Understanding Light: Theories, Speed, and Geometric Optics
Nature of Light:
1) Corpuscular Theory: Proposed by Pythagoras, this theory suggests that light consists of tiny particles emitted from luminous bodies. Newton further developed this idea, stating that light is formed of small particles. When these particles encounter a surface separating two optically distinct media, they are either repelled (reflected) or attracted (refracted), following the laws of elastic collisions.
Elastic Collision Laws: The incident ray, the reflected ray, and the normal line all lie in the same plane. The angle of incidence equals the angle of reflection.
Refraction Laws: The incident ray, the refracted ray, and the normal line all lie in the same plane. The sines of the angles of incidence and refraction are inversely proportional to the propagation speeds of light in the respective media. VT = V1 = VTseni = V2sin t -> seni / sin t = V2 / V1
2) Wave Theory: This theory posits that light is a wave. When a wavefront encounters a surface separating two optically distinct media, part of it is reflected, and another part is refracted. Consider a wavefront incident on two optically distinct halves. One ray has already entered the second half, covering a certain distance. Similar triangles are formed, leading to: seni / B `B = sin t -> seni / V1 = sin t / V2 -> seni / sin t = V1 / V2. The speed of light, c, as determined by Maxwell, is approximately 0.2999939 x 109 m/s.
3) Wave-Particle Duality: Louis de Broglie proposed that light exhibits both wave-like and particle-like properties (corpuscle-wave duality). This means that light can be considered a wave associated with a particle, depending on the phenomenon being studied. This hypothesis applies not only to light but also to any particle (e.g., an electron).
Determining the Speed of Light
Romer was the first to measure the speed of light using astronomical observations of Jupiter’s moons. By observing the timing of eclipses of Jupiter’s moon, he noticed a difference in timing depending on Earth’s position in its orbit. When Earth is closer to Jupiter, the eclipses appear earlier than expected, and when Earth is farther, they appear later. This difference in time corresponds to the extra distance light has to travel when Earth is at its farthest point from Jupiter. This distance corresponds to the diameter of Earth’s orbit. Romer calculated the speed of light to be approximately c = 0.298 x 109 m/s.
Fizeau used a toothed wheel to measure the speed of light. Light was shone through a gap in the wheel and reflected back by a mirror 8636m away. By increasing the speed of the wheel, the returning light would be blocked by a tooth. The first occultation occurred at 13.6 revolutions per second, allowing for the calculation of the speed of light: c = 0.313 x 109 m/s.
Geometric Optics
Divided into:
- Physical Optics: Studies phenomena related to the wave nature of light.
- Geometric Optics: Focuses on the geometric study of light propagation based on the following principles:
Assumptions:
- Light travels in straight lines.
- Light rays are mutually independent.
- Reflection: The incident ray, the reflected ray, and the normal line all lie in the same plane. The angle of incidence equals the angle of reflection.
- Refraction: The incident ray, the refracted ray, and the normal line all lie in the same plane. The sines of the angles of incidence and refraction are directly proportional to the speeds of light in the respective media (Huygens’ principle).
Refractive Index
Relative Refractive Index: The ratio of the speed of light in two media.
- Numerator: Speed of light in the medium from which light is coming.
- Denominator: Speed of light in the medium to which light is going.
n21 = V1 / V2
Absolute Refractive Index: The refractive index relative to a vacuum.
n1 = C / V1
n2 = C / V2
n21 = V1 / V2 = (C / V2) / (C / V1) = n2 / n1
seni / sin t = V1 / V2 = n21 = n2 / n1
n1 = n2sin t / seni
Critical Angle and Total Internal Reflection
When light passes from a denser medium (higher refractive index) to a rarer medium (lower refractive index): n1 > n2 -> sin t = n1 / n2 seni < seni –> r < i. Light bends away from the normal.
n1sin t < n2 = n1 / n2 seni > seni -> r > i.
If the angle of incidence is increased, there will be a point where the angle of refraction reaches 900 (the critical angle). If the angle of incidence is increased beyond the critical angle, total internal reflection occurs. If the light is incident at an angle greater than the critical angle, there is no refraction.
Fermat’s Principle
Fermat’s principle states that light travels along the path that takes the least time to travel between two points (A and B). ?t = ? dS / V = 1 / C ? (C / V) dS = 1 / C ? nds. This principle implies that the time taken corresponds to an extreme value. t = [(? x2+ a2) / V1] + [(? (d-x)2 + b2) / V2] -> deriving dt / dx = [x / (? x2+ a2) / V1]+[-( d-x ) / (? (d2-x 2) + b2)]–> despjand and multiplied by c -> n1= n2sin t / seni