After the danger of the plague had passed in 1667, Newton nominated himself
as a candidate for fellowship. He was elected in October of that same year
to a minor fellowship at Trinity College, but then after he was awarded his
Master's degree. He was elected to a major fellowship ion July of 1668.
In 1669, Barrow chose to resign from the Lucasian chair to devote himself to divinity. At his resignation he recommended that Newton be appointed in his place. So at the young age of 27, Isaac accepted the appointment.
His first work as a Lucasian professor and understandably the topic of his first lecture course was optics. He reached the conclusion during the plague years that white light was not a simple entity. Most every other scholar thought it was, however the chromatic aberration in the lens of a telescope convinced Newton otherwise. Newton noticed that when a thin beam of sunlight was passed through a glass prism that a spectrum of colors were formed. He then presented the argument that white light is in actuality different types of rays which are refracted at different angles, which produces a different spectral color. This prompted him to construct a refracting telescope.
Newton was elected a fellow of the Royal Society in 1672 after he donated his refracting telescope to them. This same year he also published a paper on light and color in the Philosophical Transactions of the Royal Society. The paper was well received, with the exceptions of Hooke and Huygens, which objected to Newton's attempt to prove by only experiment, that light consists of the motion of small particles rather than waves. This pulled Newton into two different directions of his own desire for fame and recognition, and the other side that feared criticism. As always he took the easiest way to escape criticism and published nothing. It is easy to see that Newton's reaction to criticism was irrational and subsequently led to his desire to humiliate Hooke in public because of his opinions. However, since Newton already had a high reputation, his theory reigned until the wave theory was revived in the 19th century.
Isaac's already poor relationship with Hooke deteriorated even more when Hooke claimed that Newton had stolen some of his results on optics. Even though peace was made between the two men by an exchange of letters, Newton turned away from the Royal Society which he associated Hooke as one of its leaders. He delayed the full account of his optical researches until after Hooke's death in 1703. Newton's appeared in 1704. It dealt majorly with light and color, the investigations of the colors of thin sheets, Newtons rings and diffraction of light.
The novel idea of 1666 was that the Earth's gravity influenced the Moon, counter balancing it by centrifugal force. From this and Keplar's third law of planetary motion, Newton was able to deduce the inverse-square law. He then found proof that Keplar's areal law was a consequence of centripetal forces and showed that if the orbital curve is an ellipse under the action of central forces then the radial dependence of the force is Inverse Square with the distance from the center.
