Back Vertex Power. 

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

Back Vertex Power.

Remember when we were talking about having two lenses in an optical system, and I showed you that just by putting space between the two lenses we could change the total power of the optical system without changing the power of the lenses? Adding distance between the lenses increased plus power (or decreased minus power).

The same thing happens with lens surfaces. Adding distance between the surfaces increases the plus power of the lens, or decreases the minus power of the lens.

It also matters which side of the lens the ray of light goes through first. If the ray goes through the more curved side first, the thickness has more effect than if the ray goes through the less curved side first. The lens has more plus power (or less minus power) if it goes through the more curved side first. The lens has less plus power (or more minus power) if it goes through the less curved side first.

In the lenses above when a ray travelling parallel to the axis goes through the plano side first no refraction occurs. The only refraction occurs at the convex surface. If the surface powers in the lens above are plano and +5.00D, then the nominal power formula, pl + 5.00 = +5.00, gives the correct power for the lens. But when the same ray goes through the +5.00 side first it is not travelling parallel to the axis by the time it reaches the plano side. So the plano side is going to cause the ray to change directions again, and the power will be greater than +5.00.

Remember when we discussed the nominal power formula that I told you the definition of 'nominal' was "in name only, not in fact; as, the nominal leader." The nominal power formula is acceptable for minus glasses lenses because we make them as thin as we can. It is also acceptable for plus glasses lenses up to about +4.00D. Over +4.00D the lens thickness begins to affect the power of the lens. When lenses are made for other optical instruments or for special purposes where we are purposely increasing the thickness, then even lenses below +4.00D will be affected.

The formulas for front and back vertex power are on pages (151-154 / 84-86) of the Optical Formulas Tutorial. Please read these pages and follow the example. Do not do the exercises yet. Also, please do not use the approximation formula. Back in the days when we did not have little cheap calculators the approximation formula was "easier" to do with paper and pencil. With calculators it has no advantage over the exact formulas. Also, do not be concerned with the "equivalent power" on page (152 / 85). If you are having fun and want to continue reading after the course is over, THEN read about the equivalent power before you go on to Section VII!

Done reading? Did you follow the examples through?

We will do a thick plus lens from both sides, then a thin plus lens with the same surface powers. Then we will do the same for a thick and thin minus lens. Then we will do a lens that should be plano. Notice what is happening for each type of lens. We will make each lens out of a 1.50 plastic, so that the index will not affect anything. Ready?

  1. The first lens has a front surface of +10.00DS, and a back surface of -2.00DS. The nominal power of this lens is +8.00DS, right? First we will consider it with a thickness of 20 mm, then we will consider it at 5mm thick. (No, the 20 mm thick one will never go in a pair of glasses. It might do in a microscope or some other imaging system; in this case it would be bi-convex. This is an exaggeration so you can see what thickness does.)

    2.   The next two lenses are for you to do for an exercise. The answers will be on the link, as always. WORK ALL OF THEM. I know it is boring. Do it anyway.  Make a table for each one like the one above.  Notice the pattern of what happens depending on the thickness and the order in which the ray meets the surfaces.
     
  2. This lens has a front surface of +2.00DS, and a back surface of -10.00DS. The nominal power of this lens is -8.00DS, right? First we will consider it with a thickness of 20 mm, then we will consider it at 5 mm thick.

    3.  
  3. Now for the 'plano' lens. Front surface power of +6.00DS, back surface power of -6.00DS, first thickness 20 mm, second thickness 5 mm, all of 1.50 plastic.

    4.  
     

    Click here for the answers.
     
     

    OK, here is what I would like you to take away from this lesson.

    1. Be able to determine the front or back vertex power of a lens.
    2. We do not round this power to 1/8 diopter steps. The lab computer takes this calculation into account when it tells you what surface power to place on the back of the lens. This is not something that you will do when you order the lenses. It is not something that you need to keep in mind when you dispense the glasses. Since it is not something that you will order, or record on the wearer's records, you do not need to round it to eighths.
    3. Realize that the thicker the lens the more plus (less minus) power it has.
    4. Realize that the side that the ray goes through first is the one acted on by the thickness. So,
    5. If the first surface the ray goes through is the most curved surface (and convex) then the power will be more plus than if the first surface is the least curved surface. This, along with the fact that minus lenses in glasses do not get very thick, is the reason this is of interest in high plus Rx's, but not in high minus Rx's.
    6. The back vertex power is what the wearer of the glasses is seeing.
    7. The back vertex power is what the focimeter (lensometer) gives us when we place the glasses with the temples pointing away. The optics of the focimeter insures this.
    8. When we turn the glasses around and read the difference between the distance and reading powers for the nominal add power, we are taking the difference between front vertex powers. This is the correct way to read add power if the segment is on the front surface of the lens. In the increasingly rare instances where the bifocal segment is on the back surface of the lens, the differences should be read from the back, as the distance is.
    9. Front vertex power is used in Contact Lenses. (Do not ask me why. I do not know.)

    OK, go back to the Optical Formulas Tutorial and do the exercises on page (154 / 86). Check your answers in the back of the book.  Also, read pages 419-423 in Systems for Ophthalmic Dispensing, and do problems 8-13 on page 424.