Lens-maker’s formula

Lenses are transparent mediums bounded by two surfaces; of which, at least one must be curved. When the gap between two surfaces of a lens is very small, it is considered thin. When the focal length is positive, a lens will be converging; if it is negative, it will be diverging. As a consequence, we can conclude that a convex lens does not have to be a converging lens and that a concave lens does not have to be diverging. The lens-maker’s formula allows us to calculate a value for every lens. This topic will demonstrate how it works. Let’s get started!

What is the Lens-maker’s formula?

A lens is made of a transparent material and used to refract light. Surfaces can either consist of two curved surfaces or one curved surface and one plane surface. There are generally two types of lenses: converging (convex) and diverging (concave). Variables of the lens-maker’s formula are focal length, curvature radius of curved surfaces, and refractive index of the transparent material. With these components, lenses with specified focal lengths can be constructed. The formula can be applied to either type of lens. One must follow the sign convention when applying the lens-maker’s equation. 

Focal Length and Radius of Curvature Definition

Parallel light rays incident on a lens appear to diverge from a point, or to converge to a point, when incident upon a lens. We refer to this point as the focal point. In addition to the focal point, focal length refers to the distance between the optical centre and the focus.

Two spheres constitute a lens’s curved surfaces. We call these spheres’ radii, the radii of curvature of the lens. Different lenses have different radii.

What is a thin lens?

When a lens is thin, its thickness is relatively insignificant in comparison to its curvature radius. This is because the thickness (t) is substantially smaller than the two curvature radii (R1 and R2).

Lens formulas for concave and convex lenses consider the focal length, image distance, and object distance. 

The formula is as follows: 1/f = 1/v – 1/u 

In the above equation f is the focal length of the lens; v is the distance from the formed image; and u is the distance between the object and optical centre of the lens.

There are two types of thin lenses-

Understanding the difference between convergent and divergent lenses is necessary before developing a formula for thin lenses.

1. A convergent lens allows light rays parallel to an optical axis to pass through and converge at a common point behind it. This point is called the focal point (f) or focus.
2. Diverging lenses diverge light rays parallel to the optic axis through their centre. Optical illusions are created when the light sources appear to be coming from the same source (f) in front of the lens.

Lens-Maker Formula

There are a variety of optical equipment that utilise lenses according to their focal length. Lenses have a set focal length determined by the refractive index of the material and the curvature radius of the two surfaces. To help applicants better understand the lens-maker’s formula, Lens manufacturers use the lens-maker’s formula to design lenses with the correct focal length.

•  It is used to make the lenses of a particular power from the glass of a given refractive index.
• The lens maker formula is-

          1/f = (n-1) x (1/R1 – 1/R2)

Where f = focal length of a lens 

              n = refractive index

              R1 and R2 = the radius of curvature of both surfaces.

Limitations of the lens-maker’s formula

As a result of the lens-maker’s formula, the following limitations apply:

• A thin lens is needed for the space between refracting surfaces. Thicker lenses do not work better.
• It is essential that both sides of the lens use the same medium; inconsistent mediums will not work. 

Characteristics of Image formation with a thin lens

For convex lenses, knowing the thin lens formula is not enough. You must understand what happens to light when it passes through converging and diverging lenses.

1. Parallel rays will intersect at point f when they go through converging lenses on the opposite side.
2. In front of diverging lenses, parallel rays appear to emerge from point f.
3. It does not matter whether light rays travel through converging or diverging lenses.
4. Converging lenses emit light parallel to their axes when light enters through their focal points.
5. As with a diverging lens, light will also emerge parallel to its axis as it goes toward the focal point.

Negative focal lengths are associated with concave or divergent lenses. The image distance is also negative when the picture is displayed on the side where the object is positioned. In this case, the picture is virtual. Conversely, a convex or converging lens has a positive focal length.

Conclusion

The article explains about the lens maker’s formula. Lenses are transparent mediums bounded by two surfaces; of which, at least one must be curved. The lens-maker’s formula allows us to calculate a value for every lens. Variables of the lens-maker’s formula are focal length, curvature radius of curved surfaces, and refractive index of the transparent material. The lens maker formula is  1/f = (n-1) x (1/R1 – 1/R2).