Physics of Light: Wave-Particle Duality and Optics

The Nature of Light

The question regarding the nature of light has been a problem from antiquity until the 20th century. During this period, two theories were developed: the corpuscular theory, which considered that light is composed of particles or corpuscles, and the wave theory, which defended that light behaves like a wave. Both theories were valid as they explained the phenomena of reflection and refraction. However, the wave theory could also explain oscillatory phenomena such as interference and diffraction, as well as why the speed of light is greater in less dense media. Additionally, the development of Maxwell's electromagnetism in the 19th century stated that the wave theory was correct and that light was an electromagnetic wave.

In the 20th century, Einstein had to use the particle theory to explain certain phenomena of emission and absorption of light in matter, such as the photoelectric effect. From this point, the concept of wave-particle duality of light was introduced into physics; that is, it had two natures: sometimes it acted as an electromagnetic wave and sometimes as a stream of particles called photons with a given energy.

Reflection and Refraction

When a wave crashes onto the surface of two media with different refractive indices, a part of the wave is reflected and another part is refracted into the second medium. The following laws apply:

• 1. Both beams (reflected and refracted) are in the same plane, which is perpendicular to the contact surface.
• 2. The angle of incidence equals the angle of reflection.
• 3. The angle of incidence and the angle of refraction are related by Snell's Law: n1 sin(θ1) = n2 sin(θ2) (where n is the refractive index). According to Snell's Law, if n2 is greater, the ray moves closer to the normal. It also relates the angles with the speed since n = c / v, so: sin(θ2) / sin(θ1) = v1 / v2.

Lens Power and Focal Distance

The power of a lens is the inverse of the focal length and is measured in diopters. This is determined by n (the refractive index of the lens) and R1 and R2 (the radii of curvature of the first and second sides of the lens, assuming the lens is always in air). Depending on the value and the sign of the radii of curvature, the power will be positive (converging) or negative (diverging). When the lenses are symmetrical (biconcave or biconvex), then R1 = -R2.

The focal length f* is the distance between the lens and the image focus. The image focus is the location of the image of an object point at infinity. The object focal length f is the distance to the object focus, which is the point whose image is formed at infinity. It equals the focal length with the opposite sign (f = -f*).