Light: Reflection, Refraction, and Wave Theory

• In a dark room it is impossible to see
• In lit rooms, lights reflects off objects
• Reflected light enables people to see things

Light Phenomena

• Light transmits through transparent mediums enabling sight
• Light phenomena includes image formation by mirrors, twinkling stars, rainbows, and bending of light

Light Travel

• Light travels in straight lines
• A small light source casts a sharp shadow on an opaque object, thus illustrating this straight path of light, which is indicated as a ray of light

Diffraction of Light

• Light bends around opaque objects if the object is very small
• Straight-line treatment of optics using rays fails when an object is very small
• To explain diffraction, light is considered as waves

Wave Theory

• The wave theory of light becomes inadequate for treating the interaction of light with matter
• Light behaves somewhat like a stream of particles
• Modern quantum theory reconciles particle properties of light with wave nature, defining light as neither a wave nor a particle

Chapter Focus

• Reflection and refraction of light, using straight-line propagation
• Reflection of light by spherical mirrors, refraction of light, and their application in real-life situations will be discussed

Reflection of Light

• A highly polished surface reflects most of the light falling on it, such as a mirror

Laws of Reflection

• Angle of incidence equals the angle of reflection
• Incident ray, normal to the mirror at the point of incidence, and reflected ray all lie in the same plane

Plane Mirrors

• Plane mirrors produce virtual and erect images
• Image size equals object size in plane mirrors
• Image is as far behind the mirror as the object is in front
• The image in plane mirrors is laterally inverted

Curved Mirrors

• Curved surfaces can be considered as curved mirrors
• Spherical mirrors are curved mirrors, with a reflecting surface forming a part of the surface of a sphere

Spherical Mirrors

• A spherical mirror has a reflecting surface curved inwards or outwards
• Concave Mirror: A type of spherical mirror whose reflecting surface is curved inwards, facing towards the center of the sphere
• Convex Mirror: A spherical mirror whose reflecting surface is curved outwards
• Diagrams of these mirrors have the back shaded

Spherical Mirror Terms

• The center of the reflecting surface of a spherical mirror is a point called the pole
• The pole lies on the surface of the mirror
• The letter P usually represents the mirror pole

Center of Curvature

• The reflecting surface of a spherical mirror is part of a sphere
• The center of Curvature is located at the center of this sphere
• The letter C represents the center of curvature of the spherical mirror
• The center of curvature is not part of the mirror, existing outside it
• In concave mirrors, the center of curvature lies in front
• In concave mirrors, the center of curvature is behind the mirror

Radius of Curvature

• The radius of curvature of the mirror is the radius of the sphere of which the mirror's reflecting surface is a part
• The letter R represents the radius of curvature of the mirror
• The distance PC equals the radius of curvature

Principal Axis

• The principal axis is a straight line passing through the pole and the center of curvature of a spherical mirror
• The principal axis is normal to the mirror at its pole

Concave Mirrors and Sunlight

• Directing the reflecting surface of a concave mirror towards the Sun will allow it to direct the light
• The light will be reflected onto a sheet of paper held close to it
• The sheet of paper should be moved back and forth until a bright and sharp light spot is found on the surface
• The paper will begin to burn and produce smoke after some time, eventually catching fire

Focus of Concave Mirror

• Sunlight is converged at a point as a bright spot by the mirror
• This spot is the image of the Sun and the focus of the concave mirror
• The heat produced due to sunlight concentration will ignite the paper
• The focal point of the mirror is the distance of the sharp bright spot
• The distance is the approximate value of the focal length of the mirror

Principal Focus

• Rays parallel to the principal axis falling on concave mirrors converge at a point after reflection
• This is the Principal Focus of the Concave Mirror

Convex Mirrors

• Rays parallel to the principal axis appear to come from a point on the principal axis

Principal Focus

• The principal focus is the point on the principal axis where reflected rays appear to diverge from
• Letter F notation
• The distance between the pole and the principal focus of a spherical mirror

Focal Length

• The distance between the pole and the principal focus of a spherical mirror, represented by the letter "f."

Aperture

• The reflecting surface of a spherical mirror is generally spherical with a circular outline
• Aperture is the diameter of the reflecting surface, which is represented by MN
• Mirrors discussed have an aperture much smaller than their radius of curvature

Radius of Curvature Formula

• For small apertures, the radius of curvature is twice the focal length (R = 2f)
• The principal focus lies midway between the pole and the center of curvature

Spherical Mirrors

• Plane mirrors produce images, and the image's nature, size, and position depend on the object
• In concave mirrors for different object positions, images are real, virtual, enlarged, diminished, or same size

Concave Mirror Summary

Ray Diagrams

• Ray diagrams can be used to study spherical mirror images
• Extended objects act as point sources producing infinite rays, but only two rays are needed for clarity
• Intersection of at least two reflected rays indicates the image position

Ray Diagram Rules

• Parallel ray after reflection goes through the principal focus of a concave mirror or appears to diverge from focus of a convex mirror
• Ray passing through principal focus after reflection emerges parallel to principal axis
• Ray passing through center of curvature reflects back along the same path
• Oblique ray is incident towards pole P, reflecting obliquely making equal angles with principal axis

Concave Mirror Images

• Image changes depending on the object
• In all cases laws of reflection are followed

Concave Mirror Uses

• Torches, search-lights, headlights to get parallel light
• Shaving mirrors for larger images of the face
• Dentists mirrors to see large images of the teeth
• Concentrating sunlight for solar furnaces

Convex Mirror Images

• Used to study image formation, which differ from concave mirror images

Convex Mirror Images

Convex Mirror Properties

• Used in plane, convex, and concave mirrors to achieve full image

Convex Mirror Applications

• Rear-view mirrors: vehicles use convex side mirrors to see wide field
• Enables driver to see traffic providing an erect, diminished image with a wider field of view

Key Definitions

• Principal focus: location where parallel rays converge or appear to diverge.
• Radius of curvature: radius of sphere, mirror is part of.
• Focal length: distance between pole and principal focus.
• Sign conventions: always placing the object to left of the mirror

New Cartesian Sign Convention

• Distances parallel to principal axis measured from the pole are negative Distances measured from the pole towards the right along +x aixs, the origin are positive
• Object on the left side, and all distance parallel to the principal axis are measured from the mirror
• Height above the principal axis are taken as positive
• Height below principle axis are taken as negative

Mirror Formula

• The mirror formula which shows the relationship between the object-distance (u), and focal length (f) 1 1 1 + = v u f

Magnification Formula

• Magnification produced by a spherical mirror relative extent

• The height of the image is magnified with respect to the object size

• height of the Image h' over the height of the object h

                h'  
    m= 
                h      
  
                h′     v
  

  Magnification (m) = = −
  h u

• Positive sign in magnification says that the image is virtual

• Negative sign in magnification indicates that the image is real