Optical Physics and Gravitational Fields: Principles and Phenomena
Optical Physics
Scientific Methods
Described since the 17th century, plasmonics can be traced back to Galileo Galilei.
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Leucippus and Democritus proposed that vision was preferentially produced by objects’ images that reach the eyes and then the soul, giving life to individuals’ vision.
17th Century
At the end of the Pythagorean school, the eyes were thought to emit a beam of fire that caught invisible entities. In the 17th century, rational Arabs introduced concepts close to those studied by scientists. Important scientists of the 17th century were Galileo (who introduced alternative methods of scientific treatment to measure the velocity of phenomena) and the study of light. Grimaldi studied diffraction and refraction, and Snell studied refraction.
First Half of the 17th Century
In the second half of the 17th century, theories about light were formulated. Newton, in 1671, enunciated a theory on light. He was a clergyman and political economist with social power. He tried to explain how light was, formulating the corpuscular theory. He discovered the phenomenon that distinguishes light from non-light colors. For Newton, light was composed of particles with very small mass moving at very high velocities. This explained the propagation of light, shadows, and penumbras. He explained reflection.
Second Half of the 17th Century
Huygens stated in 1678 that light is a wave, like sound waves. He deduced that light travels slower in water than in air. Ether explained and allowed the propagation of waves in a vacuum.
Principles of the 19th Century
Young identified the interference of light, exclusive to light waves. In 1815, Snell discovered the diffraction of light waves.
20th Century
Photoelectric Phenomenon: When a metallic plate receives light, it releases electrons. In 1905, Einstein explained that in this experiment, light (a wave phenomenon) presents a corpuscular component. When a metallic plate receives light, it releases electrons.
Refractive Index: The ratio between the velocity of light in a vacuum and the velocity of propagation in a medium. When light penetrates a more refractive medium, its wavelength changes to a smaller value, and the phenomenon of reflection also occurs.
Law of Incidence: The incident ray propagates in the medium of incidence.
Reflection: The angle of incidence is equal to the angle of reflection.
Diffuse Reflection: Due to irregularities, the incident beam presents a surface that does not reflect in all directions.
Specular Reflection: Reflection on a very smooth polished surface is the deviation that a ray experiences when passing from one medium to another.
Refraction: The deviation that a ray experiences when passing from one medium to another.
Snell’s Law of Refraction: The angle of incidence and the angle of refraction are related by the equation ().
Limit Angle: The angle of incidence that corresponds to a refraction of 90°. It is obtained when a wave passes from one medium to another with a smaller refractive index.
Total Internal Reflection: A phenomenon that occurs when the angle of incidence is greater than the limit angle. In these cases, the rays do not penetrate the surface of the medium.
Dispersion: The separation of light.
Light: A ray of light in its different components according to the refractive index of each one.
Spectrum: A set of colors.
White Light: Polychromatic light composed of several colors.
Monochromatic Light: A single color.
Interference: The coincidence of two or more waves at the same point.
Illuminated Stripes: When the distance between the paths is an integer number of wavelengths.
Diffraction: The change in the direction of wave propagation when there is a change of medium or when an obstacle is encountered in its path. This phenomenon occurs in objects whose dimensions are of the same order as the wavelength.
Huygens’ Principle: Explains the phenomenon of diffraction. When a wave reaches an aperture, the points of the wave act as new sources of elementary waves in phase.
Polarization: Exclusive to transverse waves, consisting of the vibration of the electric and magnetic fields in a preferential direction.
Types
Linear: The electromagnetic field vector always vibrates in one direction.
Circular: Obtained by adding two linearly polarized waves in perpendicular directions with the same frequency and a phase difference of pi/2 radians.
Elliptical: Obtained by adding waves in perpendicular directions with different amplitudes and a phase difference of pi/2 radians.
Absorption of Light: When unpolarized light reflects on a surface, the reflected light appears linearly polarized. This occurs when the angle of incidence plus the angle of refraction equals pi/2.
Common Uses
Radio Waves: Medium waves.
Microwaves: Ovens.
Visible Light: From 4000 to 7000 Angstroms.
Ultraviolet: 400 to 1 nanometer, capable of accumulating in cell nuclei.
Geometric Optics
Studies the path of light during reflections and refractions on the separation surfaces of media.
Optical System: Materials limited by surfaces.
Propagation: Of any natural origin.
