PAGE References to Optical Formulas Tutorial:  (first reference is to edition 1 / second reference is to edition 2).

OK folks, here it is -- what you've been waiting half a semester for -- something practical and understandable, and what we're here for!

We discussed the parts of the eye globe, and briefly covered the 'fact' that there is what we call a 'normal' eye. This eye has a length of 24 mm. The power of the front surface of the cornea is about 43D, and, if it were in air, the power of the crystalline lens at rest (its minimum power, not accommodating) would be about 20D. This adds up to 63D. But the 'schematic' eye is said to have 60D of power: a little is lost when the ray exits the cornea into aqueous, since this means it is going from a material with higher index to a material of lower index. Go back to page (22 / 28) in the textbook for the average indices of refraction for the parts of the eye.

In the diagram above we have an eye that is at rest looking at an object that is 20 feet away. The rays that are reflecting off of the object and heading toward the eye are considered to be parallel, and since this is 'straight-ahead' gaze, the rays are traveling parallel to the axis of the cornea and lens. The eye has just exactly the correct power to bring the rays of light to a perfect focus on the retina of the eye.

So we will define the 'normal' eye as bringing parallel rays of light to a point focus on the retina when it is at rest. This is an emmetropic eye. If the eye at rest does not bring parallel rays to a point focus, it is ametropic.

Time for the textbook again. Please read pages (55-59 / 69-73).

Done? Just for a quick review of what is in the book:

1.       If the focus is behind the retina the eye has too ________ power, so we give it _______ power in the glasses lens to bring the image into focus on the retina.

      When the focus is behind the retina we say the eye is ________. A characteristic of _________ lenses is that they are used to correct for ____________.
                                       .
2.      If the focus is in front of the retina the eye has too ________ power, so we give it _______ power in the glasses lens to bring the image into focus on the retina.

    When the focus is in front of the retina we say the eye is ________. A characteristic of _________ lenses is that they are used to correct for ____________.
                                      .
3.     If the refracting surfaces (cornea and lens) have the power that is considered normal, but the eye globe is too long or to short, we say that the condition is __________.

    If the eye globe is 24 mm, but the refracting surfaces (cornea or lens) have too much or to little power, we say that the condition is ___________.

Now we look at Rx's. We can take any Rx, determine what the major powers are that we would put on an optical cross or that we would get on the power drum of the focimeter (lensometer), and we can tell what the lens is correcting for.

The Rx +3.00sph has +3.00D of power in every direction. Plus lenses correct for hyperopia, so the eye globe has 3D of hyperopia. (We do not know if the hyperopia is axial or refractive.) The eye at rest, without a glasses lens or contact lens, will bring parallel rays of light to a point focus behind the retina (if the light could get there.) What would be ON the retina, and therefore what would be seen, would be a fuzzy image.

The Rx -3.00sph has -3.00D of power in every direction. Minus lenses correct for myopia, so the eye globe has 3D of myopia. (We do not know if the myopia is axial or refractive.) The eye at rest, without a glasses lens or contact lens, will bring parallel rays of light to a point focus in front of the retina. What would be ON the retina, and therefore what would be seen, would be a fuzzy image.

How do you tell the fuzzy image from the hyperopic eye apart from the fuzzy image from the myopic eye? Without knowing more than that the image is fuzzy, you don't.

pl -3.00 x180:     

 The Rx pl -3.00 x180 has no power in one direction (horizontal) and -3.00D power in the other direction (vertical.) In one direction the eye needs no correction, in the other direction it is myopic. The eye at rest, without a glasses lens or a contact lens, will bring parallel rays of light to a line focus on the retina.  This gives a clear but distorted image, since the object was round, not a line.
 
 

 -2.00 -1.00 x180:     

 The Rx -2.00 -1.00 x180 has -2D of power in one direction and -3D of power in the other direction. In one direction the eye needs 2D of minus power to give a LINE focus, in the other direction it needs 3D of minus power to give a LINE focus.  Both of these focal lines occur in front of the retina in the uncorrected eye.  The image on the retina in the uncorrected eye is fuzzy and distorted.
 

Here are some problems for you to do. I filled in the answers to the first one. You fill in the answers to the rest.

                                    major powers        corrects for
1. Rx -1.00 -1.50 x180        (2 myopic lines)
2. Rx +1.00 +1.50 x180      
3. Rx +1.00 -1.00 x080       
4. Rx +3.25 +0.50 x135      
5. Rx pl -2.50 x062             
6. Rx -8.25 +1.00 x115       
7. Rx +1.00 -1.50 x002