Optics - General Introduction - What we will cover

  • The Nature of Light
  • Geometric Optics
  • Reflection and Refraction
  • Mirrors and Lenses
  • Lens Formula
  • Optical Instruments
  • Dispersion of Light
  • Interference of Light
  • Diffraction of Light
  • Polarization of Light
  1. Reflection and Refraction:
  • Reflection: The bouncing back of light waves from a surface is called reflection.
    • Angle of incidence = Angle of reflection (law of reflection).
    • Types of reflection: Regular reflection and Diffuse reflection.
  • Refraction: The bending of light waves as they pass from one medium to another is called refraction.
    • Snell’s Law: n1 sinθ1 = n2 sinθ2, where n is the refractive index and θ is the angle of incidence or refraction.
  1. Mirrors:
  • Types of mirrors: Plane mirror, Concave mirror, Convex mirror.
  • Characteristics of images formed by mirrors:
    • Plane mirror: Virtual, erect, and same size as the object.
    • Concave mirror:
      • Object at infinity: Real, inverted, and focused at the focus.
      • Object between infinity and focus: Real, inverted, and beyond the focus.
      • Object at focus: No image formed.
    • Convex mirror: Virtual, erect, and diminished in size.
  1. Lenses:
  • Types of lenses: Convex lens, Concave lens.
  • Lens formula: (1/v) - (1/u) = (1/f), where v is the image distance, u is the object distance, and f is the focal length of the lens.
  • Characteristics of images formed by lenses:
    • Convex lens:
      • Object beyond 2f: Real, inverted, and diminished.
      • Object at 2f: Real, inverted, and same size.
      • Object between f and 2f: Real, inverted, and magnified.
      • Object at f: No image formed.
    • Concave lens: Virtual, erect, and diminished.
  1. Lens Formula Example:
  • Object distance (u) = 15 cm
  • Focal length (f) = 10 cm
  • Using the lens formula: (1/v) - (1/15) = (1/10)
  • Solving for v: v ≈ 30 cm
  • Image distance (v) ≈ 30 cm
  1. Optical Instruments - Microscope:
  • Compound microscope:
    • Objective lens: Provides magnified real image of the object.
    • Eyepiece lens: Magnifies the real image formed by the objective lens.
  • Magnification of a compound microscope: Magnification = (Magnification of the objective lens) x (Magnification of the eyepiece lens)
  1. Optical Instruments - Telescope:
  • Astronomical telescope:
    • Objective lens: Forms a real inverted image at the focal point of the eyepiece lens.
    • Eyepiece lens: Magnifies the real inverted image formed by the objective lens.
  • Magnification of an astronomical telescope: Magnification = (Magnification of the objective lens) x (Magnification of the eyepiece lens)
  1. Dispersion of Light:
  • Dispersion: The splitting of white light into its constituent colors when it passes through a prism.
  • Deviation: The angle by which each color is bent as it passes through the prism.
  • The order of colors in a dispersed spectrum: Violet, Indigo, Blue, Green, Yellow, Orange, Red (VIBGYOR).
  1. Interference of Light:
  • Interference: The combination of two or more light waves to form a resultant wave.
  • Conditions for constructive interference: When the path difference between two waves is equal to an integral multiple of the wavelength.
  • Conditions for destructive interference: When the path difference between two waves is equal to an odd half integral multiple of the wavelength.
  1. Interference - Example:
  • Young’s double-slit experiment:
    • Setup: A light source, two narrow slits, and a screen to observe the interference pattern.
    • When the path difference between the two waves is an integral multiple of the wavelength, bright fringes (constructive interference) are observed.
    • When the path difference between the two waves is a half integral multiple of the wavelength, dark fringes (destructive interference) are observed.
  1. Diffraction of Light:
  • Diffraction: The bending of light waves as they pass through an opening or around an obstacle.
  • Diffraction pattern: The pattern formed on a screen when light waves pass through a single slit, double slits, or a diffraction grating.
  • Diffraction limit: The minimum separation between two objects for them to be resolved as separate entities. 21. Polarization of Light:
  • Polarization: The phenomenon in which light waves vibrate in a single plane instead of in all directions.
    • Polarizing filters: Filters that allow only light waves vibrating in a specific direction to pass through.
    • Malus’ Law: Intensity of polarized light transmitted through a polarizer is given by I = I₀ cos²θ, where I₀ is the initial intensity and θ is the angle between the polarizer and the direction of polarization. 22. Polarization of Light - Example:
  • Malus’ Law example:
    • Initial intensity (I₀) = 10 W/m²
    • Angle between polarizer and direction of polarization (θ) = 30°
    • Using Malus’ Law: I = I₀ cos²θ = 10 cos²30° ≈ 8.66 W/m²
    • Intensity of polarized light (I) ≈ 8.66 W/m² 23. Interference of Light - Young's Double-slit Experiment:
  • Interference in a double-slit experiment:
    • Setup: A light source, two narrow slits, and a screen to observe the interference pattern.
    • Young’s equation: dsinθ = mλ, where d is the slit separation, θ is the angle of observation, m is the order of the fringe, and λ is the wavelength of light. 24. Interference of Light - Example:
  • Young’s double-slit experiment example:
    • Slit separation (d) = 0.1 mm
    • Angle of observation (θ) = 30°
    • Order of the fringe (m) = 3
    • Wavelength of light (λ) = 500 nm
    • Using Young’s equation: (0.1 × 10⁻³) sin30° = 3 × (500 × 10⁻⁹)
    • Solving for d: d ≈ 9.42 × 10⁻⁶ m
    • Slit separation (d) ≈ 9.42 μm 25. Diffraction of Light - Single Slit Diffraction:
  • Diffraction due to a single slit:
    • Diffraction pattern: Central bright fringe surrounded by alternating dark and bright fringes.
    • Width of central bright fringe: 2λL/d, where L is the distance between the slit and the screen, and d is the slit width. 26. Diffraction of Light - Example:
  • Single slit diffraction example:
    • Wavelength of light (λ) = 600 nm
    • Distance between slit and screen (L) = 2 m
    • Slit width (d) = 0.1 mm
    • Using the formula: 2 × (600 × 10⁻⁹) × 2 / (0.1 × 10⁻³) = 0.024 m
    • Width of central bright fringe ≈ 24 mm 27. Diffraction of Light - Double Slit Diffraction:
  • Diffraction due to double slits:
    • Interference pattern superimposed on the diffraction pattern.
    • Separation between adjacent fringes: λL/d, where L is the distance between the slits and the screen, and d is the slit separation. 28. Diffraction of Light - Example:
  • Double slit diffraction example:
    • Wavelength of light (λ) = 500 nm
    • Distance between slits and screen (L) = 1 m
    • Slit separation (d) = 0.1 mm
    • Using the formula: (500 × 10⁻⁹) × 1 / (0.1 × 10⁻³) = 0.005 m
    • Separation between adjacent fringes ≈ 5 mm 29. Optical Instruments - Human Eye:
  • The human eye:
    • Structure: Cornea, iris, lens, retina, and optic nerve.
    • Accommodation: The ability of the lens to change its shape to focus on objects at various distances.
    • Defects of vision: Myopia (nearsightedness), Hypermetropia (farsightedness), and Presbyopia (age-related loss of accommodation). 30. Optical Instruments - Cameras:
  • Cameras:
    • Structure: Lens, diaphragm, shutter, and image sensor (film or digital).
    • Aperture: The size of the lens opening determined by the diaphragm.
    • Shutter speed: The length of time the shutter remains open.
    • Exposure: The amount of light reaching the image sensor, controlled by the aperture and shutter speed.