Concave Mirror Image Formation at Center of Curvature

Understanding how a concave mirror forms an image requires considering the path of light rays. When an object is placed at the center of curvature (C), specific rules of reflection apply.

Ray Tracing Principles

• A ray starting from the object, passing through the center of curvature (C), strikes the mirror normally (perpendicularly).
• Such a ray reflects back along the same path towards C.
• Another ray from the top of the object, parallel to the principal axis, reflects through the focal point (F).
• The point where these reflected rays intersect forms the image.

Image Characteristics at C

When the object is precisely at the center of curvature (C):

• Position: The reflected rays traveling back through C from the object at C meet exactly at C. Hence, the image is formed at the center of curvature itself.
• Nature: Since the rays converge naturally (without needing virtual extensions) to form the image, it is a real image.
• Orientation: The image formed is inverted relative to the object. Thus, it is an inverted image.
• Size: Using the mirror formula, $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$, where $u = R$ (object distance) and $f = R/2$ (focal length), we find $v = R$. The magnification $m = -\frac{v}{u} = -\frac{R}{R} = -1$. A magnification of magnitude 1 indicates the image is the same size as the object.

Therefore, the image formed is real, inverted, and of the same size.