Light – Reflection and Refraction

9.1 Reflection of Light

Reflection: The process where a highly polished surface, like a mirror, reflects most of the light falling on it back into the same medium.
Laws of Reflection:
- The angle of incidence is equal to the angle of reflection.
- The incident ray, the normal to the mirror at the point of incidence, and the reflected ray all lie in the same plane.

9.2 Spherical Mirrors

Concave Mirror: A spherical mirror whose reflecting surface is curved inwards, facing towards the centre of the sphere.
Convex Mirror: A spherical mirror whose reflecting surface is curved outwards.
Pole (P): The centre point of the reflecting surface of a spherical mirror.
Centre of Curvature (C): The centre of the sphere of which the mirror's reflecting surface forms a part.
Radius of Curvature (R): The radius of the sphere of which the reflecting surface forms a part. The relationship is given by R = 2f.
Principal Axis: A straight line passing through the pole and the centre of curvature of a spherical mirror.
Principal Focus (F): The point on the principal axis where parallel incident rays converge (for a concave mirror) or appear to diverge from (for a convex mirror) after reflection.
Focal Length (f): The distance between the pole and the principal focus of a spherical mirror.

Concave Mirror Images: Varies with the position of the object relative to points P, F, and C. Images can be real and inverted (magnified, diminished, or same size) or virtual and erect (when the object is between P and F).
Convex Mirror Images: Always forms a virtual, erect, and highly diminished image behind the mirror, irrespective of the object's position.
Uses of Concave Mirrors: Employed in torches, search-lights, vehicle headlights to get powerful parallel beams, shaving mirrors, dentist mirrors, and solar furnaces.
Uses of Convex Mirrors: Preferred as rear-view mirrors in vehicles because they provide an erect image and a much wider field of view.

New Cartesian Sign Convention: The pole of the mirror acts as the origin. Objects are placed to the left; distances in the direction of incident light (right) are positive, against it (left) are negative; heights upwards are positive, downwards are negative.
Mirror Formula: The mathematical relationship between object distance (u), image distance (v), and focal length (f):
1/v + 1/u = 1/f
Magnification (m): The ratio of the height of the image (h') to the height of the object (h), relating to object and image distances:
m = h'/h = -v/u

9.3 Refraction of Light

Refraction: The change in direction of propagation of light when it travels obliquely from one transparent medium to another due to a change in its speed.
Refraction through a Glass Slab: When passing through a rectangular slab, light bends towards the normal as it enters glass (rarer to denser) and away from the normal as it exits (denser to rarer). The emergent ray remains parallel to the incident ray but is laterally shifted.

Laws of Refraction:
- The incident ray, the refracted ray, and the normal to the interface at the point of incidence all lie in the same plane.
- Snell's Law: The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for a given pair of media: sin i / sin r = constant.
Refractive Index (n): The constant in Snell's law representing the relative speed of light between media. Relative refractive index (n21) is v1 / v2, whereas absolute refractive index (nm) is measured relative to vacuum: nm = c / v.
Optical Density: Refers to a medium's capacity to refract light; is distinct from mass density (e.g., kerosene is optically denser than water though its mass density is lower).

Convex Lens (Converging): A lens bounded by two spherical surfaces bulging outwards; thicker in the middle than at the edges.
Concave Lens (Diverging): A lens bounded by two spherical surfaces curved inwards; thicker at the edges than in the middle.
Convex Lens Images: Depending on the position, it can form real and inverted images (diminished, same size, or magnified) or a virtual, erect, and magnified image (when the object is between focus F1 and optical centre O).
Concave Lens Images: Always produces a virtual, erect, and diminished image on the same side as the object.

Lens Formula: The relation between object distance (u), image distance (v), and focal length (f) of a spherical lens:
1/v - 1/u = 1/f
Lens Magnification (m): Defined as m = h'/h = v/u.
Power of a Lens (P): The measure of convergence or divergence a lens achieves, defined as the reciprocal of its focal length in meters:
P = 1/f.
Dioptre (D): The SI unit of power of a lens. Power is positive for convex lenses and negative for concave lenses.
Power of Combined Lenses: The net power of lenses in contact is the algebraic sum of individual powers: P = P1 + P2 + P3 + ...

Chapter 9: Light – Reflection and Refraction