Reflection and absorption coefficient of a given surface at `0^@C` for a fixed wavelength are 0.5 (each). At the same temperature and wavelength the transmission (coefficient) of surface will be-

Options

A. 0.5
B. 1
C. zero
D. in between zero and one

Explanation

To find the transmission coefficient of a given surface at \(0^\circ C\) for a fixed wavelength, we can use the relationship between the reflection coefficient (\(R\)), absorption coefficient (\(A\)), and transmission coefficient (\(T\)).

### Step-by-Step Solution:

1. **Understand the Coefficients**:
- Reflection coefficient (\(R\)) = 0.5
- Absorption coefficient (\(A\)) = 0.5
- Transmission coefficient (\(T\)) is what we need to find.

2. **Use the Relationship**:
The relationship between these coefficients is given by the equation:
\[ R + A + T = 1 \]
where \(R\) is the reflection coefficient, \(A\) is the absorption coefficient, and \(T\) is the transmission coefficient.

3. **Substitute Known Values**:
Substitute the known values of \(R\) and \(A\) into the equation:
\[ 0.5 + 0.5 + T = 1 \]

4. **Simplify the Equation**:
Combine the reflection and absorption coefficients:
\[ 1 + T = 1 \]

5. **Solve for Transmission Coefficient**:
To find \(T\), subtract 1 from both sides:
\[ T = 1 - 1 = 0 \]

6. **Conclusion**:
The transmission coefficient (\(T\)) of the surface at \(0^\circ C\) for the fixed wavelength is \(0\).

### Final Answer:
The transmission coefficient of the surface is \(0\).

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