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### Miscellaneous Information

*a. LensTtilt*: The position of the optical center will vary with the tilt of the lens before the eyes. The ideal tilt of standard lenses is 8 degrees in on the bottom of the lens. Such a tilt places the optical center 4mm below the center of the pupil when the line of sight passes normally through the lens surface.

When the lens is tilted, the incident light strikes the lens obliquely, inducing marginal or radial astigmatism even though the light passes through the center of the lens.

The change in power of the sphere through tilting is determined by the formula:

F (1 + 1/3 sin

^{2}a). The created cylinder power is determined by the formula: F (tan

^{2}a), where a = the angle of tilt.

If a cylinder lens is tilted on its axis, no actual sphere power is induced however the total new cylinder power is increased by the formula previously noted.

The effect of tilting a minus spherical lens is the production of minus cylinder at the axis of rotation - 180 degrees. The cylinder power increases with both the degree of the tilt and the power of the lens.

A simplified formula to determine the change in sphere power is to take (1/10 the amount of tilt)

^{2}= the percentage of power added to the original sphere. The increase in the cylindrical correct is approximately equal to 3x the induced sphere increase.

Examples of simplified formula:

A +3.00D sphere tilted 20 degrees will result in what spherical power increase? - (20/10)

^{2}= 4%, .04 x 3.00D = 0.12D

A +3.00D sphere tilted 20 degrees will result in a compound effect of +3.12 combined with +0.40 cylinder. Simplified formula - (20/10)

^{2}= 4%, .04 x 3.00D = 0.12D

A +1.00D sphere tilted 45 degrees will result in a compound effect of +1.16, combined with +1.00 cylinder.

An under corrected myope will therefore be able to obtain better distance acuity by tilting his glasses. For example, the effect of tilting a –10.00 diopter lens 10 degrees along the horizontal axis results in an optical correction of –10.10 –0.31 x 180 which gives a spherical equivalent of –10.25D. If the same lens is tilted 30 degrees, the resultant effective optical correction is –10.83 –3.33 x 180 with a spherical equivalent of –12.50 diopters. This is why an under-corrected myope tilts their spectacles to attain better distance vision.

**Question**: A point source is placed 50 cm from a cylindrical lens of +5.00 diopters, axis 90 degrees. Find the position and direction of the line foci formed by this lens.

**Answer**: Do this yourself to understand how this works.

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