Dispersion of light by prisms

The average speed of light is less than in a transparent medium. Light of frequencies closer to the natural frequency of the electron oscillators in a medium travels more slowly in the medium. This is because there are more interactions between the light and the medium. Since the natural or resonant frequency of most transparent materials is in the ultraviolet part of the spectrum, visible light of higher frequencies ravels more slowly than light of lower frequencies. Since different frequencies of light travel at different speeds in transparent material, they will refract differently and bend at different angles.

Fig. 6.11. Dispersion of white light.

When light is bent twice at nonparallel boundaries, as in a prism, the separation of different colours of light is quite apparent. Visible light, also known as white light, consists of a collection of component colors. These colors are often observed as light passes through a triangular prism. Upon passage through the prism, the white light is separated into its component colors – red, orange, yellow, green, blue, indigo, and violet (Fig. 6.11). This separation of light into colours arranged according to their frequency is called dispersion.

Different materials are distinguished from each other by their different optical densities. The optical density is simply a measure of the tendency of a material to slow down light as it travels through it. A light wave traveling through a transparent material interacts with the atoms of that material. When a light wave impinges upon an atom of the material, it is absorbed by that atom. The absorbed energy causes the electrons in the atom to vibrate. If the frequency of the light wave does not match the resonant frequency of the vibrating electrons, then the light will be reemitted by the atom at the same frequency at which it impinged upon it. The light wave then travels through the interatomic vacuum towards the next atom of the material. Once it impinges upon the next atom, the process of absorption and reemission is repeated.

The optical density of a material is the result of the tendency of the atoms of a material to maintain the absorbed energy of the light wave in the form of vibrating electrons before reemitting it as a new electromagnetic disturbance. Thus, while a light wave travels through a vacuum at a speed of c (3.00 x 108 m/s), it travels through a transparent material at speeds less than c. The index of refraction value (n) provides a quantitative expression of the optical density of a given medium. Materials with higher index of refraction values have a tendency to hold onto the absorbed light energy for greater lengths of time before reemitting it to the interatomic void. The more closely that the frequency of the light wave matches the resonant frequency of the electrons of the atoms of a material, the greater the optical density and the greater the index of refraction. A light wave would be slowed down to a greater extent when passing through such a material.

The index of refraction values are dependent upon the frequency of light. For visible light, the n value does not show a large variation with frequency, but nonetheless it shows a variation. For instance, the n value for frequencies of violet light is 1.53; and the n value for frequencies of red light is 1.51. The absorption and reemission process causes the higher frequency (lower wavelength) violet light to travel slower through crown glass than the lower frequency (higher wavelength) red light. It is this difference in n value for the varying frequencies (and wavelengths) that causes the dispersion of light by a triangular prism. Violet light, being slowed down to a greater extent by the absorption and reemission process, refracts more than red light. Upon entry of white light at the first boundary of a triangular prism, there will be a slight separation of the white light into the component colors of the spectrum. Upon exiting the triangular prism at the second boundary, the separation becomes even greater and ROYGBIV is observed in its splendor.

The difference in how much the angle of the beam has changed upon entering and leaving the prism is called the angle of deviation. The dispersion of light is more apparent with a triangular prism. This is because the surfaces of the triangular prism are slanted allowing for the different wavelengths to hit the prism and leave the prism at different speeds (http://www.physicsclassroom.com/class/refrn/u14l4a.cfm).

Exercise 44. Answer the questions to the text.

1. What colours is white light separated into when it pases through the prism? List the colours of the visible spectrum in the correct order.

2. What is dispersion?

3. What is the optical density?

4. What does the index of refraction depend on?

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