Optics Lecture 1: Geometrical Optics
Recommended article : 【Physics】 Physics Table of Contents
2. Image
1. Fermat’s Principle
⑴ Fermat’s Law (Fermat’s principle)
① The law that light travels along the path that takes the least time
② Theory that encompasses the laws of reflection and refraction
③ To understand its profound significance, the concept of quantum optics is required
⑵ Law of Reflection
① Terminology
○ Normal : A line perpendicular to the interface when light reflects at the boundary
○ Incident : Light approaching the boundary
○ Reflection : Light bouncing back from the boundary
② Law 1. The angle of incidence is equal to the angle of reflection.
③ Law 2. The incident ray and the reflected ray lie in the same plane.
⑶ Snell’s Law
① Definition of refractive index n
○ c : Speed of light in a vacuum
○ v : Speed of light in a medium
② Law 1.
③ Law 2. The incident ray and the refracted ray lie in the same plane.
⑷ Total Internal Reflection
① Implication of the law of refraction
② Critical angle (θc)
○ (Note) The critical angle of diamond is 24.5°, the smallest known critical angle to date.
③ How fish see the world
Figure. 2. How fish see the world
④ Optical Fiber
Figure. 3. Structure of Optical Fiber
○ Definition : A bundle of glass, fused silica, or plastic that can transmit light over hundreds of meters or more
○ Diameter ranges from 0.05 μm to 0.6 cm
○ Structure : Core, Cladding
○ The material used for the core has a higher refractive index than that used for the cladding
○ Practical applications
○ Multiple layers of optical fiber are used in practice: Optical fiber is too thin for geometric optics approximation (i.e., Snell’s law) to apply.
○ Overlapping light of various frequencies is used for information transmission: Unlike electrons where Pauli’s exclusion principle applies, light can overlap.
○ Bending of the fiber causes irregular reflections, leading to blurred images → To prevent this, graded index is used.
○ ~0.2 dB/km loss
○ Classification based on material
○ Glass or plastic: Visible light, near-infrared range
○ Fused silica: Ultraviolet range to near-infrared range
○ Classification based on usage
○ Reflecting probes
○ Transmissive probes
○ Dip probes
⑸ Negative Refraction Index
① Classification of materials
○ Type 1: ε > 0, μ > 0: Normal optical materials, right-handed propagating wave
○ Type 2: ε < 0, μ > 0: Electromagnetic plasma, decaying electromagnetic waves, many metals (UV - optical), thin wire structures (GHz)
○ Type 3: ε > 0, μ < 0: Magnetic plasma, decaying electromagnetic waves, structured materials, natural magnetism (~GHz)
○ Type 4: ε < 0, μ < 0: Negative refraction index, left-handed propagating wave, artificial metamaterial
② References
○ V. G. Veselago, Usp. Fiz. Nauk 92, 517 (1967)
○ V. G. Veselago, Soviet Physics Uspekhi 10, 509 (1968)
○ R. A. Shelby et al., Science 292, 77 (2001): Experimental evidence
⑹ Dispersion
① Prism Experiment
Figure. 1. Prism Experiment
② Explanation 1.
○ 1st. The frequency of light remains constant even when the medium changes.
○ 2nd. The speed of light increases as wavelength in the medium increases. As speed of light increases, refractive index decreases.
○ 3rd. Longer wavelengths (shorter frequencies) result in less bending of light.
③ Explanation 2.
○ Short wavelengths correspond to shorter time spent within atoms.
○ Short wavelengths result in more collisions and resonance absorption.
④ Complexity of wavelengths due to various reasons
○ Interaction of atoms results in a variety of resonant wavelength ranges.
○ Motion of atoms also alters the resonant wavelength ranges.
○ To observe specific resonant wavelength ranges, cooled atoms need to be observed.
⑤ Application: Rainbow
○ Refraction → Internal reflection → Refraction lead to dispersion of colors
○ Longer wavelengths (closer to red) result in less bending.
2. Image
⑴ Type 1. Plane Mirror
① Constructed so that the mirror surface is the perpendicular bisector of the object and the image.
