Oblique Meridian & Off-Axis Power Calculator

How the power changes around one lens

For −2.00 −4.00 × 180 the power runs from the sphere alone along the axis to sphere plus cylinder at 90° from it:

The calculator's working line may show sin²(150°) where you expect sin²(30°). The two are equal: it takes the difference between the numbers as typed.

The formula

Using it for prism

Prentice's rule needs the power in the direction of decentration. For −1.00 −3.00 × 45 the calculator gives -2.50 D along 90, so an eye looking 10 mm below the optical centre gets 10 × 2.50 ÷ 10 = 2.50 Δ, base down.

Because the cylinder is oblique, the same decentration also produces prism sideways, about 1.50 Δ in this case (worked by hand: C × sin 45° × cos 45° × 10 ÷ 10). The sin² value gives the vertical part exactly; the sideways part needs the full calculation.

Edge thickness at a frame corner

Worked by hand for the same −2.00 −4.00 × 180 in a lens 52 mm wide and 40 mm deep. The lower outer corner lies about 37° from the horizontal, where sin²37° ≈ 0.36 gives about −3.45 D; the table above brackets it between -3.00 D at 30 and -4.00 D at 45.

Thickness grows with the power and with the square of the distance from the centre. The corner is about 33 mm out, the top and bottom 20 mm and the sides 26 mm, so 33² × 3.45 ≈ 3,760 beats 20² × 6.00 = 2,400 at the top and 26² × 2.00 ≈ 1,350 at the side: the corner is the thickest point of the edge even though the vertical meridian is the strongest. The lens thickness calculator turns a power and distance into millimetres.

Limits

• Plus-cylinder prescriptions must be transposed first; use the plus to minus converter.
• The result describes the lens surface along one meridian. A lensmeter reads only the two principal meridians.
• See the medical disclaimer.

Questions