18

• Light behaves as a wave of short wavelength.
• A ray of light indicates the direction of propagation of light.
• In the absence of obstacles, light rays travel in straight lines.
• Reflection and refraction occur when light meets a surface separating two transparent media, causing the light rays to bend.
• Diffraction occurs when light bends around the edge of an obstacle, but this effect is often negligible in geometrical optics.

• Laws of Reflection:
  1. The angle of incidence (i) is equal to the angle of reflection (r).
  2. The incident ray, the reflected ray, and the normal to the reflecting surface are coplanar (lie in the same plane).

• Reflected rays from a point source S placed before a plane mirror appear to diverge from a point I behind the mirror.
• The point I is the image of the object S.
• The distance from the object to the mirror (SA) is equal to the distance from the image to the mirror (AI), i.e., SA = AI.

• The basic laws of reflection are the same for plane and curved surfaces.
• A normal can be drawn from any point of the curved surface by first drawing the tangent plane from that point and then drawing the line perpendicular to that plane.
• Angles of incidence and reflection are defined from this normal.

• A spherical mirror is a part cut from a hollow sphere.
• Spherical mirrors are generally constructed from glass with one surface silvered.
• Convex Mirror: Reflection takes place at the convex (outer) surface.
• Concave Mirror: Reflection takes place at the concave (inner) surface.
• Center of Curvature: The center of the sphere of which the mirror is a part.
• Radius of Curvature: The radius of the sphere of which the mirror is a part.
• Pole: The point on the mirror at the middle of the surface.
• Principal Axis: The line joining the pole and the center of curvature.

• Suppose a light beam travelling in a direction parallel to the principal axis is incident on a concave mirror.

Extended Objects and Magnification

When an object AB is placed perpendicular to the principal axis of a spherical mirror, the image A'B' is formed. Two key rays, one parallel to the principal axis (BD) and another directed towards the centre of curvature (BE), are used to trace the image of point B (B'). A perpendicular from B' to the principal axis gives A', the image of A. Figure 18.8 illustrates this setup in different scenarios.

Lateral Magnification: The ratio of the height of the image (h₂) to the height of the object (h₁) is called lateral or transverse magnification. By convention, heights above the principal axis are positive, and heights below are negative. Erect images have positive heights, and inverted images have negative heights. Considering the ray BP hitting the mirror at the pole P, the right-angled triangles ABP and A'B'P are similar.

Refraction at Plane Surfaces

When a light ray encounters a surface separating two transparent media, it bends. This bending is governed by Snell's Law.

• The principal axis must pass through the focus F.
• The lateral or transverse magnification is defined as m = h2/h1, where h2 = height of the image and h1 = height of the object.

• The power P of a lens is defined as P = 1/f, where f is the focal length.
• The SI unit of power of a lens is m–1, also known as dioptre.
• The focal length of a converging lens is positive and that of a diverging lens is negative. Thus, the power of a converging lens is positive and that of a diverging lens is negative.

• Consider two lenses L1 and L2 placed in contact with focal lengths f1 and f2, respectively.
• If the combination is replaced by a single lens of focal length F such that it forms the image of O at the same position I.