Question

Collect the information about the lenses available in an optical shop find out how the focal legnth of a lens may be determined by the given power of lens

Answer 1

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.

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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.
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Focal length of a lens  may be determined as :

       Power of lens = P  Dioptres
       Focal length = 1 / P  meters  or  100 / P  cm.
    
       focal length of a lens = (μ - 1) [1/R1 - 1/R2]

   where μ = refractive index of glass
         R1 and  R2 = Radius of curvature of spherical lens surfaces

Answer 2

1) convex lenses

people suffering from farsightednss or hypermetropia cannot see nearby objects clearly rather they so these converging lenses are prescribed . Depending on requirement Plano.

convex or double convex may be prescribed

2) concave lenses

people suffering from short sightedness or myopia focus an object's fron distance at a location in front of retina . so they are prescribed diverging lenses . Depending on requirement planoconcave 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 are not both focused correctly at the same time