Physics: Electromagnetic Waves

Mirror Equation

• Negative values for image distance indicate image is located behind the mirror
• Negative/positive sign in front of numerical value for physical quantity represents info about direction
• In case of image distance, negative value always indicates existence of virtual image located behind mirror
• In case of image height, a positive value indicates an upright image

Lenses

• Piece of glass or other transparent material takes on appropriate shape, it's possible that parallel incident rays would either converge to a point or appear to be diverging from a point

Refraction Rules

• Converging Lens:
  • Any incident ray traveling parallel to principal axis of converging lens will refract through lens and travel through focal point on opposite side of lens
  • Any incident ray traveling through focal point on the way to lens will refract through lens and travel parallel to principal axis
  • Incident ray that passes through center of lens will in effect continue in same direction that it had when it entered lens
• Diverging Lens:
  • Any incident ray traveling parallel to principal axis of diverging lens will refract through lens and travel in line with focal point (ex: in a direction such that its extension will pass through focal point)
  • Any incident ray traveling towards focal point on the way to lens will refract through lens and travel parallel to principal axis
  • An incident ray that passes through center of lens will in effect continue in same direction that it had when it entered lens

Lens Characteristics

• Converging Lenses:
  • Light rays are converging to a point after refracting through the lens, real image is formed
  • Real image is formed whenever refracted light pass through image location
  • Converging lenses are capable of producing both real/virtual images
• Diverging Lenses:
  • Always produce virtual images
  • Image will be located on the object side of lens
  • Image will be upright and reduced in size (smaller than object)

Dispersion

• Visible/white light is a collection of component colors
• Upon passage through prism, white light is separated into component colors (red, orange, yellow, green, blue, violet)
• Prism is a transparent glass with 2 flat surfaces angled at an angle
• Spectrum is a band of colors scattered by light entering glass prism
• Causes of Dispersion:
  • Each color's light has a distinct wavelength
  • White light disperses to 7 colors because each color has a different wavelength
  • Red light has the longest wavelength, violet light has the shortest
  • In vacuum, all colors of light travel at the same speed

EM Waves

• Waves transmit information/energy from one point to another in signal form
• No material object makes this journey
• Obtained by including time factor
• Oscillation form through space/mass medium
• Can travel through empty space; mostly invisible
• 3 Wave Types:
  • Mechanical Wave: oscillation of matter and responsible for energy transfer through medium
  • Longitudinal wave: particle movement parallel to energy motion
  • Transverse wave: particle movement at right angles/perpendicular to energy motion
  • Combination of both longitudinal and transverse
  • Surface wave: particles travel in circular motion

Electromagnetic Spectrum

• Properties and Formula:
  • Speed (c), frequency (f), wavelength (λ)
  • Wavelength/Frequency Relationship:
    • All parts of EM spectrum travel at the same speed
    • Wavelength and frequency have an inversely proportional relationship
    • Wavelength increases = frequency decreases
    • Wavelength, frequency, energy:
      • Short wavelengths = high frequency = high energy
      • Long wavelengths = low frequency = low energy
• Notes:
  • EM waves don’t require media in which to travel or move
  • EM waves are transverse waves because they are made of vibrating electric and magnetic fields at right angles to each other, and to the direction waves are traveling

Reflection and Refraction

• Reflection of Light:
  • Incident Ray vs Reflected Ray:
    • Incident ray: plenty of light rays reflect object from all directions
    • Reflected ray: light that bounced from surface and reached your eye
  • Reflection Law:
    • Incident ray, reflected ray, and the normal all lie in the similar plane called the plane of incidence
    • Incidence angle=reflection angle; regardless of wavelength or pair of materials
  • Reflection Types:
    • Specular reflection: when image is reflected from a smooth surface (specular means having properties of a mirror)
    • Diffuse reflection: reflection that happens on rough surfaces

Refraction of Light

• Refraction: travels at a particular angle different refractive index into a medium/substance that has a refractive index (n)
• Refractive index (n): light speed in free space : speed in given medium
• Determined by optical density or "inert tendency" of material's molecules to keep absorbed energy of EM wave in form of oscillating electrons before releasing it back as a new disturbance
• Measure of light ray bending as it travels from one medium to another
• Snell's Law (Refraction Law):
  • Describes the relationship between the angle of incidence and refraction as light passes through 2 different media
  • n1sinθ1 = n2sinθ2
• Common Refractive Indices:
  • Various light colors move at different rates in any transparent material (glass/water)
  • Various colors' lights bend through different angles due to differences in velocity
  • Red travels fastest, violet travels slowest
  • Thus, red light bends least, violet bends most
  • Thus, white light dispersion into 7 colors happens when various colored photons bend at different angles while passing through a glass prism
• Visible Light Spectrum:
  • Optical density: measure of the tendency of material to slow down light as it travels through it
  • Tendency of atoms to maintain absorbed energy of light wave in form of vibrating electrons before reemitting it as a new EM disturbance
  • Snell's Law:
    • Light wave travels through a vacuum at a speed of c (3.00 x 10^8 m/s), it travels through a transparent material at a speed less than c
    • Index of refraction value (n): provides a quantitative expression of the optical density of a given medium
    • Materials with higher index of refraction values have a tendency to hold onto absorbed light energy for greater lengths of time before reemitting it to interatomic void
  • Angle of Deviation:
    • Amount of overall refraction caused by light ray passage is often expressed in terms of the angle of deviation
    • Angle made between the incident ray of light entering the first face of the prism and the refracted ray that emerges from the second face of the prism
  • Rainbow:
    • Example of white light dispersion
    • High # of tiny water droplets remain hanging in the air shortly after rain
    • Each drop functions as a tiny prism
    • When sunlight strikes these droplets, white light divides into 7 distinct colors