Reflection of Light: Plane and Curved Surfaces

Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. In Physics, we focus on how light behaves when it hits smooth surfaces like mirrors.

1. Laws of Reflection

The reflection of light is governed by two fundamental laws:

• First Law: The incident ray, the reflected ray, and the normal at the point of incidence all lie in the same plane.
• Second Law: The angle of incidence (i) is equal to the angle of reflection (r). That is, i = r.

2. Reflection at Plane Surfaces

A plane mirror is a flat reflecting surface. The images formed by plane mirrors have the following characteristics:

• The image is virtual (cannot be caught on a screen).
• The image is upright (erect).
• The image is the same size as the object.
• The image is laterally inverted (left becomes right).
• The image distance from the mirror (v) is equal to the object distance from the mirror (u).

Inclined Mirrors

When two plane mirrors are inclined at an angle θ, the number of images (n) formed is given by the formula:
n = (360/θ) - 1.
If 360/θ is an odd number and the object is not on the bisector, n = 360/θ.

3. Applications of Reflection

• Periscope: Uses two plane mirrors inclined at 45° to the horizontal to see over obstacles.
• Kaleidoscope: Uses mirrors inclined (usually at 60°) to produce beautiful symmetrical patterns.
• Sextant: An instrument used to measure the angle between two visible objects, primarily for navigation, based on the laws of reflection.

4. Reflection at Curved Mirrors

Curved mirrors are parts of a hollow sphere. There are two types:

• Concave (Converging) Mirror: The reflecting surface curves inwards. It can form both real and virtual images depending on the object's position.
• Convex (Diverging) Mirror: The reflecting surface curves outwards. It always forms a virtual, erect, and diminished image.

Key Terms:

• Pole (P): The center of the mirror surface.
• Center of Curvature (C): The center of the sphere from which the mirror was cut.
• Principal Axis: The line passing through P and C.
• Principal Focus (F): The point where parallel rays converge (concave) or appear to diverge from (convex) after reflection.
• Focal Length (f): The distance between P and F. f = R/2, where R is the radius of curvature.

5. The Mirror Formula and Magnification

To solve numerical problems, we use the Mirror Formula:

1/f = 1/u + 1/v

Sign Convention (Real is Positive):

• f is positive for concave mirrors, negative for convex mirrors.
• u is always positive for a real object.
• v is positive for real images (formed in front), negative for virtual images (formed behind).

Linear Magnification (m)

Magnification is the ratio of image size to object size:
m = v/u = Image Height / Object Height