Question

What factors determine the focal length of a lens?

Answer 1

Hint: The focal length depends on color because varying color alters wavelength, which converts the focus changes and henceforth focal length. It also depends on the curvature of the lens. The focal length of a lens is defined by the refractive index of the glass, the curvature radii of the surfaces, and the medium in which the lens remains.

Complete step-by-step answer:
Focal length is the characteristic of the lens. Curvature is described as the reciprocal of the radius of the circle describing the curve; the thicker the lens, the more potent it is and the smaller the focal length are. Also, the refractive index defines how much the light is twisted on entering a denser medium. Better lenses have greater refractive indices as they can be thinner for the same power.
The distance to the film does not affect the focal length. Several factors affect the focal length. They are the curvature (or radius) of the two lens coverings—besides the thickness of the lens and the refractive index of the glass.
The reason these factors affect the focal length is that a lens adjusts images due to refraction. This is the beam being turned at the air/glass surface. This bending is dependent on the incidence angle, which is determined by Snell's law. Its focal length will alter with the distance near the covering from the principal axis, turning different rays by varying quantities. This is what causes a lens focus.
So, focal length depends on the radius of curvature, the refractive index of lens material, and the medium's refractive index in which the lens is placed.

Note: Focal length is the length between the middle of the lens and the principal foci. To determine the lens's focal length, we should recognize the image distance (v) from the lens and the object distance (u) from the lens.
$\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}$