How Does Lens Shape Affect Focal Lengths?

[sskk221]

Let's say that there are three lenses A (all of which are semicircles: flat on one side, curved on the other). One lense is a short and curved D, another lense is a very elongated and narrow D (longer than the first lense), and the third lense is as long as the second lense but has a sharper curvature. How would you rank the focal lengths of these lenses? In other words, how is focal length of a lense related to its shape? More curved = shorter focal length? Longer lens = longer focal length?

 

[Stonebridge]

Generally, yes. The more the lens surface is curved, the shorter the focal length.
For a thin lens, there is a formula called the Lensmakers Formula which says
F=(n-1)[(1/R1) - (1/R2)]
F is the focal length of the lens
n is the refractive index of the material
R1 is the radius of curvature of the surface nearest the object
R2 is the radius of curvature of the surface farthest the object
For a flat surface, R is infinite and the 1/R term is zero.
This formula is an approximation for lenses which are not too thick.