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Physics Notes: Behaviour of visible light rays 3.Spectrum from triangular prism

Visible light  2. The visible spectrum of light and triangular prism experiments - helps explain the formation of a rainbow by raindrops

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INDEX of physics optics notes on visible light rays involving reflection, refraction and diffraction


2. The visible spectrum of light and triangular prism experiments

See also Refraction of waves and scientific model

The refraction of a single wavelength light ray by a 600 triangular prism.

You get refraction twice as the laser beam passes through two boundaries.

From the diagram on the right:

1. air ==> glass: The light beam slows down in the more dense glass, so the ray bends towards the normal.

angle of incidence i1 > angle of refraction r1

2. glass ==> air: The light beam speeds up in the less dense air, so the ray bends away from the normal.

angle of incidence i2 < angle of refraction r2

2. is the opposite to refraction 1.

Note that when using a single wavelength of light from a laser beam there is no splitting of the colour - contrast the above diagram with the diagram below showing the dispersion of white light into all its constituent colours - the visible spectrum.

 

The production of the visible spectrum with a triangular prism - white light is dispersed into all its colours.

I remember it as VIBGYOR sounded phonetically for violet, indigo, blue, green, yellow, orange and red.

Important trend to know: violet === decreasing frequency, increasing wavelength ===> red

(The sequence is preceded by invisible ultra-violet light and succeeded by invisible infra-red light.)

The different colours we experience are due to differences in photon energy, wavelength and frequency (all of which are related), and this is irrespective of what medium the light travels through - vacuum, air, glass, anything transparent.

However, in a vacuum or in air (very low density) all the colours have the same speed.

BUT, in dense transparent materials like glass the speed of each colour actually varies.

The shorter the wavelength of the light colour, the slower the light colour travels in dense materials.

The slower the light travels the more it is refracted when passing through a media boundary to a more dense medium - the smaller the angle of refraction.

Therefore the shorter wavelength violet light is refracted much more than the longer wavelength red light.

The rule is illustrated by the diagram below and it should correspond to the diagram above on how to produce the spectrum of visible light with a triangular glass/Perspex prism.

It is this difference in the degree of refraction of each colour that allows a prism to separate the colours and produce the 'rainbow' of light we call the visible spectrum.

The wave theory of refraction explains why you can produce the visible spectrum in this way.

In the diagram above Refraction A explains the 1st refraction (air to Δ glass prism) and Refraction B explains the 2nd refraction (Δ glass prism to air).

Therefore when white light passes through the ∆ prism all the different colours separate out to give the visible spectrum.

The theory behind the formation of the visible spectrum (refer to diagram below too)

This spreading out into the different colours due to different refraction angles is called dispersion to give what we refer to as the visible spectrum of light.

You can demonstrate the above diagram with the ray box experiments by passing the white light beam through different coloured filters and measuring the angles of the refracted rays.

With the triangular prism you will observe different angles for different colours from the double refraction effects.

However, with a rectangular block, all the different coloured rays will emerge at the same angle. This is because there are two parallel surfaces and the two refraction effects at the two parallel interfaces cancel each other out.

The shape of the prism allows two sets of refractions to take place and give a greater spread of the different wavelengths of the colours.

When the light enters the prism the rays bend towards the normal after the boundary - the first refraction is from a less dense to a more dense medium (waves slowing down).

When the light exits the prism the rays bend away from the normal after the boundary - the second refraction is from a more dense to a less dense medium (waves speeding up).

At both boundaries, the colours have different speeds and so refract at different angles - that's what causes them to spread out or disperse. In any liquid or solid material ...

the shorter the wavelength the slower the rays-waves move in the material, and ...

... the shorter the wavelength the greater the change in speed, so the greater the angle the light rays-waves are deviated or diffracted.

A nice visible light spectrum from a glass pendant hanging up by a brightly sunlit window.

 

Spectroscopy

In the past 60o triangular prisms have been used in emission spectrometers for analysing light from high temperature sources like stars. However, these days diffraction gratings are used to separate the different wavelengths of visible light.

 

The formation of a rainbow - you need to refer to the diagram above too.

The formation of a rainbow can be partly explained by considering a water droplet to behave like a prism. It involves refraction and reflection. I've just used a red, green and blue ray diagram to give (I hope!) the basic ideas to explain how a rainbow is formed.

Imagine a ray of sunlight entering the water drop at point A. On going from less dense air to more dense water refraction occurs at the boundary. The shorter wavelength blue light slows down more and refracts at a greater angle - the order being blue > green > red. You may of course get some reflection too, but lets concentrate on the refracted rays.

At point B, some internal reflection occurs inside the water drop (and maybe some refraction).

At point C a second refraction takes place as the rays move from a more dense medium to a less dense medium. A second dispersion takes place to produce the final rainbow effect of the visible spectrum. You may also get internal reflection too.

If you understand the prism experiment to produce the visible spectrum, you should have no trouble in having some idea on how a rainbow is formed - but it is not a true visible spectrum - there are many complications which we don't need to go into in detail. BUT, the ray diagram explains the general idea of why you get a separation of white light into the colours of a rainbow - due to different angles of refraction of the different colours.

Further notes (NOT needed for a GCSE physics exam, just for the more curious!)

However, the light rays are hitting the water drop over half of its surface, and, depending on the angle of incidence, you may get reflection, refraction or both at each interface (air ==> water and water ==> air). You should realise that the colours in the diagram do not match the order in the rainbow. The different colours actually come from raindrops at different heights, so although the refraction angles are different the rainbow seems to come from one narrow band in the sky.

In other words there are lots of other complications in what actually happens when sunlight passes through raindrops. Also, what you see is only part of the rainbow. It is actually a full disc, but you only see half a circle because of the ground and your own specific viewing angle!

The photograph is actually of a double rainbow. If the sun is at a low angle, you can sometimes get other internal reflections and a second lot of refractions producing a fainter secondary rainbow. If you look carefully, the colours are reversed - another complication! The two figures were added for human interest when taking the photograph at Blackrock, Co. Louth, in Ireland in 2005.

 

INDEX notes: Visible light rays - reflection, refraction and diffraction


Keywords, phrases and learning objectives for the behaviour of visible light rays

Know how and explain, by refraction, the formation of the visible spectrum of light using a triangular prism experiment.

Know this experiment helps explain the formation rainbow colours by raindrops and how visible light can be analysed by spectroscopy.


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INDEX notes: Visible light rays - reflection, refraction and diffraction

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