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
- 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.
- 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.
- 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.
- 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
- 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)
- 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)
- 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).
- 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.
- 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.
- 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.