Understanding Light: Wave-Particle Duality

Light and Its Nature

• Light comprises particles dispersing in all directions from a glowing bulb
• Early theories, including Newton's, proposed light consisted of particles called "corpuscles."
• Huygens later disproved the particle theory, suggesting light is energy transmitted as a wave
• Light doesn't need a material medium to travel, distinguishing it from mechanical waves like sound
• Light is an electromagnetic (EM) wave, a non-mechanical wave that doesn't require particles to propagate
• Einstein's photoelectric effect reinvigorated the particle theory, asserting light is made of photons
• When light strikes a metal surface, electrons are ejected, a phenomenon explained by the photon theory
• Light exhibits a dual nature: behaving as both a wave and a particle
• Whether light appears as a wave or particle depends on how it's observed and studied
• Light is referred to as electromagnetic radiation that human eyes can detect.
• Human eyes can detect lights but not all EM waves.
• The electromagnetic spectrum is broad, including gamma rays, X-rays, infrared, ultraviolet, and radio waves
• Light exhibits properties like interference, diffraction, and polarization, which supports the wave nature theory

Properties of Light

• Light's intensity relies on the number of particles, where brighter light indicates more photons
• Dim light has fewer photons and a darker light has fewer particles
• Photons are the particles, or “packets” of light.
• Light travels at 3 x 10^8 meters per second in a vacuum, but its speed can change in other mediums
• Light travels in a straight line, this is called the rectilinear motion of light

Light Interaction with Surfaces

• When light hits a surface, it can be reflected back, transmitted through, or absorbed as heat
• No surface is a 100% reflector, absorber, or transmitter
• Light undergoes reflection, transmission, and absorption when it encounters a surface

Viewing Objects

• Light enables us to see things through reflection
• Transparent objects like air (oxygen, carbon dioxide) are invisible because they don't reflect light
• Opaque objects reflect light and are visible
• Seeing an object requires a light source, an opaque object, and functional eyes

Reflection of Light

• Reflection occurs when light bounces off a smooth, polished surface back into the same medium

Incident Ray, Reflected Ray, and Normal

• The incident ray is the ray of light that strikes a surface.
• The point where the incident ray touches a reflective surface requires a normal line for angle measurement.
• A normal is perpendicular to the surface
• The angle of incidence is the angle between the incident ray and the normal.
• The reflected ray is the ray that bounces back after hitting the surface
• A reflected ray goes back into the same medium
• The angle of reflection is the angle between the reflected ray and the normal

Laws of Reflection

• Angle of incidence equals the angle of reflection, irrespective of the type of reflection
• Incident ray, reflected ray, and normal all lie in the same plane (co-planar)

Plane Mirrors

• Plane Mirrors make images the same distance from the mirror as the object
• A minimum of two rays are needed to form an image
• The intersection point of reflected rays produces an image
• For images created with plane mirrors, corresponding parts of the object and image are in line with each other

Characteristics of images in plane mirrors

• The distance between the the object and the mirror is the same as the distance between the image and the mirror.
• The size of the image is the same as the size of the object
• Virtual (not real) and erect(upright) images are formed by plane mirrors
• Images formed are laterally inverted (right becomes left)

Examples of Lateral Inversion

• Right hand looks like left hand
• Ambulance is written backwards
• The drivers ahead can see it straight in their mirror

Example Problem

• Angle of incidence is 60 degrees
• Using laws of reflection, supplementary angles, and basic geometry, the angle of reflection off the second mirror will be 30 degrees

Spherical Mirrors

• Two types of spherical mirrors: concave and convex

Concave Mirror

• If there is a light parallel to the principal axis, it will converge to the focus
• Concave mirrors collect the light
• Dented inwards

Convex Mirror

• Light gets diverged relative to the focus
• Convex mirrors diverges the light
• If you stood far away from a convex mirror, the image is smaller and it's hard to see
• Bulges outwards

Spherical Mirror Terminology

• Center of Curvature (C): The center of the sphere which the spherical mirror is apart of
• Pole (P): The point where a line intersects the mirror
• Principal Axis: The straight line joining the pole and center of curvature
• Principal Focus (F): The midpoint between the pole and center of curvature
• Aperture: The diameter of the reflecting surface of the mirror
• Focal Length (f): Distance between the pole and principal focus
• Radius of Curvature (R): Distance between the pole and center of curvature
• R = 2f

