A smooth and highly polished reflecting surface is called a mirror.
(i) Plane Mirror: A highly polished plane surface is called a plane mirror.
Different properties of image formed by plane mirror:
Size of image = Size of object
Magnification = Unity
Distance of image = Distance of object
Fig: Image formed by a plane mirror
A plane mirror may form a virtual as well as real image.
A man may see his full image in a mirror of half height of man.
When two plane mirrors are held at an angle θ, the number of images of an object placed between them is given as below:
(a) n = [(360° / θ) – 1 ], where 360° / θ is an integer.
(b) n = integral part of 360° / θ, when 360° is not an integer.
[A plane mirror may form a real image, when the pencil of light incident on the mirror is convergent. Children, during their play form an image of sun as wall by a strip of plane mirror.]
Kaleidoscope and periscope employ the principle of image formation by plane mirror.
If keeping an object fixed a plane mirror is rotated in its plane by an angle θ, then the reflected ray rotates in the same direction by an angle 2 θ.
Focal length as well as radius of curvature of a plane mirror is infinity. Power of a plane mirror is zero.
An image formed by a plane mirror is virtual, erect, laterally inverted, of same size as that of object and at the same distance as the object from the mirror.
(ii) Spherical Mirror: A highly polished curved surface whose reflecting surface is a cut part of a hollows at glass sphere is called a spherical mirror. Spherical mirrors are of two types:
(a) Concave Mirror: A spherical mirror whose bent in surface is reflecting surface, is called a concave mirror.
(b) Convex Mirror: A spherical mirror whose bulging out surface is reflecting surface, is called a convex mirror.
Fig: Concave mirror vs convex mirrorSome Terms Related to Spherical Mirrors are Given Below:
(i) Centre of Curvature: It is the centre of the sphere of which the mirror or lens is a part.
(ii) Radius of Curvature (R): The radius of the hollow sphere of which the mirror is a part, is called radius of curvature.
(iii) Pole: The central point of the spherical mirror is called its pole (P).
(iv) Focus: When a parallel beam of light rays is incident on a spherical mirror, then after reflection it meets or appears to meet at a point on principal axis, which is called focus of the spherical mirror.
(v) Focal Length: The distance between the pole and focus is called focal length (f).
Relation between focal length and radius of curvature is given by
The power of a mirror is given as P = 1/f (metre)
(vi) Mirror formula: 1/f = 1/v + 1/u
where, f = focal length of the mirror, u = distance of the object and v = distance of the image.
Fig: Concave mirror
Fig: Convex mirror
Newton’s formula for a concave mirror:
where x1 and x2 are the distances of object and image from the focus.
The ratio of height of image (1) formed by a mirror to the height of the object (O) is called linear magnification (m).
Lin ear magnification (m) = I/O = -v/u
Areal and Axial Magnification:
The ratio of area of image to the area of object is called areal magnification.
Areal magnification =
When a small sized object is placed linearly along the principle axis, then its longitudinal or axial magnification is given by
Sign Convention for Spherical Mirrors:
In the image formed by a plane mirror the right side of the object appears as left side and vise-versa. This phenomena is called lateral inversion.
When object is placed between pole and focus of a concave mirror, then its virtual, erect and magnified image is formed.
A convex mirror forms a virtual, erect and diminished image for all conditions of object.
The focal length of concave mirror is taken negative and for a convex mirror taken as positive.