Reflection and Mirror Formula


Reflection

When a light ray incident on a smooth surface bounces back to the same medium, it is called reflection.

Laws of Reflection :

(i) Angle of incidence is equal to the angle of reflection.

i.e., i = r

(ii) The incident ray, the reflected ray and the normal at the point of incidence, all lie in the same plane.

These laws hold at each point on any reflecting surface whether plane or curved.

Spherical Mirror : A spherical mirror is simply a part cut off from the surface of a hollow sphere which has been made smooth and silver polished as one side.

Spherical mirrors are of two types :

(i) Concave mirror : If outer side or bulging side of the spherical surface is silver polished, it is called a concave mirror.

(ii) Convex mirror : If inner side of a spherical surface is silver polished, it is called a convex mirror.

Relation between Focal Length and Radius of Curvature : The distance between centre (C) of spherical surface and pole (P) of mirror is called the radius of curvature. It is denoted by R.

The rays parallel to the principal axis (CP) after striking the mirror meet at a point (F) (in concave mirror) or appear to come from a point F (in convex mirror). This point is called the focus (F) of mirror. The distance of focus (F) from pole (P) of a mirror is called the focal length of the mirror. It is denoted by f. The focal length f is half of the radius of curvature.

Mirror Formula : The mirror formula is

Where u = distance of object from mirror;

v = distance of image from mirror;

and f = focal length of mirror.

 

Magnification Produced by Mirror : The ratio of the size of image to the size of object is called the magnification produced by the mirror.

Mirror Formula

Mirror Formula :

(i) For concave mirror :  M1M2 is a concave mirror having pole P, focus F and centre of curvature C.

An object AB is placed in front of mirror with point B on the principal axis. The image formed by mirror is A′B′ The perpendicular dropped from point of incidence D on principal axis is DN

By Sign Convention

Distance of object from mirror = – u

Distance of image from mirror = – v

Focal length of mirror PE = – f

Radius of curvature of mirror PC = – R = – 2f

Substituting these values in (4), we get

 

(ii) For convex mirror : M1M2 is convex mirror having pole P, focus F and centre of curvature C. AB is object placed in front of mirror. A ray AD incident parallel to principal axis, after reflection is bent towards it appears to come from focus F. Another ray AE directed towards centre of curvature, after reflection, retraces its path. Both rays appear to meet at  A′ . Thus, A′B is virtual and erect image of object AB. Drop a perpendicular from point of incidence D on the principal axis to cut at N.

If aperture of mirror is very small, then point will be very close to P, so NF = PF

By sign convention, BP = – u, PC = + R, PB’ = +u, PF = + f

Substituting these values in (4), we get