Radiation Intensity At Given Distance Using Beer's Law Calculator

Beer's Law Formula:

\[ I_{\lambda x} = I_{\lambda o} \times \exp(-(\alpha_{\lambda} \times x)) \]

Radiation Intensity at Distance x (Iλx):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Beer's Law?

Beer's Law (also known as the Beer-Lambert Law) describes how the intensity of radiation decreases as it passes through a medium. It states that the absorbance of light is proportional to the concentration of the absorbing material and the path length through the medium.

2. How Does the Calculator Work?

The calculator uses Beer's Law formula:

\[ I_{\lambda x} = I_{\lambda o} \times \exp(-(\alpha_{\lambda} \times x)) \]

Where:

\( I_{\lambda x} \) — Radiation intensity at distance x (W/sr)
\( I_{\lambda o} \) — Initial radiation intensity (W/sr)
\( \alpha_{\lambda} \) — Monochromatic absorption coefficient
\( x \) — Distance through the medium (m)
\( \exp \) — Exponential function

Explanation: The formula calculates how much radiation intensity remains after traveling a certain distance through an absorbing medium, considering the material's absorption properties.

3. Importance of Radiation Intensity Calculation

Details: Calculating radiation intensity at different distances is crucial for various applications including radiation safety, optical measurements, spectroscopy, and designing radiation shielding systems.

4. Using the Calculator

Tips: Enter initial radiation intensity in W/sr, monochromatic absorption coefficient, and distance in meters. All values must be valid (intensity > 0, absorption coefficient ≥ 0, distance ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: What is the exponential function in this context?
A: The exponential function describes how radiation intensity decreases exponentially with distance through an absorbing medium.

Q2: What units are used for radiation intensity?
A: Radiation intensity is typically measured in watts per steradian (W/sr), which represents radiant power per unit solid angle.

Q3: How does absorption coefficient affect the result?
A: Higher absorption coefficients result in faster attenuation of radiation intensity with distance.

Q4: What are typical values for absorption coefficients?
A: Absorption coefficients vary widely depending on the material and wavelength, ranging from near-zero for transparent materials to very high values for strongly absorbing materials.

Q5: Is this calculator applicable to all types of radiation?
A: This calculator applies to electromagnetic radiation where Beer's Law is valid, typically in optical and UV spectroscopy applications.