Under what conditions does a convex mirror form a real image? 

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A convex mirror is made by applying a reflective coating on the outside of a piece of a curved surface. The center of curvature of and the focal point of the mirror are thus on one side of the mirror, but the object is on the other side. (Please see the attached reference link for the illustration.) 

When the light rays hit the mirror, they are reflected back in a way that that the angle of reflection (the angle the reflected ray makes with the normal to the surface) is equal to the angle of incidence (the angle the incident ray makes with the normal.) Because the mirror is convex, the reflected rays point away from the focal point of the mirror, or diverge. Therefore, the rays do not intersect, but their extensions do intersect, forming a virtual image. This is true no matter how far away the object is located from the mirror. Again, please see the reference link for the diagram of the image formation by a convex mirror.

As discussed above and can be seen from the diagram, it is impossible to obtain a real image in a convex mirror. The convex mirrors always form virtual images.

 

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