Len’s Power & Focal Length Calculation

The power of a lens is measured in dioptic power by quarters. The power can be either PLUS or MINUS. A plus lens will converge light to focal point and a minus lens will diverge light to an imaginary focal point (focal point is located in front of the lens by tracing the diverging light rays backwards). You can find the power of a lens if you know the focal length with the formula

D (power in diopters) = 1 / f (focal length)

For example if light rays pass through a lens and they CONVERGE to a point at a point 1.50 mm from the lens your power would be;

D = 1 / 1.50 = +0.67

The power is PLUS because the light is CONVERGING. Remember the stronger a prescription is the quicker it will converge or diverge light. So, the longer the focal length the lower the power of the lens, the shorter the focal length the higher the power of the lens.

For example a lens with a focal length of 0.25 mm would be stronger than a lens with a focal length of 0.50 mm.

D = 1 / 0.25 = 4 diopters

vs

D = 1 / 0.50 = 2 diopters

You can also find the focal length of a lens if you know the power. By rearranging the variable in the formula you would get f = 1 / D. Let’s say you know that the power of a lens is -3.50 and need to know the focal length. This can be calculated by;

f = 1 / -3.50 = -0.285 mm

The minus sign is important to know if the light rays are diverging or converging. In this example since the POWER of the lens is in MINUS form we already know that it is DIVERGING.

Practice Problems

1) What is the power of a lens that converges at a point 0.15 mm behind a lens?

2) What is the power of a lens that diverges light at a point 1.10 mm in front of a lens?

3) What is the focal length of a 5.00 diopter lens?

4) Light comes to a focal length 0.75 mm in front of a lens, what is the power of this lens?

Answers

1) D = 1 / f = 1 / 0.15 = +6.67 (plus because it converges)

2) D = 1 / 1.10 = - 0.91 (minus because it diverges light)

3) f = 1 / 5 = 0.20 mm

4) D = 1 / 0.75 = - 1.33 (minus because it comes to a focal point IN FRONT of the lens which is from diverging light).

Spherical Equivalent

The equation for spherical equivalent gives us the refractive power of the eye in SPHERICAL form by taking half the CYL power and adding it to the SPH power.

Dse = (CYL/2) + SPH

For example if you have the following RX: -1.00 -2.00 090 the spherical equivalent would be half of the CYL (-2.00 divided by 2 = -1.00) plus the SPH power (-1.00) of the lens. This would give you a total of -3.00 D of power.

Practice Problems

What are the Spherical Equivalents of the following RXs?

1) -2.00 -1.00 090

2) Plano -2.00 090

3) +1.50 -1.50 090

4) +1.00 -2.00 090

Answers

1) -2.50

2) -1.00

3) +0.75

4) Plano (PL)