History of Optics
Around 500-300 BC in the early Greeks, important figures such as Democritus believed that the reason our eyes could see was because our eyes emitted light, or simulacra as he called it, and once it hit a surface it would reflect back into our eyes. The scripts that the Greeks wrote on simulacra were dismissed in the Arab world around the year 800-900, when famous mathematicians and physicists such as Al-Kindi and Alhazen thought that it must be the other way around. They thought that there must be other sources for light, such as the sun, fire, etc. that emit something, and that it is reflected on a surface and goes back into our eyes. It took humans about 1000 years to resolve this question. Alhazen did a lot in the field of optics and came close to discovering the law of refraction Snell’s law.
Fast forward to the middle ages, and we have Newton and Huygens trying to explain light in two different ways. Newton meant that light was particles traveling through the air (check out our blog post on that topic too) and Huygens thought that light was a wave. About a hundred years later the consensus of the two different thoughts was that light was a wave, and you could prove it through an interference experiment, as in the picture below.
Finally, in the 20th century, several physicists (explained in this post) helped determine that light could indeed be both a particle and a wave.
In this post we’re going to investigate the optics in light.
(Source for this posts material https://ocw.mit.edu/courses/mechanical-engineering/2-71-optics-spring-2009/index.htm)
Before we begin, we’ve explained a lot about the properties of light through previous posts (1, 2, 3). So, to make a long story short, let’s just consider light as a form of energy which is transmitted as an electromagnetic wave. This transmitted wave is wave propagation, and is related through the equation
c = λ*f (in free space or uniform medium)
Where c is the speed of light, λ is the wavelength, and f is the frequency. In addition, a period is
In 1D, you can see multiple waves in the picture below propagating with a specific wavelength, speed and direction. We see that the wave is replicating itself, as it moves from left to right.
Light does not usually propagate along a straight line, but in three dimensions. The wave propagation can be many shapes, for example a planar or spherical wavefront. A planar wavefront is where the wave phase is constant along a planar surface, as you see in the top part of the image below. Here the wavefront propagates, as time evolves, at the wave speed without changing shape. This means that the wavefronts are invariant to propagation. It is not a physical front, but rather that the energy is moving as the wave propagates.
A spherical wavefront is where the wave phase is constant along a spherical surface. Here the wavefront also propagates with time at the wave speed and expands outwards while preserving the wave’s energy.
In the two wavefronts above, the energy density in the planar wavefront is constant, while the energy density in the spherical wavefront is decreasing.
In optics we often don’t look at wavefronts, but rather look at rays. Rays are basically the normal to the wavefronts, as you see in the picture below. In free space or uniform medium, rays can only propagate in straight lines. We’ll get back to in which cases rays propagate along non-linear paths.
Interaction with Matter
Rays interact with matter in many different ways of light-matter interactions, but for the purpose of this post we’ll look more closely at two types:
Absorption is strongly dependent on wavelength, because different wavelengths carry different energy and thereby different photons will interact differently with various types of matter. Absorption is described through what is known as Beer’s Law:
Iout = Iine-2αL
The intensity of rays of light decreases exponentially as it passes through a uniform medium with the linear decay constant α, meaning the intensity changes with distance in an absorbing medium.
When light travels from one medium to the next it bends. Refraction is the change in direction and phase velocity of a wave due to a change in the medium in which the wave is travelling [https://en.wikibooks.org/wiki/Optics/Refraction]. The refractive index, n, is the optical “density” of a dialectic medium. In free space we have the speed of light equal to c = 3*10^8 m/s, while in another medium, i.e. a dielectric medium such as glass, we have:
In other words, we can think of it as the speed of light (can) changes when light enters a material or that the wavelength changes, but the frequency stays the same.
When you have an incident light ray going from one medium to the next, some of the light energy is reflected back in to the first medium, while the rest is refracted towards the second material.
Reflection and Refraction
The law of reflection states that when you have an incoming ray of light from medium 1 to medium 2, a reflection at the boundary will be at the same angle as the incoming angle.
In cases where you do not have total reflection, the incoming ray of light bends, where some is transmitted and some is reflected.
The angle of refraction is described through Snell’s law:
n1sinθ1 = n2sinθ2
Become the World’s Greatest Painter Today
So, what is the use of learning the laws of reflection and refraction? Well, you can use it to become the world’s greatest painter without ever having touched a paint brush before. The picture below is the infamous “The Music Lesson” by Johannes Vermeer.
Johannes Vermeer is considered one of the greatest painters of all time, who’s paintings were so good that many believed he might have used optics to paint such life like paintings. One theory how that might have occurred comes from an entrepreneur, Tim Jenson, who in 2008 used mirrors and lenses to match colors of reflected light to recreate the picture above. How accurate was this technique? Well just look at the picture below:
Check out the trailer below (or see the movie), and you too can paint like the Greats today!