Mirror formula | Class 10 science | Concave mirror | Convex mirror | Physics

Mirror formula | Class 10 science | Concave mirror | Convex mirror | Physics

Spherical Mirror

:A mirror which is a part of a sphere is called spherical mirror.

Kinds of spherical mirror

:Spherical mirrors are of two types. These are

(a) Concave mirror or Converging mirror

(b) Convex mirror or Diverging mirror

Convex mirror

: Convex mirrors or diverging mirrors are those mirrors in which the reflecting surface is curved outwards.

Concave mirrors

: Concave mirrors or converging mirrors are those mirrors in which the reflecting surface is curved inwards.

Some terms related to spherical mirrors:

Centre of curvature

(a)The centre of curvature (C) of a spherical mirror is the centre of the hollow sphere of

glass whose part is spherical mirror.

(b) It is generally denoted by 'C' .

Radius of Curvature

● The radius of curvature (R) of a spherical mirror is the radius of the hollow sphere of

glass, of which the spherical mirror is apart.

Pole of spherical mirror

● The pole (P) of a spherical mirror is the centre of the mirror.

Principal axis

● The principal axis of a spherical mirror is a straight line passing through the centre o

curvature C and pole P of the spherical mirror.

Principal focus

● The principal focus (F) of a concave mirror is a point on the principal axis at which the

rays of light incident on the mirror, in a direction parallel to the principal axis, actually

meet after reflection from the mirror.

● The principal focus (F) of a convex mirror is a point on the principal axis from which the

rays of light incident on the mirror, in a direction parallel to the principal axis, appear to

diverge after reflection from the mirror.

Focal length

● The focal length (f) of a mirror is the distance between its pole (P) and principal focus(F).

Relation between focal length and radius of curvature

● For spherical mirrors of small aperture, R =2f.

Sign Conventions for Spherical Mirrors

According to New Cartesian Sign Conventions,

● All distances are measured from the pole of the mirror.

● The distances measured in the direction of incidence of light are taken as positive and

viceversa.

● The heights above the principal axis are taken as positive and viceversa.

Rules for tracing images formed by Spherical Mirrors

Rule 1: A ray which is parallel to the principal axis after reflection passes through the

principal focus in case of a concave mirror or appears to diverge from the principal focus in

case of a convex mirror.

Rule 2: A ray passing through the principal focus of a concave mirror or a ray which is

directed towards the principal focus of a convex mirror emerges parallel to the principal

axis after reflection.

Rule 3: A ray passing through the centre of curvature of a concave mirror or directed

towards the centre of curvature of a convex mirror is reflected back along the same path.

Rule 4: A ray incident obliquely towards the pole of a concave mirror or a convex mirror is

reflected obliquely as per the laws of reflection.

Image formation by a concave mirror

● Ray Diagrams

● Characteristics of images formed

Position of object Position of image Size of image Nature of image

At infinity At focus F Highly diminished Real and inverted

Beyond C Between F and C Diminished Real and inverted

At C At C Equal to size of object Real and inverted

Between C and F Beyond C Enlarged Real and inverted

At F At infinity Highly enlarged Real and inverted

Between F and P Behind the mirror Enlarged Virtual and erect

Image formation by a convex mirror

● Ray Diagrams

● Characteristics of images formed

Position of object Position of image Size of image Nature of image

At infinity At focus F behind

the mirror

Highly diminished,

point sized

Virtual and erect

Anywhere between

infinity and the pole

of the mirror

Between P and F

behind the mirror

Diminished Virtual and erect

Sign Convention for Reflection by Spherical Mirrors

While dealing with the reflection of light by spherical mirrors, we shall follow a set of sign

conventions called the New Cartesian Sign Convention. In this convention, the pole (P) of

the mirror is taken as the origin. The principal axis of the mirror is taken as the x-axis (X’X)

of the coordinate system. The conventions are as follows:

● The object is always placed to the left of the mirror. This implies that the light

from the object falls on the mirror from the left-hand side.

● All distances parallel to the principal axis are measured from the pole of the

mirror.

● All the distances measured to the right of the origin (along + x-axis) are taken as

positive while those measured to the left of the origin (along – x-axis) are taken as

negative.

● Distances measured perpendicular to and above the principal axis (along + y-axis)

are taken as positive.

● Distances measured perpendicular to and below the principal axis (along –y-axis)

are taken as negative.

The New Cartesian Sign Convention for spherical mirrors

● Mirror Formula

The object distance (u), image distance (v) and focal length (f) of a spherical mirror are

related as

1/v + 1/u = 1/f

● Linear Magnification (m)

The magnification produced by a spherical mirror indicates the extent to which an object's

image is magnified in relation to the object size.

Magnification is defined as the ratio of the image's height to the object's height. The letter

m is commonly used to represent it.

If h is the object's height and h' is the image's height, then the magnification m produced by

a spherical mirror can be written as

m =Height of the Image/Height of the object =h′/h

m is negative for real images and positive for virtual images.