Plano-Convex Lens - Equation and Explanation

As the most common type of lens element, a plano-convex lens is a convergent lens with one flat surface and one convex surface that allow for light to be focused, collected and collimated. More specifically, the two surfaces of a plano-convex lense function together by focusing parallel light rays to a positive focal point. In doing so, the plano-convex lens forms real images that can be easily manipulated through the use of spatial filters. The asymmetry of plano-convex lenses reduces spherical aberration in applications where the image and object lie at unequal distances from the lens. The curved surface of a plano-convex lens has a focusing effect on light-rays, while the plane surface does not have a focusing or de-focusing effect. Some common applications for plano-convex lenses include light collimation or monochromatic processes that are required in pharmaceutical, industrial, robotics or defense sects.

To further enhance the capabilities of plano-convex lenses, antireflective coatings can be added to meet various optical systems, lasers and assemblies’ requirements. When used to cut steel or other thick materials, plano-convex lenses provide users with a greater cut width, which, as a result, supports the ability of the laser’s oxygen to enter the material and assist in the cutting rocess. Furthermore, when used for these cutting applications, plano-convex lenses have also been shown to provide a greater depth of field that is required to maintain a taperless edge.

The maximum sharp focus is achieved when the curved portion of the lens is oriented toward the object. Plano-convex lenses are used for applying focus to an optical system, and collimating diverging light beams. Plano-convex lenses have both positive focal lengths and an orientation that plays a crucial role in determining image quality. Low spherical aberration is obtained if the lens is orientated in a way that causes the collimated beam to enter or exit the curved surface, thereby making the plano side face towards the point source or focus.
 

Understanding Plano-Convex Lens Specifics

The minimum order quantity of plano-convex elements ranges between 100 and 1000 units.

The focal length of the lens can be calculated using a simple equation, as follows:

         1/f = (n-1) (1/R_f – 1/R_b)

In this equation, f is the focal length of the lens, whereas Rf and Rb represent the radii of curvature of the front and back bounding surfaces. For plano-convex lenses, Rf > 0 and Rb = ∞.

References

1. "Introduction to Lenses" – Florida State University
2. "Plano-Convex Lenses" – Ophir Optics
3. “Plano-Convex Lenses” – OPHIR
4. "Plano-convex lens, standard grade" - Sunex

This article was updated on the 26^th October, 2018.