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Reflection by a Concave Surface

Reflection by a Concave Surface

A concave surface may be looked upon as made up of a number of planes inclined to each other. Parallel rays falling on a concave wiaror are reflected as convergent rays, which meet on the axis at
a point (F, Fig. 3) called the principal focus, midway between the rnirror and its optical centre C. The distance of the principal focus from the mirror is called the focal length of the mirror.

If the luminous point be situated at F, then the diverging rays would be reflected as parallel to each other and to the axis.
If the luminous point is at the centre of the concavity of the mirror (C), the rays return along the same lines, so that the point is its own image.

Fig 3

If the luminous point be at A the focus will be at a, and it is obvious that if the luminous point be moved to a, its focus will be at A; these two points therefore, A and a, bear a reciprocal relation to eachother, and are called conjugate foci.
If the lumiinous point is beyond the centre, its conjugate focus is between the principal focus and the centre.

If the luminous point is between the principal focus and the centre, then its conjugate is beyond the centre ; so that the nearer the luminous point approaches the principal focus, the greater is the distance at which the reflected rays meet.

If tile luminous point be nearer thc mirror than F, the principal focus, the rays will be reflected as divergent, and will therefore never meet: if, however, we continue these diverging rays backwards, they will unite at a point (x) behind the mirror; this point is called the virtual focus, and an observer situated in the path of reflected rays will receive them as if they came from this point.

Fig 4

Thus it follows that:

Concave mirrors produce two kinds of images or none at all, according to the distance of the object, as may be seen by looking at oneself in a concave mirror. If the mirror is placed nearer than its principal focus, then one sees an enlarged virtual image, which increases slightly in size as the concave mirror is made to recede; this image becomes confused and disappears as the principal focus of the mirror is reached; on moving the mirror still further away (that is beyond its focus) one obtains an enlarged inverted image, which diminishes as the mirror is still further withdrawn.

Reflection by a Convex Surface
Parallel rays falling on such a surface are reflected as divergent, hence never meet; but if the diverging rays thus, fortned are carried backwards by lines, then an imaginary image is formed which is called negative, and at a point called the principal focus(F).

Foci of convex mirrors are therefore virtual; and the image, whatever the position of the object, is always virtual, erect, and smaller than the object. The radius of the mirror is double the principal of the focus.

Fig 5