Difference Between Concave and Convex

Difference Between Concave and Convex

Mirrors and glasses are fascinating. Mirrors can allow you to see your reflection or see another person’s reflection from a different angle. Glasses can improve your sense of sight or correct any difficulty you may have with your vision. The invention of mirrors and eyeglasses paved the way for many scientific advances. To this day, these tools are still used in automobiles, medical devices, and educational tools.

But mirrors and eyeglasses are designed for this purpose by making them concave or convex. These two shapes are often interchangeable, perhaps because of the play on words. But, what does concave and convex mean? If you’re wondering, you’ve come to the right article. This article will give you definitions of concave and convex and explain each of them to you. We will also look at the different aspects of these terms and how they are understood in different fields. We hope that at the end of this article you will be able to tell what is concave and convex and how their disparity and terminology affect the functionality of objects.

What is Convex and Concave?

What is convex and concave? To answer this question, it will be useful to determine the common usage of these terms. Concave and convex are two forms. They are normally used to elucidate eyeglasses, lenses, or any optical object. In mathematics, they are used to call up graphs with the aperture facing upwards or downwards.

These two terms are adjectives used to refer to a curved line. Think of concave and convex parts as portions of a spherical or circular shape. However, these terms do not strictly refer to round figures. They can also refer to polygons, which are shapes with edges.

Concave and Convex Definition

What is the definition of concave? What is the meaning of convex? What is the difference between concave and convex? Let’s start by understanding their etymology.

Concave comes from the Latin word “con” which means “together” and “cavus” which implies “hollow”. From the Latin “concavus”, the word was invented at the end of Middle English as “concave”, which is the word we use now.

Convex, surprisingly, shares almost the same meaning depending on the etymology. It is derived from the Latin word “convexus”, which means arched or domed. If they share the same definition based on their etymology what is the difference between convex and concave?

According to their grammatical definition, concave defines a figure that curves inward. Their closest example is hourglass. Conversely, convex refers to a shape that curves outward. The closest example is football.

According to dictionaries, the concave is a term that can function either as an adjective or as a verb. As an adjective, it describes an object or surface that curves inward or moves inward. As a verb, it refers to the act of forming to curl or dig in. Convex acts as an adjective as well as a verb, except that it refers to an object or surface that curves outward. It also means to have a shape that imitates a bulb or to become bulbous in shape. As a verb, it shares the definition with concave.

How does the difference between concave and convex mirrors or glasses affect their function? In Optics, the convex and concave definition focuses on image formation and the passage of light. In a convex lens (also called a positive lens), the figure is formed by the focusing or convergence of light. In a concave lens (also called a negative lens), the figure is formed by diverging or spreading the light. It is, therefore, preferable to use a convex lens if you want nearby objects to appear larger. It is used to create eyeglasses for people with farsightedness. If you want close objects to appear smaller, you should use a concave lens. This type of lens is therefore used to make glasses for people who are short-sighted.

In mathematics, polygons are classified as concave or convex depending on their angular measurement. If the inside angles of the polygon are less than 180 degrees, then it is a convex polygon. Nevertheless, it is the other.

In mathematical functions, a function with a variable is concave if the line segments connecting two separate points are not located above the graph. Therefore, a function with a variable is convex if the line segments connecting the two points of the function are not below the graph.

In finance, convexity is called the measure of the degree of the curve in a bond price/yield relationship. It illustrates how the duration of the bond is affected by the rise or fall in the interest rate. When the bond yield curve has negative convexity, it is considered to be concave.

Concave and convex are found in various references in several areas. These terms provide a good description and are often used in the literature. Ultimately, the difference between concave and convex has something to do with shape, regardless of the field in which it is used. 

Concave vs Convex Comparison Table

To further illustrate the distinction, here is a table showing the main differences between the two terms:

Basis of Comparison   Concave Convex
Etymology Concavus Convexus
Direction Curving inward Curving outward
Reference in Optics Focuses or converges the light Diverges or spreads out the light
Reference in Math functions Line segments are not above the graph Line segments are not below the graph
Reference in Finance Convexity Negative convexity

It is true that there are many disparities in these terms. However, because they usually refer to a form and form imply images, individuals often have difficulty evoking what they mean. Therefore, when terms are explained to someone, it is useful to use drawings and illustrations to help clarify the distinction.

Conclusion of the Main Difference Between Concave vs Convex

How are the terms different? Well, the differences will depend on the area in question. However, you can use working words to speed up your memory about the boundary between these two areas. You can use “out” as a working word for “concave” and “in” as a working word for “convex”.

You can visualize them in the same way as you visualize larger and smaller symbols. Knowledge of these terms and their use in various fields will be very helpful in grasping other complex concepts. We hope that the article has clarified the difference between convex and concave so that you can overcome any confusion that may arise.