Introduction to Light Dispersion

By Lim Jerome (2O2)22

Light- A wave motion and contains many different wavelengths which represent the different colours

Dispersion- The way light is split up into the different colours (When entering a different medium)

Dispersion of Light

The speed of light is slower in optically denser medium. When the white light enters a medium at an angle, the light beam is bent or refracted. But also, the speed of light through a medium varies slightly with the wavelength or frequency of the light. Thus, each wavelength of the different colours of white light is refracted at a slightly different angle when passing through a medium at an angle. This spreading out of the beam of white light is called dispersion or chromatic dispersion.

Summary of Light Dispersion

Light dispersion is the way white light is split up into different colours when entering a different medium. (Best represented through a glass prism)

When white light travels from air to glass prism, it slows down (Glass has higher optical density than air)

It splits up into different colours within the prism as the different colours of white light slow down and bend by different amounts (different wavelengths) and bends again and splits further into the colours of a rainbow as it goes out of the prism and results in a spectrum

Air

Glass

Spectrum

Colours of the Spectrum

You can remember the order by the name ROY G. BIV. Note that in the illustration in the previous slide, the colours are distinctly separated. In reality, they blend into each other, such that there are colours in between. For example, there is red-orange in between red and orange.

Examples of Light Dispersion in Daily Life

Rainbow Explanation: The white light from the

Sun enters the rain drop and the rain drop is like the glass prism but the colours of white light does not bend and slow down too much as the rain drop is water, have lower refractive index so we still get the spectrum but not as separated

Refraction and Reflection of Light in Water Droplet

The light enters the droplet at a decreasing speed and bends towards the normal as water has a higher optical density than air (Refraction)

The light then reflects when it strikes the surface of the droplet at more than 42 degrees as the droplet has a critical angle of 42 degrees. (Total Internal Reflection)

The light ray increases its speed again and bends away from the normal as it leaves the droplet and enter the lower optically denser medium, air. (Refraction)

Air

water

Other entry locations into the droplet may result in similar paths or even in light continuing through the droplet and out the opposite side without significant internal reflection.

The path of light in a water droplet works in a similar way as in the glass prisms shown earlier on

The refraction of light at two boundaries of the droplet results in the dispersion of light into a spectrum of colours. The shorter wavelength blue and violet light refract a slightly greater amount than the longer wavelength red light. Since the boundaries are not parallel to each other, the double refraction results in a distinct separation of the light into its component colours.

Summary

The decrease in speed upon entry of light into a water droplet causes a bending of the path of light towards the normal as water has a higher optical density than air. And upon exiting the droplet, light speeds up and bends away from the normal. The droplet causes a deviation in the path of light as it enters and exits the drop.

Maximum Angle at which Light should Leave Droplet to See the Rainbow

To see a primary bow in the sky above the horizon, the anti solar point, the shadow of your head, must be less than 42 degrees below the horizon.

42 Degrees

Why? The position of a rainbow in the sky is always in the

opposite direction of the Sun with respect to the observer. The bow is centred on the shadow of the observer's head, or more exactly at the antisolar point (which is below the horizon during the daytime), appearing at an angle of approximately 40°–42° to the line between the observer's head and its shadow.

Antisolar point

As a result, if the Sun is higher than 42°, then the rainbow is below the horizon and cannot be seen as there are usually not enough raindrops between the horizon (that is: eye height) and the ground, to contribute. One exception is when the observer is at the top of a mountain or a similar vantage point, for example an aeroplane . Another exception occurs when the rainbow is produced by a garden sprinkler. Although in this case to get sufficient drops they must be very small, resulting in a quite colourless bow.

Why No Rainbow at Night?

Sun rises Sun sets

Direction of antisolar point

To the sun

If we look at the ground on a sunny day, the shadow of our head marks the point called the antisolar point, 180° away from the sun. If the sun is in the sky, the antisolar point is below the horizon. If the sun has set, the antisolar point is above the horizon.

Rainbow as a 3D Cone