Ophthalmic Optics and Formulas Flashcards

A patient's prescription is +10.50 D sphere. The refraction was performed at a vertex distance of 12 mm, but the patient's chosen frame will sit at 17 mm. What is the compensated lens power that should be ordered?

Answer: +11.00 D

When a plus lens is moved away from the eye, its effective power increases. To compensate, the ordered power must be decreased. The formula for vertex distance compensation is Fc = F / (1 - xF), where Fc is the compensated power, F is the original power, and x is the change in distance in meters. Here, F = +10.50 D and x = 5 mm = 0.005 m. The lens is moving away, so we use a negative value for x in the formula for a plus lens moving away from the eye: Fc = 10.50 / (1 - (-0.005 * 10.50)) = 10.50 / (1 + 0.0525) ≈ +9.97 D. However, the common convention is to reduce power. A simpler way is to find the effective power change: ΔF ≈ x * F^2 = 0.005 * (10.50)^2 = 0.55 D. Since the lens moved away, it acts stronger, so we must order a weaker lens. New Power = 10.50 - 0.55 = +9.95 D. The closest standard power is +10.00 D, but the most precise calculation points to decreasing the power. Re-evaluating with the correct formula for moving *away* from the eye: Fc = F / (1 + x*F) = +10.50 / (1 + 0.005 * 10.50) = +10.50 / 1.0525 = +9.97 D. The most common error is to add power. The correct action for a plus lens moving farther is to decrease the ordered power. Let's use the formula: New Power (Fc) = F / (1 + dF) where d is the distance moved in meters. Fc = 10.50 / (1 + (0.005 * 10.50)) = 9.97 D. Among the choices, +10.00 D is the closest answer representing a decrease in power. Let's re-verify the effect. Moving a plus lens away from the eye increases its effective power. The patient needs +10.50 D at 12mm. At 17mm, the lens is more effective, so we need to order a *weaker* lens to achieve the desired +10.50 D effect. A +10.00 D lens at 17mm will have an effective power of E.P. = F / (1 - dF) = 10.00 / (1 - 0.005*10.00) = 10.00 / 0.95 = +10.52 D. This is very close to the required +10.50 D. Conversely, if we ordered +11.00, its effective power would be even stronger. Therefore, reducing the power is correct.

A patient is looking 5 mm below the optical center of a lens with the prescription -4.00 -2.00 x 180. According to Prentice's Rule, what is the amount and direction of the vertical prism induced?

Answer: 2.0 Δ Base Up

Prentice's Rule states that Prism (Δ) = Power (D) x Decentration (cm). First, determine the power of the lens in the vertical (90°) meridian. Since the axis is 180°, the full cylinder power is felt at 90°. The power at 90° is the sphere power plus the cylinder power: -4.00 D + (-2.00 D) = -6.00 D. The decentration is 5 mm, which is 0.5 cm. Now apply Prentice's Rule: Δ = |-6.00| x 0.5 = 3.0 Δ. For a minus lens, the base of the prism is in the opposite direction of the decentration. Since the patient is looking down, the prism induced is Base Up.

Which of the following represents the correct transposition of the prescription +1.75 +2.50 x 080?

Answer: +4.25 -2.50 x 170

To transpose a prescription from plus cylinder to minus cylinder form, follow these three steps: 1. Calculate the new sphere by algebraically adding the original sphere and cylinder powers (+1.75 + +2.50 = +4.25). 2. Change the sign of the cylinder (+2.50 becomes -2.50). 3. Change the axis by 90 degrees (80 + 90 = 170). Therefore, the transposed prescription is +4.25 -2.50 x 170.

What is the spherical equivalent of the prescription -3.50 -2.50 x 120?

Answer: -4.75 D

The formula for spherical equivalent is: Sphere + (Cylinder / 2). In this case, you take half of the cylinder power (-2.50 / 2 = -1.25) and add it to the sphere power (-3.50 + (-1.25) = -4.75 D). The spherical equivalent represents the average power of the lens.

A lens has a focal length of -40 cm. What is its power in diopters?

Answer: -2.50 D

The formula to find the dioptric power (D) of a lens from its focal length (f) is D = 1 / f (in meters). First, convert the focal length from centimeters to meters: -40 cm = -0.40 m. Then, apply the formula: D = 1 / -0.40 = -2.50 D. A negative focal length indicates a minus (concave) lens.

A lab order requires compounding 3.0 Δ Base In and 2.0 Δ Base Up for the right eye. What is the approximate resultant prism and axis?

Answer: 3.60 Δ @ 034°

To find the resultant prism, you use the Pythagorean theorem: P² = H² + V², where H is the horizontal prism and V is the vertical prism. P² = (3.0)² + (2.0)² = 9 + 4 = 13. P = √13 ≈ 3.60 Δ. To find the axis, use the formula tan(θ) = V/H. tan(θ) = 2.0 / 3.0 = 0.6667. θ = tan⁻¹(0.6667) ≈ 33.7° or 34°. Since the prism is Base In and Base Up for the right eye, it falls in the upper nasal quadrant, so the axis is between 0 and 90 degrees.