Nominal power formula.

Nominal power formula

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

I looked up the word 'nominal' in my medium-sized Webster's dictionary. Meaning #3 is "in name only, not in fact; as, the nominal leader." If you go to the lumber yard to buy 2x4's, what will you get? Lumber with dimensions of 2" by 4"? I don't think so! You get lumber with dimensions 1.75" x 3.50". Right? 2x4 is the nominal dimension of the lumber, but the lumber is not, in fact, that size.

Well, here we have the nominal power formula for our lenses. What does this mean? Does it mean that the lens will not really be the power that we get from this formula?

Yup, that is EXACTLY what it means!

What actually determines the power of a lens?

  1. The curvature of the front surface.
  2. The curvature of the back surface.
  3. The material the lens is made from.
  4. The material on each side of the lens (may be the same on each side, or may be two different materials).
  5. The thickness of the lens.
  6. The wavelength of the light going through the lens
  7. Which surface the ray of light enters first.
OK, you say, we have taken care of #3, the material of the lens, and #1-2, the curvatures of the surfaces, when we determined the surface power of the lens. And we are taking care of #4 by assuming that the lens is in air. #6, you may remember, is taken care of by assuming that the index of refraction is for yellow light, because that is the color that our eye is most sensitive to. What about #5 and #7?

We will deal with #5 and #7 later in the semester. We did not really 'fix' numbers 4 and 6, we only made assumptions about them. We DO need to remember that we are making assumptions about them. So, we have a NOMINAL power formula that uses just the surface curves of the lens. Some people call this the thin lens power formula, because it assumes that the lens has no thickness, so the thickness will not affect the power of the lens. This nominal power formula is fine for our glasses lenses for a lens power that is less than about +4.00 D; above that the assumption that the lens thickness is negligible is no longer valid.

Now, go back and re-read those paragraphs. There are some really good test questions there. For glasses lenses, what lens powers are the nominal lens formula good for? What effects the power of a lens? What wavelength of light is the index of refraction computed for? . . .

We used curvature and lens material index to find the power of each surface. Now we will find the lens power from the surface powers.

The nominal lens formula says that you can add together the powers of the front and back surfaces of the lens, and you will have the nominal power of the lens.

Look at page 32 of Optical Formulas Tutorial Ed 1 or page 47 of  Optical Formulas Tutorial Ed 2.  When we defined surfaces, we defined a concave surface as having minus power and a convex surface as having plus power. Go back and check these definitions again.

Now look at the BENT design lenses diagrammed on page (32 / 47). The first one, labeled plano power, has one plus surface and one minus surface, and the curvatures of the two surfaces are the same. The second and third lenses also have one plus and one minus surface.  In the lens where the minus surface is more curved and therefore has more power than the plus surface, the lens has minus power. In the lens that has a plus surface is that is more curved than the minus surface,the plus surface has more power and the lens is a plus lens.

Now look at the FLAT lens designs on page (32-33 / 47). In each of the lenses where both surfaces are convex, both surfaces are plus surfaces, and the lens will be a plus power lens. In the lenses where both surfaces are concave, the lenses are minus power lenses.

Read through page (33 / 50), and do the exercises that follow. You add the surfaces together for the first set; for questions (5-8, 20-23)  you need to remember to subtract the power of the surface you know from the power of the lens. For question (4 / 19), you need to remember what equi-convex means.

Check your answers in the back of the book.

Here are a few more. DO THEM FIRST before you click on the answers.

  1. Find the nominal power if:

    2.  
  2. Find the back surface if

    3.  
  3. Find the front surface if

    4.  
  4. I need a lens with power +3.50D. If I use a lens blank with a front surface of +8.00D, what back surface do I need to make?

    5.  
  5. I have a lens with a front surface of +9.25D and a back surface of -2.25D. What is the power of the lens?

    6.  
  6. I want my lens to have a power of -3.00D. What back surface do I need if the front surface is +8.00D?
The answers are here.





Click here for  Radius of Curvature, Surface power, if you have not done it already.

 Click here for  Lensmaker's Equation.  Do Radius of Curvature first.



 
 
 

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