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### THE RAINBOW - EXPLANATION

Of all the optical phenomenon in every day life, the rainbow is loveliest.

Reflection of sun light by the rain drops is certainly an essential  element of an explanation but refraction-plays a role, too.

The following figure shows crucial path of light

The circle represents the cross section of a spherical rain drop. For the light ray, the sequence is Refraction, Reflection, and Refraction.

The angle (less than 90o) between the incident direction and the emergent direction is called as "Return Angle".

A Ray from the sun strikes the spherical rain drop and some light is refracted into the water. Here we may ignore the portion that is reflected by the drops' surface. Next, the Ray proceeds to the far side of drop and is reflected there. Now we may ignore the portion that is refracted. Finally, the ray strikes the underside of drop and is refracted out into the air.

In precisely which direction does the emergent ray travel?

Two rules - i) Snell's Law for Refraction & ii) Equality of the angles of incidence and reflection

suffice for answering that question. Once the initial point of contact between the rain drop and the ray from the sun has been specified. Also because the index of refraction depends on color, we must specify the color of light.

Lets start considering Red. Working out the complete path for many rays-i.e. for many different initial points of contact-reveals a surprising geometric property: The return angle for red light never exceeds 42.5 deg C, and most rays have a return angle 42 deg.

So return angle will decide the color of light reaching our vision of sight. Hence, different colors emerge from different sets of rain drops and produce a colored Rainbow.

### What are Light Pipes

Sending light in a staright line is easy. Getting it around corners -with out losing intensity, is a different story.

Even when a light beam reflects from a good silvered mirror, not all of the incident light bounces off; some is absorbed by metal, as much as 20%. A sequence of reflections, in which 20% is lost at each bounce, will quickly reduce a powerful beam to a faint trace of its former itself.

A light pipe is made of glass, designed in such a fashion that there is no refraction of Light out of glass, and hence, there is no loss of intensity.

The Glass just "pipes" the light up and around the curve.

In commercial use, light pipes are drawn out as very long, fine fibers of glass. The diameter is about 0.1mm and field of applications itself is called fiber optics.

### SPEED OF LIGHT IN VACUUM

Newton composed his "Opticks", which he published in 1704, he addressed the question of speed and wrote as follows:

[Light is propogated from luminous bodies in Time, and speeds about seven or eight minutes of an hour in passing from Sun to Earth.

This was observed first by Roemer, and then by others, by means of eclipses of satellites of Jupiter. For these eclipses, when the Earth is between the Sun and Jupiter, happen about seven or eight minutes sooner than they ought to do by the tables, and when the Earth is beyond the Sun they happen seven or eight minutes later than they ought  to do; The reason being, that the lights of satellites has farther to go in the latter case than in the former by diameter of earths orbit. ]

Newton is referring to Olaus Roemers calculations of 1676.

The Astronomers of seventeenth century had studied 'IO' (satellie of Jupiter) ever since Galileo discovered the Moons of Jupiter in 1610. They noted the eclipses and sought to predict their recurrence. But the eclipses -as

observed on Earth - did not recur perfectly periodical. If one used observations made when the Earth was nearest to Jupiter to predict when eclipses will terminate when the earth is farthest from Jupiter (about half a year

later), then the eclipses actually seem to terminate later than caluclated. The delay reasoned Roemer, is due to travel time for light to cross Earth's Orbit.

Newton gives the Time for Light to travel from Sun to Earth as 7 or 8 minutes. Let us average and take 15 minutes as the time for light to cross diameter of Earth's Orbit.

Already in Newton's day, the diameter of Earth's orbit was known to be 3 x 1011 meters.

Speed of Light in Vacuum = Diameter of Earth's Orbit / Apparent delay in eclipse termination
= 3x10¹¹/900 Sec = 3x10⁸ m/sec