Reflection of light by curved mirror

Reflection of light by curved mirror

A curved mirror can be produced from a spherical surface. Such mirrors are called spherical mirrors.

When a light is reflected from the outside of the spherical mirror surface, it is called a convex or diverging mirror. if a light is reflected from inside of this curve mirror, it is concave or converging mirror.

Application of spherical mirrors

1. Concave mirrors are used in torches, head lamps of a car , telescope and shaving mirrors.
2. Convex mirrors are used in side mirror of a car and in supermarket.

Definition

1. The Center of curvature C

The center of curvature C is the center of the sphere from which the mirror is cut out.

1. The Pole

The pole P of a spherical mirror is the mid-point of the mirror.

1. The principal axis

The principal axis of a spherical mirror is the line PC between the pole P and the center of curvature C.

1. The radius of curvature r

This the distance from the center of curvature C to the pole or any part of the mirror

1. The Principal focus F

The principal focus of a concave mirror is the point where rays that are parallel and close to the principal axis converge after reflection

The principal focus of a concave mirror is the point from which rays parallel and close to the principal axis appear to diverge from after reflection.

1. The focal length f

The focal length of a spherical mirror is the distance between the principal focus F and the pole P.

1. Aperture.

The diameter of the circular rim of the mirror, is called the aperture of the mirror. Hence, aperture is a part of mirror, through which rays of light entered.

1.    Incident on the mirror parallel to principal axis. After reflection from the mirror, it actually passes through mirror focus F (in case of a concave mirror) or appears to come from it (in case of a convex mirror).
2. Incident on the mirror through focus F (in case of a concave mirror) or in direction of focus F (in case of convex mirror).
   After reflection from the mirror, it goes parallel to the principal axis.
3. Incident in the mirror through centre of curvature C (in case of a concave mirror) or in direction of centre of curvature C (in case of a convex mirror).
   After reflection from the mirror, it returns back along the path of incidence.

Sign convention 
(a) Definition: It is a convention, which fixes the signs of different distances measured. The sign convention followed is the New Cartesian sign convention.
(b) Rules: It gives following rules:

1. All distances are measured from the pole of the mirror (along the principal axis).
2. The distance measured in the same direction as the direction of incident light,are taken as positive.
3. The distances measured opposite to the direction of incident light, are taken as negative.
4. The distances measured above the principal axis, are taken positive and the distance taken below the principal axis, are taken negative.

(c) Facts: According to above mentioned rules of sign convention:

1. Radius of curvature and focal length of a concave mirror are taken as negative and the same for convex mirror are taken positive.
2. The distance of an object is always negative.
3. The distance of real image is negative, while that of a virtual image is positive.
4. The size of object is always positive but size of real image is always negative while size of virtual image is positive for mirrors.

(d) Explanation: (with example) The new convention is also called cartesian coordinate convention.
Pole (P) of the mirror is taken as the origin. Reflecting face of the mirror is taken towards ‘ left. Light is made incident from left to right which makes positive direction. Object facing the mirror, is on the left of the origin. Its distance from pole measured from pole (origin) from right to left becomes negative. Real image is formed in front of the mirror to the left of pole. Its distance also becomes negative.

Virtual image is formed behind the mirror. Its distance from pole measured from left to right becomes positive.

For concave mirror, centre of curvature and focus lie in front of it to the left of pole. Their distances (radius of curvature and focal length) become negative.
For convex mirror, centre of curvature and focus lie behind to the right. Their distances become positive.

Real object stands erect. Its height, being upward, is taken positive.

Real image is formed inverted. Its height is taken negative.
Virtual image is formed erect. Its height is taken positive.

Mirror formula 
The equation relating the object distance (u), the image distance (v) and the mirror focal length (f), is called the mirror formula. It is also called Gaussian formula.

Assumptions made 
Following assumptions are made in derivation of the mirror formula.

1. The mirror has a small aperture.
2. The point object lies on to the principal axis and placed perpendicular.
3. The incident rays make small angles with the mirror surface or the principal axis.

Image-real and virtual  
(a) Image: When rays of light starting from a point object, after reflection (or refraction), meet at a point or appear to come from a point, then this point is called the image of the point object.
(b) Real Image: If the reflected (or refracted) rays actually meet at the point, then the
image is real.
(c) Virtual Image:If the reflected (or refracted) rays appear to come from the point, then the image is virtual.
(d) Distinction: Real image of a big object (combination of real images of its different points) is always inverted. It can be obtained on a screen.
Virtual image of a big object (combination of virtual images of its different points) is always erect. It cannot be obtained on a screen.

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