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Chapter 13: Problem 97

Define spectral transmissivity of a medium of thickness \(L\) in terms of \((a)\) spectral intensities and \((b)\) the spectral absorption coefficient.

Short Answer

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Question: Define spectral transmissivity of a medium of thickness L in terms of (a) spectral intensities and (b) the spectral absorption coefficient. Answer: Spectral transmissivity (T) of a medium of thickness L can be defined in terms of (a) the spectral intensities (I, I_0) as T = I/I_0 and (b) the spectral absorption coefficient (α) as T = e^{-αL}.

Step by step solution

01

Define spectral transmissivity

Spectral transmissivity (T) is the ratio of the transmitted spectral intensity (I) to the incident spectral intensity (I_0) at a specific wavelength: T = \frac{I}{I_0}
02

Apply the Beer-Lambert law

The Beer-Lambert law relates the transmitted spectral intensity (I), incident spectral intensity (I_0), and the spectral absorption coefficient (α) with the thickness of the medium (L): I = I_0 e^{-αL}
03

Calculate the spectral transmissivity

Use the equation from Step 2 to find the transmitted spectral intensity (I) in terms of the incident spectral intensity (I_0), the spectral absorption coefficient (α), and the thickness of the medium (L). Then, substitute this equation into the spectral transmissivity equation from Step 1: T = \frac{I}{I_0} = \frac{I_0 e^{-αL}}{I_0} = e^{-αL}
04

Define spectral transmissivity in terms of spectral intensities and spectral absorption coefficient

Spectral transmissivity (T) of a medium of thickness L can be defined in terms of the spectral intensities (I, I_0) and the spectral absorption coefficient (α) as: T = e^{-αL}

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Most popular questions from this chapter

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