Difference between revisions of Diopters

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=== Cylinder ===

A cylindrical lens of focal power P <sub>cyl </sub> has a power P at the angle θ of its axis: <math>P = P_{cyl} ( \sin\theta)^2</math> ==== Axis ==== L' axis is usually in degrees modulo 180. It is common for 0 to be written as 180 in some regions. ==== Transposition ==== We can understand why there are two different ways to write a combination of spherical and cylindrical lens, using the Pythagorean trigonometric identity and the complementary angle identity: <math>( \sin\theta)^2 + (\cos\theta)^2 = 1</math> <math> - 90^{\circ}\right)}</math> <math>

A cylindrical lens of focal power P <sub>cyl </sub> has a power P at the angle θ of its axis: <math>P = P_{cyl} ( \sin\theta)^2</math>

==== Axis ====

L' axis is usually in degrees modulo 180. It is common for 0 to be written as 180 in some regions.

==== Transposition ====

We can understand why there are two different ways to write a combination of spherical and cylindrical lens, using the Pythagorean trigonometric identity and the complementary angle identity: <math>( \sin\theta)^2 + (\cos\theta)^2 = 1</math> <math> - 90^{\circ}\right)}</math> <math>P_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math>

We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (like subtracting 90 degrees, since the axis is modulo 180 degrees) to the axis, we get an equivalent combination.

~~P_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math>~~

We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (like subtracting 90 degrees, since the axis is modulo 180 degrees) to the axis, we get an equivalent combination.

For example, - 1 sph - 1 cyl 1 axis is the same as - 2 sph +1 cyl 91 axis.

@@ Line 90: / Line 90: @@
 === Cylinder ===
- A cylindrical lens of focal power P <sub>cyl </sub> has a power P at the angle θ of its axis: <math>P = P_{cyl} ( \sin\theta)^2</math> ==== Axis ==== L' axis is usually in degrees modulo 180. It is common for 0 to be written as 180 in some regions. ==== Transposition ==== We can understand why there are two different ways to write a combination of spherical and cylindrical lens, using the Pythagorean trigonometric identity and the complementary angle identity: <math>( \sin\theta)^2 + (\cos\theta)^2 = 1</math> <math> - 90^{\circ}\right)}</math> <math>
+A cylindrical lens of focal power P <sub>cyl </sub> has a power P at the angle θ of its axis: <math>P = P_{cyl} ( \sin\theta)^2</math>
+==== Axis ====
+L' axis is usually in degrees modulo 180. It is common for 0 to be written as 180 in some regions.
+==== Transposition ====
+We can understand why there are two different ways to write a combination of spherical and cylindrical lens, using the Pythagorean trigonometric identity and the complementary angle identity: <math>( \sin\theta)^2 + (\cos\theta)^2 = 1</math> <math> - 90^{\circ}\right)}</math> <math>P_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math>
+We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (like subtracting 90 degrees, since the axis is modulo 180 degrees) to the axis, we get an equivalent combination.
-P_{cyl}\right)(\sin{\left(\theta - 90^{\circ}\right)})^2</math>
- We can see that by adding the cylindrical power to the spherical power and inverting the cylinder and adding 90 degrees (like subtracting 90 degrees, since the axis is modulo 180 degrees) to the axis, we get an equivalent combination.
 For example, - 1 sph - 1 cyl 1 axis is the same as - 2 sph +1 cyl 91 axis.

Difference between revisions of Diopters

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