Lecture 29: Light Waves, Wave Optics, and Polarization

Models of Light

• Ray Optics:

  • Treats light as a ray or a beam traveling from one location to another.
  • Explains phenomena such as light bending (refraction), bouncing (reflection), transmission, and absorption.
  • Applicable to understanding mirrors, lenses, and rainbows.
  • Valued for its simplicity, though it cannot explain all properties of light.

• Wave Optics:

  • Expands the model to include the wave nature of light.
  • Allows for the quantification of interference and diffraction.

• Electromagnetic Optics:

  • Accounts for the wave nature while explicitly including the fact that light is composed of electric field and magnetic field vectors oscillating in space.
  • Used to explain and quantify light polarization.

• Quantum Optics:

  • The most complicated and mathematically rigorous model.
  • Used when other models fall short to explain complex phenomena such as the photoelectric effect, lasers, and semiconductors.
  • Covers all phenomena included in Ray, Wave, and Electromagnetic Optics.

Huygens Principle

• Definition: Huygens principle states that every point on a wave can be treated as a source of a spherical wave that propagates through time and space.
• Interference of Wavelets: These individual spherical waves interact through interference. The total wave is represented by the sum total of the amplitudes of every individual spherical wave.
• Plane Waves:
  • A plane wave travels through space with all wave crests and troughs aligned in straight lines.
  • Represented by parallel lines in space marking the wave crests.
  • According to Huygens principle, each point on a crest acts as a spherical wave source, and their collective interference results in the plane wave.
• Behavior at Openings:
  • When a plane wave passes through a small opening, it curves at the edges.
  • The degree of curving is determined by the relationship between the wavelength of the light and the size of the opening.
  • Width vs. Wavelength:
    • The larger the width of the opening compared to the wavelength, the less pronounced the curving.
    • The smaller the width of the opening compared to the wavelength, the more pronounced the curving becomes.

Diffraction

• Definition: Diffraction is the bending of light as it travels around a corner or through a small opening.
• Scale Requirements: While diffraction happens with all light waves, the effect is only noticeable when the opening size is on the same scale as the wavelength of the light.
• Wavelength Correlation: All other factors being equal, longer wavelengths will experience more bending than shorter wavelengths.
• Universal Wave Property: Diffraction is not limited to visible light. It applies to:
  • Water waves: Observed in ripple tanks where smaller openings result in more spreading.
  • Radio waves: These diffract around terrain features like buildings and mountains.

Diffraction Gratings and Experimental Observations

• Mechanism: A diffraction grating is a component with regularly spaced openings. It creates a periodic pattern that diffracts light through several different angles due to regions of constructive and destructive interference.
• Laser Pointer Experiments: In a demonstration conducted at a distance of $1\,m$ from a screen:
  • Grating 1 ($1000\,lines/mm$):
    • Blue Laser: Produced bright spots of constructive interference spaced $46\,cm$ apart.
    • Green Laser: Spaced farther apart at $65\,cm$ because green light has a larger wavelength than blue light, causing more bending.
    • Red Laser: Produced the largest spacing at $90\,cm$, as red has the longest wavelength of visible light.
  • Grating 2 ($500\,lines/mm$):
    • Red Laser: When the spacing of the grating was increased (fewer lines per millimeter), the light bent less, spreading out only $36\,cm$.
• White Light Diffraction:
  • Since white light contains all colors, a grating splits the light into a rainbow pattern.
  • Longer wavelengths (reds) bend the most, while shorter wavelengths (purples/blues) bend the least.
• Scientific and Practical Applications:
  • Clean Room Engineering: Using diffraction gratings and Charge-Coupled Devices (CCDs) to measure the intensity and specific wavelengths emitted by custom-designed devices.
  • Astrophysics: Determining the composition of stars, including the sun, by analyzing emitted wavelengths to identify specific gases.
  • Consumer Goods: "Rainbow glasses" function as diffraction gratings.
• Resolution Limits: Diffraction limits the ability of imaging devices (cameras and microscopes) to see small objects.
  • Limit Formula: Most devices can only focus on sizes larger than approximately $\frac{1}{2}$ the wavelength of the light used.
  • Visible Light Constraint: If the smallest visible wavelength is $400\,nm$, the smallest object focusable is approximately $200\,nm$. Objects smaller than this cannot be seen with visible light.

Thin Film Interference

• Definition: An interference pattern created when light waves reflect off both the top and bottom interfaces of a thin layer of material.
• Natural Examples: Rainbow patterns seen in oily water puddles are caused by thin film interference. As the thickness of the oil varies, different wavelengths undergo constructive interference.
• Physics of Thickness:
  • Constructive Interference: Occurs when the thin film thickness is equal to exactly $\frac{1}{4}$ of the wavelength of the light. This color will be reflected with high intensity.
  • Destructive Interference: Occurs when the thin film thickness is equal to exactly $\frac{1}{2}$ of the wavelength of the light. This specific color will not be reflected at all.
• Optical Flatness Testing:
  • Two pieces of glass can be tested for flatness using a monochromatic (single wavelength) light source, such as a sodium light.
  • Changing the air gap thickness between the glass pieces creates circular fringes. If the glass were perfectly flat, these fringes would appear as straight lines.
• Anti-Reflection Coatings: By layering multiple thin films, manufacturers can eliminate reflections on optical devices like eyeglasses, cameras, and microscopes.

Polarization

• Nature of Light Waves: Light is a transverse wave where electric and magnetic fields oscillate at right angles to each other and at right angles to the direction of motion.
• Definition of Polarization: A property of transverse waves where the electric field components are oriented in a single direction.
• Polarizing Filters: These filters block electric fields oriented in any direction other than the filter's specific orientation.
• Non-Polarized Light: Most light sources generate waves with all orientations. This can be simplified as $50\,\%$ horizontal and $50\,\%$ vertical electric field components.
• Three-Polarizer Experiment:
  • Filter 1: Set to vertical; blocks all horizontal components.
  • Filter 2: Set at a 90-degree angle to the first; blocks all remaining light, resulting in total darkness.
  • Filter 3 (Insertion): If a third polarizer is placed between the first two at a random angle, light passes through again. This is because the middle filter allows through a component of the vertical light oriented at its specific angle, and the final horizontal filter then allows through the horizontal component of that angled light.
• Brewster's Angle: Light reflecting off a surface at a very steep angle (greater than Brewster's angle) will have only one polarization. The other polarization is not reflected.
• Practical Applications:
  • Sunglasses: Polarized lenses eliminate glare from steeply angled reflections.
  • Display Technology: LCD screens and monitors generate polarized light; tilting one's head $90\,degrees$ while wearing polarized sunglasses can make the screen appear black.
  • Stress Analysis: Heat-treated windshields in vehicles exhibit polarization effects.
• Birefringence:
  • Some objects have an index of refraction that changes based on the polarization of light.
  • One polarization bends more than the other (cross-polarization).
  • A birefringent crystal placed over text creates a double image. Rotating a polarizing filter over the crystal will block one image and then the other, depending on the filter's orientation.