Optics: Reflection of Light

• Optics is the branch of physics that studies the behavior and properties of light

Reflection of Light

• Reflection is the phenomenon where light bounces back into the same medium after striking a surface

• Laws of reflection:

  • The angle of incidence is equal to the angle of reflection

  • The incident ray, the reflected ray, and the normal to the surface at the point of incidence, all lie in the same plane

• Types of reflection:

  • Regular reflection: Occurs on smooth surfaces, producing a clear image

  • Irregular reflection: Occurs on rough surfaces, scattering light in different directions, and producing a diffused reflection

• Image formed by a plane mirror

  • Virtual and erect

  • Laterally inverted

  • Same size as the object

  • Image distance is equal to the object distance from the mirror

Spherical Mirrors

• Spherical mirrors are curved mirrors, which are part of a hollow sphere

• Types of spherical mirrors:

  • Concave mirror: A converging mirror with the reflecting surface curved inward

  • Convex mirror: A diverging mirror with the reflecting surface curved outward

• Important terms related to spherical mirrors:

  • Pole (P): The center of the reflecting surface of the mirror

  • Center of curvature (C): The center of the sphere of which the mirror is a part

  • Radius of curvature (R): The distance between the pole and the center of curvature

  • Principal axis: The straight line passing through the pole and the center of curvature

  • Focus (F): The point on the principal axis where parallel rays converge (concave mirror) or appear to diverge from (convex mirror) after reflection

  • Focal length (f): The distance between the pole and the focus; f = R/2

• Image formation by concave mirrors:

  • Object at infinity: Image at focus, real, inverted, highly diminished

  • Object beyond C: Image between F and C, real, inverted, diminished

  • Object at C: Image at C, real, inverted, same size

  • Object between F and C: Image beyond C, real, inverted, enlarged

  • Object at F: Image at infinity, real, inverted, highly enlarged

  • Object between P and F: Image behind the mirror, virtual, erect, enlarged

• Image formation by convex mirrors:

  • Object at infinity: Image at focus, virtual, erect, highly diminished

  • Object at any other position: Image between P and F, virtual, erect, diminished

• Uses of spherical mirrors:

  • Concave mirrors: Used in torches, searchlights, headlights of vehicles, shaving mirrors, and by dentists to see enlarged images of teeth

  • Convex mirrors: Used as rear-view mirrors in vehicles to provide a wider field of view

Mirror Formula and Magnification

• Mirror formula: 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance

• Sign convention:

  • Distances measured in the direction of incident light are taken as positive

  • Distances measured opposite to the direction of incident light are taken as negative

  • Heights above the principal axis are taken as positive

  • Heights below the principal axis are taken as negative

• Magnification (m): The ratio of the height of the image (h') to the height of the object (h), or m = h'/h = -v/u

  • A positive sign of magnification indicates a virtual and erect image

  • A negative sign of magnification indicates a real and inverted image

  • If |m| > 1, the image is enlarged

  • If |m| = 1, the image is the same size as the object

  • If |m| < 1, the image is diminished

Refraction of Light

• Refraction is the bending of light as it passes from one medium to another with different optical densities

• Laws of refraction:

  • The incident ray, the refracted ray, and the normal to the interface of two transparent media 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 constant for a given pair of media; sin i / sin r = constant = refractive index (n)

• Refractive index: The ratio of the speed of light in vacuum (c) to the speed of light in the medium (v); n = c/v

• Absolute refractive index: Refractive index of a medium with respect to vacuum or air

• Relative refractive index: Refractive index of one medium with respect to another medium

• When light travels from a rarer to a denser medium, it bends towards the normal

• When light travels from a denser to a rarer medium, it bends away from the normal

Refraction through a Glass Slab

• When light passes through a glass slab, it is refracted twice, once at the air-glass interface and again at the glass-air interface

• The emergent ray is parallel to the incident ray, but it is laterally displaced

• Lateral displacement depends on:

  • Thickness of the slab

  • Angle of incidence

  • Refractive index of the glass slab

Total Internal Reflection

• Total internal reflection (TIR) occurs when light travels from a denser to a rarer medium at an angle of incidence greater than the critical angle

• Critical angle: The angle of incidence for which the angle of refraction is 90 degrees

• Conditions for TIR:

  • Light must travel from a denser to a rarer medium

  • The angle of incidence must be greater than the critical angle

• Applications of TIR:

  • Optical fibers: Used for transmitting light signals over long distances with minimal loss

  • Prisms: Used in binoculars and periscopes to reflect light and change the direction of the image

  • Mirage: An optical illusion in deserts due to varying refractive indices of air layers

  • Sparkling of diamond: Due to its high refractive index and small critical angle