Why is the convex mirror called as the diverging mirror?

A convex mirror is called a diverging mirror because it causes parallel rays of light that strike its surface to spread out or diverge away from each other after reflection.

To understand why a convex mirror is called a diverging mirror, it's essential to first grasp the basic principle of how it works. A convex mirror is a spherical mirror with a reflective surface that bulges outwards towards the light source. Its shape is the opposite of a concave mirror, which curves inwards. The outward-curving surface is the key to its diverging properties. 

When a beam of parallel light rays, such as those coming from a distant object, hits the surface of a convex mirror, each ray reflects off the surface at a slightly different angle. Because the surface curves away from the incoming light, the reflected rays are forced to spread out. They do not converge to a single focal point in front of the mirror like they do with a concave mirror. 

Instead, if you trace these diverging rays backwards, they appear to originate from a single point behind the mirror. This point is known as the virtual focus or principal focus (F) of the convex mirror.

This diverging property of the convex mirror has several practical consequences. The most notable is the kind of image it forms. Because the reflected rays never actually meet, a convex mirror always forms a virtual image, which means the image cannot be projected onto a screen. This image is always upright and smaller than the object. 

This is a key difference from a concave mirror, which can form both real and virtual images. The smaller image size also means that the convex mirror provides a very wide field of view. The rays from a large area are reflected and compressed into a small, manageable image. This is the primary reason why convex mirrors are widely used as side-view mirrors in cars and as security mirrors in stores. 

The wide field of view allows a driver to see a much larger area behind and to the side of the vehicle than they would with a flat mirror, which is crucial for safety. Similarly, in a store, it allows a single mirror to monitor a wide area, deterring theft. 

The term "diverging mirror" is a descriptive and accurate name that precisely captures the fundamental optical property of a convex mirror—its ability to spread out light rays. This property, in turn, dictates the type of image it forms and its widespread applications in our daily lives.