Figure 2.7: Huygens principle of light refraction.
Source: Wikimedia Commons.
In order not to lose the continuity of the wavefronts across the boundary between the two media, the waves in C2 have to change direction. According to Huygens principle, this angle can be found by supposing that each part of the wavefront passing the boundary between C1 and C2 becomes a new circular wave source - an elemental wave source - with the radius of the expanding circular front now corresponding to the slowed wave speed. The tangent line along the resulting circular wavefronts then represents the new wave front. So the direction of the movement of the wave - drawn here with the black arrows, pointing perpendicular to the wave fronts - bends away from the boundary. According to Huygens, this explains Snell's law [15] for the refraction of light waves.
So it was Huygens' idea that each point of a wavefront can be considered as a new elemental wave source expanding in a circular fashion and that the resulting wave would be simply the sum of all those elemental waves. However, he could not explain with this elementary wave model why the waves expanding backwards from those elementary sources could not be treated in the same way.
Figure 2.8: Wave refraction explained with contiguous wave fronts. φ1 is the angle of incidence, φ2 is the angle of refraction.
It's not necessary for you to understand and follow Huygen's elemental waves, it is enough when you just think about the wavefronts having to be contiguous when crossing the boundary. The parallel lines figure 2.8 depict the parallel traveling wavefronts. The waves in C2 do run slower than in C1 while their frequency remains the same, which means that their wavelength λ2 in C2 has to be smaller than their wavelength λ1 in C1. This should be clear from figure 2.8.
In order to remain both contiguous and parallel, the wave fronts entering C2 must change their direction at the boundary. In C2 they will have to run more parallel to the boundary. The dashed line in figure 2.8 drawn perpendicular to the boundary between C1 and C2 is called the normal. The angles with the normal, φ1 and φ2, are called the angle of incidence and of refraction. You should understand from this that the angle of refraction is smaller than the angle of incidence when the wave speed is slower in medium C2.
So, in general, when the wave speed is slower in the medium it enters, the wave fronts will tend to run more parallel to the boundary between the two media. This effect explains a phenomenon that you can easily observe standing on the beach. Perhaps you have noticed that incoming waves often will run almost parallel to the beach as they reach the shore. That is because the shallower the water, the slower the wave speed will be. Running slower and slower the closer they get to the shore, the wave fronts will, with each further slowing, change direction a little bit, finally running almost parallel to the shore. We can imagine Huygens, living near the coast, walking along the beach of The Hague enjoying the calming sound of breaking waves while pondering the behavior of light. With his observant mind, he eventually noticed this phenomenon, which perhaps provided to him the first inklings for his wave theory of light.
Huygens' wave theory of light has become more or less high school curriculum, but you should realize that his model is purely a mathematical and mechanical model and therefore not necessarily in accordance with reality. His contemporaries also expressed a number of objections:
Why is the new wave front formed by the tangent line to the elemental waves?
What happens to the parts of those circularly expanding elemental waves which do not participate in the new wave front?
Why don't the backwards running elemental waves create backward running wave fronts?
How do circular elemental waves explain the observed linear propagation of light?
What is it that is oscillating, Christiaan?
So, the end of Newton's corpuscle model was still a long way off. The theory of light corpuscles would last until 1803 when Thomas Young, through interference experiments with sunlight, demonstrated the wave character of light convincingly and presented his results to the Royal Society in London.
3: The clockwork universe and the ether
""A scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die and a new generation grows up that is familiar with it." ~ Max Planck."
Max Planck, first quantum physicist 1858-1947
In this chapter you will be introduced to the way how light was recognized as a wave phenomenon by the discovery of interference effects. This was one of the first moments in history where Newton's ideas of the universe were severely contradicted. The acceptance of the idea of the wave character of light gave rise to speculations about in what substance it would be oscillating. An intangible ether was assumed initially. Electromagnetic effects were investigated and exactly measured in the first part of the 19th century. Electric and magnetic fields were introduced as mathematical abstractions and acquired quickly the status of objective existing phenomena.
Electromagnetic waves traveling with the velocity of light were predicted by Maxwell's theory and were soon confirmed by experiment. Sophisticated attempts to measure the speed at which the earth would travel through the assumed ether failed utterly and confirmed thereby the predicted constancy of the speed of light regardless of the position and the movement of the observer through the supposed ether.
At the brink of the twentieth century Max Planck solved the enigma regarding the radiation of a hot body by assuming exchange of electromagnetic energy in discrete amounts - quanta. His solution spelled the ultimate doom for the Newtonian vision of a 100% material universe.
Light as a wave phenomenon, interference, superposition
Thomas Young (1773-1829) let sunlight light shine through a double-slit, set in the one of the sides of a closed box. The box had a piece of frosted glass at the opposite side in order to observe the pattern that was projected by the double-slit. He created the double-slit simply by making two narrow parallel scratches on a soot-coated piece of glass. A pattern of colored light and dark bands appeared in Young's experiment on the frosted glass at the back of the box. A phenomenon that could not be explained by Newton's concept of light corpuscles. This could only be explained by assuming that light behaved as waves.
Figure 3.1: Youngs drawing of interference of monochrome light waves.
In 1803 Young presented his explanation of the results of his double-slit experiment to the Royal Society in London. He produced the above sketch to explain these dark and light bands. The cause of this phenomenon is called interference. Light waves, coming from the left - not shown here - will arrive at the narrow slits A and B. In these slits two synchronously vibrating elementary wave sources are created, in the way Huygens had already supposed. The two synchronous wave sources will generate circular wave fronts expanding from both slits. These synchronous circular expanding waves are necessarily moving exactly in phase and will have the same wavelength.
