# How can you tell if a surface is convex or concave before drawing it?

• channel1
In summary, to determine if a spherical refracting surface is convex or concave, you need to check the signs of the radius of curvature (R) and the distance from the center of curvature to the surface (s). If R and s have opposite signs, then the surface is convex, and if they have the same signs, then the surface is concave. This information can be found in the given indices of refraction, center of curvature, s, and s' of the surface.
channel1

## Homework Statement

How do you tell if a spherical refracting surface is convex or concave before drawing a ray diagram? (given the indices of refraction, center of curvature, s, and s')

## Homework Equations

"A convex surface is one that bulges out in the middle toward the object, so that its center of curvature is on the opposite side of the surface from the object. Therefore a surface is convex if R and s have opposite signs."
http://www.physnet.org/modules/pdf_modules/m222.pdf

## The Attempt at a Solution

but according to my diagrams from class, an object for either convex or concave surfaces can be inside the surface so the above quote can't be true...

If R and s have the same signs, then the surface is concave. If R and s have opposite signs, then the surface is convex.

## 1. How can you visually determine if a surface is convex or concave?

A convex surface curves outward, like the exterior of a sphere, while a concave surface curves inward, like the interior of a bowl. To determine if a surface is convex or concave, you can visually examine the curvature of the surface and see if it bulges outward or inward.

## 2. What is the mathematical definition of a convex surface?

A surface is considered convex if every line segment connecting any two points on the surface lies entirely within the surface or on its boundary. In other words, the surface does not have any indentations or holes that would allow a line segment to pass through it.

## 3. How can you use a straight edge to determine if a surface is convex or concave?

Place a straight edge on the surface and observe if there are any gaps between the straight edge and the surface. If there are no gaps, the surface is convex. If there are gaps, the surface is concave.

## 4. Can the direction of curvature on a surface determine if it is convex or concave?

Yes, the direction of curvature can help determine if a surface is convex or concave. On a convex surface, the curvature will always be pointing outward, while on a concave surface, the curvature will always be pointing inward.

## 5. How can you tell if a surface is convex or concave before drawing it?

You can determine if a surface is convex or concave by examining its defining characteristics, such as its shape and curvature. Alternatively, you can use mathematical equations and algorithms to analyze the surface and determine its convexity or concavity.

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