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We have generally the following lenses in an optical shop near our locality. The lenses are usually prescribed by the Ophthalmologist.  There could be more but there are important.

1. Convex lenses : 
     People suffering from farsightedness or hypermetropia cannot see nearby objects clearly - rather, they cannot focus them clearly on retina.  So these converging lenses are prescribed. Depending on requirement, plano convex or double convex may be prescribed.

2. Concave lenses:
         People suffering from shortsightedness or myopia focus objects from distance, at a location in front of retina. So they are prescribed diverging lenses. Depending on requirement, plano concave or double concave may be prescribed.

3. Cylindrical lenses:
          People suffering from astigmatism have a trouble that they cannot focus correctly the objects in all directions.  Objects in vertical direction and horizontal direction are not both focused correctly at the same time. 
Depending on requirement plano cylindrical or total cylindrical lenses may be prescribed.

It is also possible that people are given bifocal lenses with two lenses combined in one spectacle.

There are more lenses like achromatic cameras to correct chromatic and spherical aberrations.

Lenses used in digital cameras, cell phones, PC cameras etc. Perhaps these are available in a different shop or directly from a dealer.

Convex if we have long sight doctor arrange this lens in our eye

concave  if we have short sight we use this