⑵ Type 2. Spherical Mirror: Concave Mirror, Convex Mirror
① Spherical and Parabolic Mirrors
○ Spherical mirrors have a constant curvature but parallel rays do not converge exactly to a single point.
○ Parabolic mirrors have parallel rays that converge exactly to a single point.
② Focal Length
○ When the object distance is ∞, the image is at the focal point.
○ For a spherical mirror, f = R / 2
③ Construction Method
○ Parallel rays pass through the focus.
○ Rays passing through the focus travel parallel to the optical axis.
○ Rays heading towards the center of the mirror reflect symmetrically about the optical axis.
○ Rays passing through the center of the lens continue in a straight line.
④ Proof of Concave Mirror 1: A construction using only two rays does not require approximation.
Figure. 4. Proof of Concave Mirror 1
⑤ Proof of Concave Mirror 2: A construction using arbitrary rays requires approximation.
Figure. 5. Proof of Concave Mirror 2
⑤ Spherical Aberration: When not dealing with paraxial rays
○ When not dealing with paraxial rays, parallel rays do not converge to the focus (because it is not a parabolic mirror).
○ In the case of paraxial rays: Quadratic function, i.e., equation
of parabola
⑶ Type 3. Spherical Lens: Convex Lens, Concave Lens
① Construction Method
○ Parallel rays pass through the focus.
○ Rays passing through the focus travel parallel to the optical axis.
○ Rays heading towards the center of the lens reflect symmetrically about the optical axis.
○ Rays passing through the center of the lens continue in a straight line.
⑷ Spherical Boundary
① Proof of Spherical Boundary
Figure. 6. Proof of Spherical Boundary
② Apparent Depth
○ The apparent depth appears greater when looking from outside the water into the water (this can be approached using the concept of visual angle).
○ Proof: Negative values imply imaginary.
Figure. 7. Apparent Depth
⑸ Thin Lens Formula: Also known as the lens maker’s formula
3. Optical Devices
⑴ Optical Devices
① Converges incoming light from the outside to form an image on the retina.
② Mainly, light is well refracted at the cornea.
③ The lens finely adjusts the refractive index.
⑵ Magnifying Glass ↔ Telescope
① Since we should be able to see comfortably with our eyes, the near point (25 cm) is important.
② Magnification factor m
○ To understand how an optical device magnifies an object, we need to consider the size of the image formed on the retina.
○ The magnification factor or angular magnification m of a device is the ratio of the angular size of an object with the device to the angular size of the same object without the device.
③ Calculation of Magnification
○ The magnification is the greatest when the object is at the near point, i.e., when q = -25 cm.
○ The most comfortable state for the eye is when the object is at an infinite distance.
⑶ Microscope
Figure. 8. Microscope
① Placing the object at the focal length gives the highest magnification.
② Visible light has a significantly larger wavelength compared to atoms, making direct observation impossible.
③ When trying to see electrons with light, λ↓ → E↑
⑷ Telescope
Figure. 9. Telescope
① Collecting Power: R ↑, N ↑, t ↑
② Resolution: R ↑, λ ↓
③ Refraction: Cannot create a large angular separation
④ Reflection: Reflection can block objects at the position where the image is formed.
⑤ Example: A refracting telescope consists of two convex lenses separated by a distance of 100 cm. If the focal length of the objective lens is 20 cm, what is the angular magnification mθ of the telescope?
⑸ Astronomical Telescope
① Magnification = Focal length of objective lens ÷ Focal length of eyepiece lens
② Aligning the polar axis: To easily track celestial bodies in their daily motion.
③ Types
○ Optical telescopes: Most affected by weather conditions.
○ Radio telescopes: Observing electromagnetic waves from the ground.
○ Space telescopes: Observing short-wavelength electromagnetic waves that can’t be observed from the ground. Suitable for observing high-temperature celestial bodies.
⑹ Aberration
① Spherical Aberration: A phenomenon where not dealing with paraxial rays shortens the focal length.
② Chromatic Aberration: Refractive index varies with wavelength, causing shorter wavelengths to have shorter focal lengths.
Input : 2019.04.11 16:05