A smooth, highly polished reflecting surface is called a mirror.
When a glass plate is polished on one sided with reflecting material such silver or nickel then it becomes a mirror.
From the reflecting surface of mirror there are two types of mirror:
(i) Plane mirror (ii) Spherical or curved mirror
(i) Plane mirror : A highly polished plane surface is called a plane mirror or if a flat (totally plane) surface of a glass plate is polished one side with a reflecting material is called plane mirror.
(ii) Spherical mirror : A mirror whose polished, reflecting surface is a part of hollow sphere of glass, is called a spherical mirror. For a spherical mirror, one of the two curved surfaces is coated with a thin layer of silver followed by a coating of red lead oxide paint. Thus, one side of the spherical mirror is made opaque and the other side acts as a reflecting surface.
For the polishing side there are two type of spherical mirror:
(A) Convex mirror.
(B) Concave mirror.
(A) Concave (Converging) mirror : A spherical mirror whose inner hollow surface is the reflecting surface.
(B) Convex (diverging) mirror : A spherical mirror whose outer bulging out surface is the reflecting surface.
Terminology for spherical mirrors:
(a) Aperture : The effective width of a spherical mirror from which reflection can take place is called its aperture AA' & BB'.
(b) Pole (Vertex) : The centre of a spherical mirror is called its pole and it is denoted by letter P.
(c) Centre of curvature : The centre of the hollow sphere of which the spherical mirror is a part is called centre of curvature. It is denoted by letter C.
(d) Radius of curvature : The radius of the hollow sphere of which the spherical mirror is a part called the radius of curvature (R).
(e) Principal axis : The straight line passing through the centre of curvature C and the pole P of the spherical mirror.
(f) Normal : The normal at any point of the spherical mirror is the straight line obtained by joining that point with the centre of curvature (C) of the mirror.
(g) Principal focus or focus : The point on the principal axis where all the rays coming from infinity (parallel rays) after reflection either actually meets or appears to meet is called the focus (or focal point) of the mirror. It is denoted by letter F.
(h) Focal length :The distance between the pole (P) and the focus (F) is called focal length (f) and
(i) Focal plane :- An imaginary plane passing through the focus and at right angles to the principal axis.
(j) Real Image :- When the rays of light after getting reflected from a mirror (or after getting refracted from a lens) actually meet at a point, a real image is formed. A real image can be obtained on a screen.
(k) Virtual image : When the rays of light after getting reflected from a mirror (or after getting refracted from a lens) appear to meet at a point, a virtual image is formed. Such an image can only be seen through a mirror (or a lens) but cannot be obtained on a screen.
Rules of Image formation from the spherical mirror:
The rules of reflection from the spherical mirror are based on incident and reflection angle.
(i) A ray parallel to principal axis after reflection from the mirror passes or appears to pass through its focus by definition of focus.
(ii) A ray passing through or directed towards focus after reflection from the mirror will become parallel to the principal axis.
(iii) A ray passing through or directed towards centre of curvature after reflection from the mirror, retraces its path. as for it ∠i = 0 and so ∠r = 0.
(iv) Incident and reflected rays at the pole of a mirror are symmetrical about the principal axis.
Difference between Real and Imaginary image:
|S. No.||Real image||Virtual image|
|(1)||When reflected or refracted light rays actually intersect at a point.||When reflected or refracted light rays do not actually intersect at a point but appear to meet at a point|
|(2)||It can be obtained on a screen.||It cannot be obtained on a screen.|
|(3)||It is always inverted.||It is always erect.|
|(4)||It is always formed in front of mirror.||It is always formed behind the mirror.|
Formation of Image by a Plane mirror:
Properties of Image from flat (Plane) Mirror:
(i) Virtual and erect.
(ii) Same in size of object.
(iii) The image is formed behind the mirror (as far as the object from the mirror).
(iv) The image formed is laterally inverted.
Lateral inversion and inversion:
The phenomenon due to which the image of an object turns through an angle of 180° through vertical axis rather than horizontal axis, such that the right side of the image appears as left or vice versa is called lateral inversion.
During inversion image turns around horizontal axis through an angle of 180°.
Image formation from Concave mirror:
|S. No.||Position of the |
|Position of the image||Nature & size of the image||Ray diagram|
|(1)||At infinity.||At focus F||Real, inverted and highly diminished. (point size)|
|(2)||Between infinity and C||Between|
C & F
|Real, inverted and smaller|
than the object
|(3)||At C||At C||Real, inverted|
and same size.
|(4)||Between C & F||Between C and infinity.||Real, inverted and enlarged.|
|(5)||At F||At infinity.||Real, inverted|
Between focus and pole
|Behind the mirror.||Virtual, erect and enlarged.|
Use of Concave mirror:
(i) It is used as a shaving mirror.
(ii) It is used as a reflector in the head light of vehicles.
(iii) It is used by doctor to focus a parallel beam of light on a small area.
Formation of image from a convex mirror:
There are four rules of drawing images in convex mirror:
(i) Any ray of light travelling parallel to the principal axis of a convex mirror of the reflection appears to diverge from the principal focus of the convex mirror.
(ii) Any ray of light which travels towards the direction of principal focus of a convex mirror, after reflection will travel parallel to the principal axis of the mirror.
(iii) A ray of light which is incident along the centre of curvature(C) of a convex mirror after reflection, returns back on the same path. It is because the light ray strikes the convex mirror at right angles.
(iv) When the ray of light incident on the pole reflects or returns back on same angle from principal axis than it will reflect on the same angle of incident i = r.
Making of image from a convex mirror:
(i) When the object is at infinity
When the rays of light come (diverge) from an object situated at infinity, they are always parallel. These parallel rays, strike the convex mirror, and reflect to diverge outward from convex mirror. These rays seems (appear) to come from focus.
The characteristics of the image are virtual, erect, diminished to a point and formed at principal focus behind the convex mirror.
(ii) When the object is at a finite distance from the pole then the image is formed between pole and principal focus behind the convex mirror and image is virtual, erect and diminished.
There are only two positions of the object for showing the image formed by a convex mirror that is-
(i) When the object is at infinity.
(ii) When the object is at a finite distance from the pole of the convex mirror. Beside these positions, no other positions are possible because the focus and the centre of curvature is behind the reflecting surface of the convex mirror.
Now we can study the image formation by following table:
|S. No.||Position of the object||Position of the image||Size of image of the image||Nature of the image|
|(1)||At infinity||At F, behind mirror||Highly diminised||Virtual and erect.|
|(2)||Between infinity and pole of mirror.||Between P & F behind the mirror||Diminished||Virtual and erect.|
Used of Convex mirror:
(i) It is used as a rear view mirror in automobiles.
(ii) It is used as a reflector for street lights.
Note : A plane mirror is not useful as a rear view mirror, because its field of view is very small.
Sign convention of spherical mirror:
Whenever and wherever possible the ray of light is taken to travel from left to right.
The distances above principal axis are taken to be positive while below it is negative.
Along principal axis, distances are measured from the pole and in the direction of light are taken to be positive while opposite to it is negative.
Relation from spherical mirror:
Relation between f and R for the spherical mirror:
If Q is near to line P then from ΔQCP
tanθ ~ θ = QP/R
and from ΔQFP
tan2θ ~ 2θ = QP/f
Relation between u,v and f for curved mirror:
If an object is placed at a distance u from the pole of a mirror and its image is formed at a distance v (from the pole)
If angle is very small :
from ΔCMO, β = α + θ ⇒ θ = β - α
from ΔCMI, γ = β + θ ⇒ θ = g - β
so we can write β - α = γ - β ⇒ 2β = γ + α