Reversibility: Spreads in the same way in one direction as in another.
Independence of Other Rays: The crossing of two or more rays does not affect the trajectory.
Stigmatic Optical System: All rays that depart from one point converge at another point.
Astigmatic: All rays that do not depart from one point converge at different points.
Centered: Separation surfaces of media that have a common axis of symmetry.
Plane Mirror: Produces virtual and symmetric images.
Spherical Mirrors: Reflectors.
Concave: Reflecting surface is inside.
Convex: Reflecting surface is outside.
Spherical Diopters: Reflectors.
Diopter: A surface that separates two media with different refractive indices, isotropic and homogeneous.
Isotropic: Same physical properties in all directions.
Thin Lenses: Transparent material limited by two spherical surfaces or one flat and another spherical.
Association of Two Spherical Diopters: Spherical.
The Human Eye: The crystalline lens is a converging convex lens.
Accommodation: The organ increases its curvature and reduces its focal radius, allowing images to form on the retina.
Near Point: The closest point to the eye where an object can be placed and seen clearly. This distance is 25 cm, the minimum distance for vision.
Far Point: The farthest point from the eye where an object can be placed and seen clearly. Maximum distance of vision.
Defects of Vision
Presbyopia or Farsightedness: The person who suffers from it has a reduction in accommodation due to fatigue of the ciliary muscles, which lose elasticity. It is corrected with converging lenses called bifocals.
Myopia: An excess of convergence in the crystalline lens. It is corrected with diverging lenses.
Hypermetropia: Loss of accommodation due to a lack of convergence. This defect is corrected with converging lenses.
Astigmatism: Due to an irregularity in the curvature of the cornea. It is corrected with cylindrical lenses.
Optical Microscope: An instrument formed by two converging lenses (objective and ocular). Inverted and larger virtual image. If the object is to the left, the images are inverted and larger. If the object is to the right, the images are virtual, larger, and upright.
Luminous Impressions: The iris diaphragm regulates the light, the crystalline lens and the objective focus, and the retina and the sensor form the image.
Velocity: The time the shutter remains open.
Shutter: A device that lets in light to control the amount of light that reaches the sensor.
Diaphragm: A device that regulates the optical aperture.
Depth of Field: The zone in which the image captured by the objective is sharp.
Camera: Converging lens.
Photographic Lens: Converging lens.
Magnifying Glass: If the object is between the focus and the lens, the image is larger, upright, and virtual.
Telescope: Larger, inverted, and virtual image.
Gravitational Field
The Aristotelian Model (Geocentric)
The universe was formed by two concentric spherical regions. The Earth occupied the center of the universe. It was the region of the elements: fire, air, water, and earth. Beyond the lunar sphere was the ethereal region of the heavens, whose only element was the fifth essence, incorruptible. All the movements of the stars located in the immediate vicinity of the Earth were perfect and perpetual (circular). The universe ended in the sphere of fixed stars. Aristotle defended the concepts of mechanics. He argued that bodies tend to be situated in their natural place. In addition, bodies had natural movements: light bodies tend upward, and heavy bodies tend downward. He argued that bodies move due to an engine, which is perpetual in natural movements. In forced movements, the engine is outside the body. The main idea introduced was that to produce movement, it is necessary to apply a force.
Ptolemy’s Geocentrism
The reasons why geocentric models remained instead of heliocentric models are the following: “lack of quantitative predictions and calculations” and “if the Earth were not the center of the universe, different angles of the stars could be seen during the Earth’s trajectory.” This phenomenon is called parallax. Ptolemy justified his model by predicting eclipses and planetary movements. He demonstrated the movement of the Moon and the Sun. He observed that these planets had retrograde movements. To justify this, he used a composite of two rotations. The planet revolved around a point that, in reality, rotated with respect to the Earth. The orbit around the Earth was called the deferent, and the orbit of the planet was called the epicycle. A simple model of epicycles did not explain the movement of some planets, so Ptolemy used more epicycles on other epicycles. This generated doubts among skeptics in Poland.
Copernicus
Copernicus was born in Poland and studied mathematics, astronomy, and medicine. His hobby was observing the stars. Due to its size and heat, he considered that the Sun should be in the center of the universe. Through observation of Venus and Mercury, he could establish this hypothesis. This approach allowed him to explain the retrograde motion of the planets with simplicity.
