NOCE Ophthalmic Optics and Formulas Questions and Answers — Questions and Answers

Question 1: 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?

+11.00 D (Correct answer)
+10.00 D
+10.50 D
+9.95 D

Correct 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.

Question 2: 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?

2.0 Δ Base Up (Correct answer)
2.0 Δ Base Down
3.0 Δ Base Up
3.0 Δ Base Down

Correct 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.

Question 3: Which of the following represents the correct transposition of the prescription +1.75 +2.50 x 080?

+4.25 -2.50 x 170 (Correct answer)
+4.25 +2.50 x 170
-0.75 -2.50 x 170
-0.75 +2.50 x 080

Correct 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.

Question 4: What is the spherical equivalent of the prescription -3.50 -2.50 x 120?

-2.25 D
-4.75 D (Correct answer)
-6.00 D
-3.50 D

Correct 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.

Question 5: A lens has a focal length of -40 cm. What is its power in diopters?

+2.50 D
-2.50 D (Correct answer)
+0.025 D
-0.025 D

Correct 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.

Question 6: 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?

5.00 Δ @ 056°
5.00 Δ @ 034°
3.60 Δ @ 146°
3.60 Δ @ 034° (Correct answer)

Correct 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.

NOCE Ophthalmic Optics and Formulas Questions and Answers

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?