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GEOMETRIC OPTICS

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Speed, Frequency, & Wavelength of Light

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Speed, frequency, and wavelength of light are related by the following expression:

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In different optical media, speed and wavelength of light change, but frequency is constant. Color depends on frequency, so that the color of a ray of light is not altered as it passes through optical media except by selective nontransmittance or fluorescence. The optical characteristics of a substance can only be defined with respect to clearly specified frequencies of light. A substance to be used for lenses to refract visible light is usually tested with the yellow sodium light (D line) and the blue (F line) and the red (C line) of a rarefied hydrogen discharge tube.

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In a vacuum, the speed of all frequencies of light is the same (approximately 3 × 108 meters per second). Since the frequency of the yellow D line is approximately 5 × 1014 Hz, the wavelength of this line in a vacuum is approximately 6 × 10–7 m (0.6 μm). Similarly, the wavelengths in a vacuum of the blue F and red C lines are approximately 5 and 7 × 10–7 m, respectively.

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Index of Refraction

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If the speed of a light ray is altered by a change in the optical medium, refraction of the ray will also occur (Figure 21–1). The effect of an optical substance on the speed of light is expressed as its index of refraction, n; the higher the index, the slower the speed and the greater the effect on refraction.

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Figure 21–1.

Refraction of light as it enters a transparent medium of higher refractive index n′.

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In a vacuum, n has the value 1.00000. The absolute index of refraction of a substance is the ratio of the speed of light in a vacuum to the speed of light in the substance. The relative index of refraction of a substance is calculated with reference to the speed of light in air. The absolute index of refraction of air is about 1.0003. In optics, n is assumed to be relative to air unless specified as absolute.

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Thermal Coefficient of Index of Refraction

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The index of refraction increases with increasing temperature of the medium, but the rate of change varies from one medium to another, being approximately 150 times greater for plastic and aqueous than for glass. This makes plastic undesirable for precision optical devices. In the human eye, the problem is overcome by the maintenance of a steady temperature.

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Dispersion of Light

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In all media besides a vacuum, the index of refraction is different for each color (frequency), being larger at the blue end and ...

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