Galileo
Galileo was born in Pisa and studied medicine and physics. He built a telescope with 30x magnification lenses and observed the phases of Venus. He defended the Copernican system. He managed to see mountains and craters on the Moon. He discovered the satellites of Jupiter, confirming that there were bodies that did not have the Earth as their center. In 1632, he published his work “Dialogue Concerning the Two Chief World Systems.”
Kepler’s Laws
First Law: Planets describe elliptical orbits around the Sun, which is located at one of the foci of the elliptical orbit (perihelion, aphelion).
Second Law: This law starts from incorrect scenarios: that the planets were subjected to a force inversely proportional to the distance, that the velocity is proportional to the force, and that the orbits were circular (he had not yet stated his first law). The radius vector directed from the Sun to the planets sweeps out equal areas in equal times.
Third Law: The squares of the periods of revolution of the planets around the Sun are proportional to the cubes of the semi-major axes or the mean radii of their orbits. This is a constant for all planets, which only depends on the mass of the Sun.
Newton
Newton was a student and professor at the University of Cambridge.
Law of Universal Gravitation: All bodies attract each other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This law allows us to explain various phenomena: the protuberances of the Earth and Jupiter due to rotation, the tides, the trajectories of the planets, the variation of gravity with height, and the change in the rotation axis of the Earth.
Field Strength: The gravitational force at a point per unit mass.
Field Representation: Field lines. When the field lines are close together (high density), the field strength is higher.
Equipotential Surfaces: Points in the plane that have the same gravitational potential. In general, they are spherical surfaces with the center at the mass that creates the field.
Characteristics: They are perpendicular to the field lines at each point. The work done by the field to move a mass between two points on the same equipotential surface is zero.
Superposition Principle: When a body is subjected to the action of several gravitational forces, the total effect is the resultant of the individual effects of each field.
Conservative Forces: Forces whose work depends only on the initial and final positions and not on the path taken. The work done by a conservative force to go from point A to point B can be expressed as the variation of a function, Ep, between the initial and final points. This function is called the potential function. All central forces are conservative.
Earth’s Gravitational Field: The force of attraction that the Earth exerts on bodies towards its center of mass.
Theorem of Potential Energy: The work done by a conservative force is equal to the variation of the potential energy with the sign changed. The work done on a body is equal to the increase in its kinetic energy.
Principle of Conservation of Mechanical Energy: In a field of conservative forces, the sum of the potential energy and the kinetic energy of a body always has the same value. That is, the mechanical energy is conserved.
Gravitational Potential: The potential energy per unit mass at a point in a gravitational field.
Potential at a Point: The work done by the gravitational force to move a unit mass from that point to infinity.
Interpretation of the Sign of Work Done by a Conservative Force
If W > 0, the mass moves under the action of the gravitational field spontaneously. If W < 0, the final potential energy is less negative, and the distance is greater. The mass tends to move away. If it moves away, it is because an external force opposes the field. Then, the work is done by an external force.
Central Force Field: In any central force field, the force exerted on a body is in the same direction as the line that joins the body to the origin of the field, and its value depends exclusively on the distance between them. All central force fields are conservative. In central force fields, the vectors r and F are in the same direction, so the moment of the force from the center is zero.
Law of Conservation of Angular Momentum: The angular momentum of a particle that moves under the action of a central force is constant.
Shape of Trajectories: The potential energy of a body in a gravitational field is negative. The kinetic energy is always positive. The following cases are given depending on the total energy, E:
* If the total energy is negative and its absolute value is equal to half the potential energy, the trajectory is circular. * If the total energy is increased, an elliptical orbit is obtained. * If the total energy is zero, the body can reach infinity with zero velocity. The escape trajectory would be a parabola. * If the kinetic energy is greater than the potential energy, the velocity exceeds the parabolic trajectory and becomes a hyperbola.
A satellite changes its orbit type if its kinetic energy changes, and a change in kinetic energy requires a change in velocity.
Total Energy of an Orbit and Centripetal Force for Satellization: The resultant of all the forces acting on a body that describes a circular motion. When a mass, m, describes a circular orbit around the Earth, the only force acting on it is the force of gravitational attraction. This force is the centripetal force needed to put a satellite into orbit and achieve a total energy equal to the calculated value.
Escape Velocity: The minimum velocity a satellite needs to escape the Earth’s gravitational attraction.