Reflection

Key Definitions and Concepts

• Focus of a Concave Mirror: The point where reflected rays converge when a parallel beam of light is incident on the mirror.
• Focus of a Convex Mirror: The point from which reflected rays appear to diverge when a parallel beam of light is incident on the mirror.
• Focal Plane: The plane through the focus and perpendicular to the principal axis.
• Focal Length (f): The distance of the focus from the pole of the mirror.
• Paraxial Rays: Rays close to the principal axis. Only paraxial rays are considered in this chapter.
• Real Object: An object from which incident rays diverge.
• Virtual Object: A point towards which incident rays converge (if there were no mirror).
• Object: The point of intersection of the incident rays.
• Image: The point of intersection of the corresponding reflected rays. A real image is formed where the reflected rays intersect. A virtual image is formed at the point from which the reflected rays seem to diverge.

Image Tracing

To locate the image formed by a spherical mirror:

1. Draw two rays from the point object to the mirror.
2. Trace the reflected rays using the laws of reflection (the angle of incidence equals the angle of reflection). The line joining the point of incidence and the center of curvature is the normal.
3. The intersection of the reflected rays gives the real image. If the rays diverge, they form a virtual image at the point from which they appear to originate.

Sign Convention (Coordinate Sign Convention)

• The pole of the mirror is taken as the origin.
• The principal axis is taken as the X-axis.
• Usually, the positive direction of the axis is taken along the incident rays.
• u, v, R, and f represent the x-coordinates of the object, image, center of curvature, and focus, respectively.
• A quantity is positive if the corresponding point lies on the positive side of the origin; otherwise, it is negative.