Ray Tracing Rules for Spherical Mirrors

• A ray of light parallel to the principal axis will reflect through the focus.
• A ray passing through the focus will reflect parallel to the principal axis.
• A ray directed towards the center of curvature will reflect back along the same path.
• A ray incident on the pole will reflect at an equal angle to the principal axis

Ray Diagrams and Image Formation for Concave Mirrors

• Object Placed at Infinity
  • Rays come in parallel and converge at the focus.
  • Image at focus, diminished, real, and inverted.
• Object Placed Beyond C
  • One ray parallel to the axis reflects through F; another through C reflects back on itself.
  • Image is between C and F, diminished, real, and inverted.
• Object Positioned at C
  • One ray parallel to the axis passes through F; another through F becomes parallel.
  • Image is at C, same size, real, and inverted.
• Object Placed Between C and F
  • One ray parallel to the axis goes through F, and another through F becomes parallel
  • Image beyond C, enlarged, real, and inverted.
• Object Situated at Principal Focus
  • One ray parallel to the axis reflects through F, and the other goes through the pole.
  • This create rays that travel to infinity
• Object Between the Pole and Focus
  • One ray parallel to the axis reflects through F, with another directed towards the pole
  • Image behind the mirror, enlarged, virtual, and erect.

Ray Diagrams and Image Formation for Convex Mirrors

• Object Placed at Infinity
  • Parallel rays diverge from the mirror and converge at the focus
  • Image is at focus, highly diminished, virtual, and erect.
• Object Placed at A Finite Distance
  • One ray travels parallel to the principal axis reflects away from focus.
  • This creates an image between P and F, diminished, virtual and erect

Concave Vs Convex Mirrors

• Concave mirrors can create inverted images
• Convex Mirrors can't create inverted images
• Convex Mirrors appear smaller and further

Uses of Mirrors

• Dentists use concave mirrors to get up close and personal
• Security Mirrors are convex mirrors and appear further away, allowing to see more.

Sign Convention

• Concave mirrors have a negative focal point
• convex mirrors have a positive focal point
• In both concave and convex mirrors, the object is usually measured on the same side

Mirror and Magnification Formulas

• 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.
• Magnification: m = -v/u = height of the image / height of the object. Where:
  • If m is negative, the image is inverted and real.
  • If m is positive, it implies the image is erect (upright).

Understanding the Value of Magnification

• If the absolute value of m > 1: Image is enlarged.
• If the absolute value of m < 1: Image is diminished (smaller).
• If the absolute value of m = 1: Image is the same size as the object.

Example Problem Concave Mirror

• Concave mirror distance is negative
• Focal length is also negative
• Follow mirror formula to find out the volume and location

Example Problem Convex Mirror

• Always virtual, erect, and diminished

Reflective Index

• Light bends when crossing a boundary
• Different types of waves refract at different speeds

Laws of Reflective Index

• Incident ray, refracted ray, and normal all lie in the same plane (co-planar)

Rules For Transmitting Media

• Light from rare to dense bends toward normal. Meaning larger angle of incidence to small angle of refraction
• Light from dense to rare bends away from normal. Meaning smaller angle of incidence to larger angle of refraction
• Refraction does no occur if lights falls normally. Angle of incidence = Angle of refraction = Zero
• Refraction does not occur if both mediums have the same optical density

Glass Slabs

• Lateral displacement depends on the angle of incident, and way lights act through two normal lines.
• D depends on,
  • Refractive Indes,
  • Thickness
  • Wave Length
  • Angle of Incidence

Snells Law and Lenses

• Light through spherical lenses forms two spheres, which gives two Center of Curvature. Usually labels as "2F"
• Distances are measured from the optical center or origin
• As a rule light from paralle lights goes to F2
• If you get convex lens, it diverges to F2

Sign Convention For Lenses

• Convex = Plus
• Concave = Negative
• Focal length of concave lenses is negative and is the most active on the left
• Height is positive on both
• H is always positive

Rules to Obtain Image

• Lights starts parallel, goes to F2
• Light starts with F, end parallel
• Lights goes with O, end with unchanged.

Concave Lenses

Uses of Lenses in Applications

• Telescope and Camera = Convex lens.
• Glasses and myopias = Cuncave lenses

Wave Speed and Constant Frequency for Light

Important Equations For Reference

N21 = Vice Versa N2 = C/V