If your glasses lenses have a +2.00D SPH and -1.75CYL. Does this mean the lens is composed of both cylindrical lenses and spherical lenses?
For the Spherical lenses, if the diopetres is 2. The focal point should be 0.5m. But the distance from the lens to the retina is much less than 0.5m. So am i right to assume that the cornea and inner len of the eye perform the remaining refraction of light?
Yes, prescription glasses have exactly enough power to correct the eyes' refraction deficiency. Meaning the glass lens+ the eye lenses = focus on the retina.
The cylindrical lenses have either positive or usually negative (whichever makes the glass less heavy) diopter and they need to have an axis of the cylinder too.
In your case, the lens with both spherical and cylindrical powers is built in one lens. Like if we set the X-axis main axis of the glass each point on the surface of the glass should have a thickness.
$$ X_{sum}= X_{sph}\pm X_{cylinmder}$$ The interesting thing is almost all the work of glassmaking is done by robots these days. they pick up the half-made glasses from the racks themselves with the front side of the glass already having some diopter built into it. The final carving is done only on the back side.
It gets a bit more complicated with bifocal glasses and even some prism glasses. the prescription also should show the distance between the eyes for reading. Which is annotated by PD.
Here is a lens being carved in the Zeiss plant.
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This is the 0 and 180 degree -2.25 cylindical lens.
Normally, an eye has an optical system (lens, cornea etc.) that (in its relaxed state) focuses light coming from infinity (parallel rays) onto the retina, being some 2.5cm behind the lens. This means that a healthy eye functions as a +40 diopters optics.
Glasses are used to augment the eye's optics to compensate for deficiencies in your eye sight, not to replace them. So you always have the combination of the glasses plus the eye.
If you need +2.0 diopters glasses, that means that your eye, to achieve focus on the retina, needs rays that already converge into your eye, rays that meet 0.5m behind the lens. Or you can say that your eye only achieves +38.0 of the necessary +40.0 diopters, and requires additional +2.0 diopters in the glasses you are to wear.
Now, in addition to the spherical +2.0 diopters, you also mention a cylindrical correction. You haven't given the axis value, so for the moment let's assume it is horizontal. Then, if you do a horizontal cross-section through the glasses, you'll see a geometry that achieves the combination of +2.0 and -1.75 diopters, being +0.25, meaning a nearly flat glass profile, while in a vertical cross-section, the cylinder part is ignored, and you'll see a profile matching +2.0 diopters.
If you look through a narrow vertical slit (so you can neglect the horizontal-focusing properties of your eye), using +2.0 glasses will give you a clear focus, while with a horizontal slit, +0.25 will do.
And the axis value just tells you to rotate the two maximum-refraction and minimum-refraction axes by the appropriate amount.
