المحاضرة -4

محاضرة-3When light travels through a material, part of the light energy is absorbed by the atoms in the material. The amount of light absorbed is dependent upon the characteristics of the material and its thickness. Optical components, such as lenses and windows, are made of materials that absorb very little of the light energy. When a laser beam passes through the active medium of a laser, energy is added to the laser beam through a process called "optical gain.".
ATTENUATION OF LIGHT:
Figure 1 depicts a beam of light traveling through a piece of optical material. Some of the light energy is absorbed by the material, and some is transmitted.

Fig. 1 Attenuation of a light beam
The transmission of the optical material is given by Equation 1.
Equation 1

where: T = Transmission.
E0 = Irradiance of light incident upon the material.
E = Irradiance of light transmitted through the material.






Given: The light incident upon the material in Figure 1 has an irradiance of 2.5 mW/cm2. The irradiance of the transmitted light is 0.50 mW/cm2.
Find: The transmission.
Solution:
T = 0.20
20% of the light is transmitted.
In some cases, almost no light is absorbed, and the transmission is almost 1. In others, there is no transmission at all (T = 0).
THE EXPONENTIAL LAW OF ABSORPTION:
Obviously, any increase in the thickness of the absorbing material will decrease the irradiance of the transmitted light. Figure 2 depicts light traveling through four identical pieces of filter material, each 1 mm thick and each filter absorbing one-half the light incident upon it. Figure 3 is a plot of the transmission of this filter material as a function of total filter thickness. Transmission in this case is based upon incident and transmitted power, rather than upon irradiance. The curve in Figure 3 is called an "exponential curve." It begins at an initial value of 1.0 and approaches zero asymptotically as thickness increases. The degree of transmission for any thickness of a material is given by the exponential law of absorption, as stated in Equation 2.

Fig. 2 Transmission of light through a series of filters

Fig. 3 Transmission as a function of thickness
Equation 2
T = e^(-? x)
where: T = Transmission.
e = The natural logarithm base = 2.718.
? = The absorption coefficient of the material in cm–1.
x = The thickness of the material in cm.
the absorption coefficient is measured in terms of absorption per centimeter.

Given: The absorption coefficient of a material is 5.0 cm-1.
Find: The transmission of pieces of this material having the following thicknesses:
(a) 0.01 cm
(b) 0.10 cm
(c) 1.0 cm
Solution: A T = e^(-? x)
T = e– (5.0) (0.01)
(a) T = e–0.05
(a) T = 0.951
(b) T = e– (5.0) (0.1)
(b) T = e–0.5 (evaluate using ex key on calculator)
(b) T = 0.606
(c) T = e– (5.0) (1.0)
(c) T = e–5
(c) T = 0.0067