\text{ D} = 1.8\Delta$.
3. Determine base direction: For a plus lens, the induced base direction is the same as the decentration direction (Out). Thus, the induced prism is $1.8\Delta$ Base Out (BO).

Example 2: Spherical Minus Lens

A patient is fitted with a $-5.00$ D spherical lens in the left eye. The optical center is positioned 4 mm nasal (in) relative to the pupil. Calculate the induced prism.

1. Convert decentration to centimeters: $c = 4\text{ mm} / 10 = 0.4\text{ cm}$.
2. Apply Prentice's Rule: $P = 0.4\text{ cm} \times 5.00\text{ D} = 2.0\Delta$.
3. Determine base direction: For a minus lens, the induced base direction is the opposite of the decentration direction (In). The opposite of In is Out. Thus, the induced prism is $2.0\Delta$ Base Out (BO).

Example 3: Spherocylinder Lens

A patient wears the following prescription: OD $+3.00 -2.00 \times 090$. The lens is decentered 5 mm out. Calculate the induced prism.

1. Identify the meridian of decentration. Decentration is horizontal (Out), which corresponds to the 180-degree meridian.
2. Determine the power of the lens in the 180-degree meridian. The prescription has sphere power $+3.00$ D at axis 90 degrees. This means the sphere power of $+3.00$ D acts at 90 degrees, and the full cylinder power of $-2.00$ D acts 90 degrees away, at 180 degrees. The total power at 180 degrees is the sum of the sphere and cylinder: $+3.00 + (-2.00) = +1.00$ D.
3. Convert decentration to centimeters: $c = 5\text{ mm} / 10 = 0.5\text{ cm}$.
4. Apply Prentice's Rule: $P = 0.5\text{ cm} \times 1.00\text{ D} = 0.5\Delta$.
5. Determine base direction: Since the net power in the horizontal meridian is plus ($+1.00$ D), the induced base direction is the same as the decentration (Out). Thus, the induced prism is $0.5\Delta$ Base Out (BO).

Binocular Combined Prism

When prism is present in both lenses, we must evaluate how they interact. Horizontal and vertical prisms behave differently when combined binocularly:

Horizontal Prism Interaction

Horizontal prisms move the images laterally.

• Base In / Base In (BI / BI) and Base Out / Base Out (BO / BO) are additive. If the right eye has $2\Delta$ BI and the left eye has $1.5\Delta$ BI, the net binocular prismatic effect is $3.5\Delta$ BI. This is because both prisms work together to relieve convergence (BI) or divergence (BO) demands.
• Base In / Base Out (BI / BO) is subtractive. If one eye has BI and the other has BO, the images are shifted in the same lateral direction (yoked prism). The net binocular effect is the difference between them.

Vertical Prism Interaction

Vertical prisms move the images vertically.

• Base Up / Base Down (BU / BD) is additive. If the right eye has $1\Delta$ BU and the left eye has $2\Delta$ BD, the net vertical prismatic effect is $3\Delta$ (specified as $3\Delta$ BU OD or $3\Delta$ BD OS). This is because shifting the image down in one eye and up in the other increases the vertical disparity between the two eyes.
• Base Up / Base Up (BU / BU) and Base Down / Base Down (BD / BD) are subtractive. If both eyes have Base Up prism, both images are shifted downward together. The net vertical imbalance is the difference between them.

Binocular Combining Rules