ICSE Class 10 Physics Chapter 06 Spectrum

Chapter 6: Spectrum

Syllabus

Using a triangular prism to produce a visible spectrum from white light; Electromagnetic spectrum. Scattering of light.

Scope of syllabus: Deviation produced by a triangular prism; dependence on colour (wavelength) of light; dispersion and spectrum; electromagnetic spectrum; broad classification (names only arranged in order of increasing wavelength); properties common to all electromagnetic radiations; properties and uses of infrared and ultraviolet radiations. Simple application of scattering of light e.g. blue colour of the sky.

A. Deviation, Dispersion And Spectrum

6.1 Deviation Produced By A Triangular Prism

Fig. 6.1 shows the deviation produced by a triangular prism. When a light ray PQ of single colour enters a triangular prism ABC, it gets deviated, say, by an angle \(\delta_1\) towards the base BC at the first surface AB of the prism and travels straight as QR inside the prism. The angle of deviation \(\delta_1\) depends on the angle of incidence and the refractive index of glass with respect to air. On striking the second surface AC, the ray QR gets further deviated, say, by an angle \(\delta_2\) towards the base BC and travels straight as RS outside the prism. The angle of deviation \(\delta_2\) depends on the angle of incidence at the second surface (which depends on the angle of the prism A) and the refractive index of air with respect to glass. For the emergent ray RS, the total deviation \(\delta\) with respect to the incident ray PQ (i.e., the angle between the emergent ray RS and the direction PL of the incident ray PQ) is given as:

\[\delta = \delta_1 + \delta_2\]

The total angle of deviation \(\delta\), thus, depends upon the following three factors:

(1) the angle of incidence (i) at the first surface, (2) the angle of the prism (A), and (3) the refractive index of the material of the prism (\(\mu\)). But the refractive index depends on the colour (or wavelength \(\lambda\)) of the light used, so the angle of deviation \(\delta\) depends also on the colour (or wavelength \(\lambda\)) of the incident light.

In chapter 4, we have discussed the dependence of angle of deviation \(\delta\) on the angle of incidence i, angle of prism A and refractive index \(\mu\) of the material of prism. Here we shall discuss in detail how the deviation \(\delta\) produced by a prism depends on the colour (or wavelength \(\lambda\)) of the incident light.

Dependence of deviation on the colour (or wavelength) of light

The light of different colours have same speed in air but different speeds in a medium. If the light entering the prism is not of a single colour, subjective property of light related to its wavelength.

The table below gives the range of wavelength and frequency for light of different colours present in the white light.

Note: (1) In the above table the letter Å denotes the unit Angstrom where 1 Å = 10\(^{-10}\) m (or 10\(^{-8}\) cm). Now a days the wavelength is expressed mostly in nanometre (nm) where

1 nm = 10\(^{-9}\) m = 10 Å.

(2) In the spectrum of white light, the red colour has the longest wavelength 8000 Å (or 8 × 10\(^{-7}\)m or 800 nm) or lowest frequency 3.75 ×10\(^{14}\) Hz and the violet colour has the shortest wavelength 4000 Å (or 4 × 10\(^{-7}\)m or 400 nm) or highest frequency 7.5 ×10\(^{14}\) Hz. From the violet end to the red end of the spectrum, the wavelength increases while the frequency decreases.

Teacher's Note

Understanding why different colours have different wavelengths helps explain why a prism separates white light - each colour bends differently because light travels at different speeds in glass depending on its colour. This is why rainbows appear after rain.

6.2 Colours In White Light With Their Wavelength And Frequency Range

The white light emitted from a source consists of light of different wavelengths. The light of different wavelengths produce the sensation of different colours on the retina of our eye, so we perceive them as different colours. The prominent colours in white light are violet, indigo, blue, green, yellow, orange and red. Different colours differ in their wavelength. In fact, wavelength is the characteristic of colour, irrespective of its origin i.e., the light of the same colour obtained from different sources will have the same wavelength. In other words, colour is the subjective property of light related to its wavelength.

From the definition of refractive index:

\[\mu_{glass} = \frac{\text{Speed of light in air}}{\text{Speed of light in glass}}\]

The speed of light for different colours is same in air, but it is different for different colours in glass (medium). In glass, the speed of violet light is minimum and the speed of red light is maximum. Therefore \(\mu_{violet}\) > \(\mu_{red}\)

But \(\mu\) = sin i / sin r or sin r = sin i / \(\mu\)

Therefore, in glass, for a given value of i, the angle of refraction r is minimum for the light of violet colour and maximum for the light of red colour. i.e., \(\delta_{violet}\) > \(\delta_{red}\)

6.3 Dispersion Of White Light Through A Prism And Formation Of A Spectrum

Sir Isaac Newton, while studying the image of a heavenly body formed due to refraction of white light by a lens, found that the image is coloured at its edges. He thought that the coloured image is due to some defect of the lens. He then repeated the experiment with a carefully polished lens, but the image was still coloured. Newton then concluded that the fault is not with the lens, but there is something in the nature of white light itself due to which the image is coloured at its edges. To investigate it further, he performed another experiment with a prism.

Newton's Experiment

Newton allowed the white light from sun to enter a dark room through a small aperture in a window and placed a glass prism in the path of light rays. The light emerging out of the prism was received on a white screen. On the screen, a coloured patch like a rainbow as shown in Fig. 6.2 was obtained which was termed as spectrum.

Starting from the side of base of the prism, the order of colours in the spectrum on screen is:

Violet, Indigo, Blue, Green, Yellow, Orange, and Red. This order of colours in the spectrum can easily be remembered by the word VIBGYOR.

Conclusion: From the above experiment, Newton concluded that white light consists of seven prominent colours. Each colour corresponds to a small range of wavelength. Thus, white light is a mixture of large number of wavelengths (i.e., it is polychromatic in nature).

Note: In the spectrum, each colour is mixed with the other colour i.e., there is no sharp boundary line separating the colours. In diagram, colours are shown widely separated just for clarity. The total spread of colours is much less than that shown in the diagram. Different colours have different width on the screen.

Dispersion

The phenomenon of splitting of white light by a prism into its constituent colours is known as dispersion.

Spectrum

The band of colours seen, on passing white light through a prism is called the spectrum.

Cause of dispersion of white light and formation of spectrum

The cause of dispersion of white light is the change in speed of light with wavelength. When white light enters the first surface of a prism, light of different colours due to their different speeds in glass, gets deviated through different angles towards the base of prism i.e. the dispersion (or splitting) of white light into its constituent colours takes place at the first surface of prism. The violet colour is deviated the most, while the red colour is deviated the least. Therefore light of different colours follow different paths in glass and then strikes the second surface of prism. On the second surface of prism, only refraction takes place (from glass to air) and different colours are deviated through different angles, i.e., violet is deviated the most and red the least. As a result, the colours get further separated on refraction at the second surface. The light emerging out of the prism, thus, has different colours that spread out to form a spectrum on the screen.

Note: (1) Dispersion of white light occurs at the first surface of prism. (2) Deviation of light occurs at both the surfaces of prism. (3) The prism does not produce colours, but it only splits the various colours present in the light incident on it.

Teacher's Note

When sunlight passes through water droplets in the atmosphere, the same dispersion process creates a rainbow - each colour bends at a slightly different angle, just like in a prism, which is why we see the colours arranged in order.

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