2 Optical Spectrum. Refraction, reflection, attenuation and dispersion
2.3 Refraction, reflection, attenuation and dispersion

When light reaches the plane boundary between two media, a transmitted light in medium 1 and a reflected light in medium 1 appear. The transmitted light is the refracted light. The angles associated to the directions of the transmitted, refracted and reflected light are shown in Fig.2.

The angle of incidence, φ1, is equal to the angle of reflection angle φ3.

Refraction is the changing direction of light when it goes into a material of different refractive index, n.

image
Fig. 2. Refraction and reflection angles.

Snell’s law gives the relationship between the sine’s of the incident and refraction angles and the refractive indexes of the media as follows:

(008)

For angles larger than the critical angle we have TIR (total internal reflection) [5]. Critical Angle, φ1c , occurs at φ2=90º.

(009)

If the light hits the interface between two media at any angle larger than this critical angle, it will not pass through to the second medium at all. Instead, all of it will be reflected back into the first medium, a process known TIR. This principle is applied by traditional waveguides as optical fibres and is shown by Fig.3.

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Fig. 3. TIR effect.

Light of different frequencies propagate at different speeds through the medium. Moreover, the refractive index depends on the wavelength. Due to these effects, some dispersion appears in the medium.

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Fig. 4. Dispersion effect.

Attenuation is the loss of the optical power. Attenuation is mainly due to absorption and scattering that give rise to a loss of energy in the direction of propagation. The specific attenuation: Power loss in dB per unit length, depends on the wavelength of the radiation travelling along the medium. The attenuation coefficient, α, is given by the following equation

(010)

where P(0) is the initial power or incident power, P(L) is the power at a distance L from the initial point.

Consider a ray of light traveling in a medium of refractive index n1 = 1.44 becomes incident on a second medium of refractive index n2 = 1.4. The wavelength of the light is 1.1 µm.

Calculate the incident angle to have TIR.

SOLUTION

Snell’s Law: (011)

Critical Angle, φ1c , occurs at φ2=90 º, then (012)