cOnCavE & cOnVex .....

Convex and Concave Mirrors
Convex and concave mirrors are known collectively as spherical mirrors, since their curved reflecting surfaces are usually part of the surface of a sphere. The concave type is one in which the midpoint or vertex of the reflecting surface is farther away from the object than are the edges. The center of the imaginary sphere of which it is a part is called the center of curvature and each point of the mirror surface is, therefore, equidistant from this point. A line extending through the center of curvature and the vertex of the mirror is the principal axis, and rays parallel to it are all reflected in such a way that they meet at a point on it lying halfway between the center of curvature and the vertex. This point is called the principal focus.

The size, nature, and position of an image formed by a concave spherical mirror depend on the position of the object in relation to the principal focus and the center of curvature. If the object is at a point farther from the mirror than the center of curvature, the image is real (i.e., it is formed directly by the reflected ra

ys), inverted, and smaller than the object. If the object is at the center of curvature, the image is the same size as the object and is real and inverted. If the object is between the center of curvature and the principal focus, the image is larger, real, and inverted. If the object is inside the principal focus, the image is virtual, erect (right side up), and larger than the object. The position of the object can be found from the equation relating the focal length f of the mirror (the distance from the mirror to the principal focus), the distance do of the object from the mirror, and the distance di

of the image from the mirror: 1/f=1/do+1/di. In the case of the virtual image, this equation yields a negative image distance, indicating that the image is behind the mirror. In the case of both the real and the virtual image, the size of the image is to the size of the object as the distance of the image from the mirror is to the distance of the object from the mirror.
In a convex spherical mirror the vertex of the mirror is nearer to the object than the edges—the mirror bulges toward the object. The image formed by it is always smaller than the object and always erect. It is never real because the reflected rays diverge outward from the face of the mirror and are not brought to a focus, and the image, therefore, is determined by their prolongation behind the mirror as in the case of the plane mirror.

ImAgEs....

Real Image Formation
If a luminous object is placed at a distance greater than the focal length away from a convex lens, then it will form an inverted real image on the opposite side of the lens. The image position may be found from the lens equation or by using a ray diagram.

If the lens equation yields a negative image distance, then the image is a virtual image on the same side of the lens as the object. If it yields a negative focal length, then the lens is a diverging lens rather than the converging lens in the illustration. The lens equation can be used to calculate the image distance for either real or virtual images and for either positive on negative lenses. The linear magnification relationship allows you to predict the size of the image.

Virtual Image Formation

A virtual image is formed at the position where the paths of the principal rays cross when projected backward from their paths beyond the lens. It does not form a visible projection on a screen, it is no sense "imaginary". A reduced virtual image if formed by a single negative lens regardless of the object position. An enlarged virtual image can be formed by a positive lens by placing the object inside the principal focal point.

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Diagram that explains how and where mirrors and lenses form images. The paths of light rays are represented by lines, and standard constructions are used for certain rays that have known paths through a mirror or lens system. For example, a ray that arrives parallel to the principal axis of a converging lens will pass through its principal focus on the far side of the lens; a ray passing through the centre of a lens is not deviated. If the paths of two rays from a single point on an object are plotted through a lens or mirror system, an image of that point will be formed where the paths of those two rays cross.