Path to waves
limits of geometric optics
Geometric optics (as any model of reality) has its limits of applicability. The laws of geometric optics do not depend on the size of the observed objects and/or optical instruments, on the distances traveled by light. However, in reality when the illuminated objects are reduced, unexpected effects appear. These effects are inexplicable in the framework of geometric optics and invisible as long as the sizes of the objects were large.
These "new" effects dramatically increased at illuminating periodic structures, in which the dimensions of (periodically repeating) elements are fairly small.
In 1673, the Scottish mathematician and astronomer James Gregory described his experiment with a bird feather (the feather is a periodic structure of interlocked fibers): βLet in the Sunβs light by a small hole to a darkened house, and at the hole place a feather, (the more delicate and white the better for this purpose) and it shall direct to a white wall or paper opposite to it a number of small circles and ovals, (if I mistake them not) whereof one is somewhat white, (to wit, the middle, which is opposite to the Sun) and all the rest severally coloured."
Attempts to explain such experiments led to the creation of a new model: wave optics. The word "creation" needs to be clarified. The work that led to the appearance of wave optics continued from the 17th to the 19th centuries inclusive. The new model was the fruit of the work of many scientists. From (tentatively) Christiaan Huygens (1629-1695) and Isaac Newton (1642-1727) to (tentatively) Augustin Jean Fresnel (1788-1827), Thomas Young (1773-1829) and FranΓ§ois Arago (1786-1853).
And yet, it was a wonderful insight that arose before it was found out (proven) that visible light is a relatively small part of the spectrum of electromagnetic waves. The apotheosis was the unification of the wave theory of light with the theory of electromagnetism by James Clerk Maxwell (1831-1879).
The key parameter is the wavelength Ξ». It is defined as the distance between its two next maxima (or minima, or between two nearest points with the same phase).
Now the limit of the application of geometric optics is becoming more clearly defined: geometric optics works well when the dimensions of the observed objects, elements of optical systems are many times greater than the wavelength of light.