If transmission power of a surface is `1/6` and reflective power is `1/3`, then its absorptive power will be

Options

A. `1/3`
B. `1/2`
C. `1/6`
D. `1/12`

Answer

To find the absorptive power of a surface given its transmission power and reflective power, we can use the relationship between these three quantities. The sum of the reflective power (R), absorptive power (A), and transmissive power (T) of a surface is always equal to 1. This can be expressed mathematically as:

\[ R + A + T = 1 \]

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Reflective power (R) = \( \frac{1}{3} \)
- Transmissive power (T) = \( \frac{1}{6} \)

2. **Set Up the Equation:**
Using the relationship \( R + A + T = 1 \), we can substitute the known values into the equation:
\[ \frac{1}{3} + A + \frac{1}{6} = 1 \]

3. **Combine the Terms:**
To combine \( \frac{1}{3} \) and \( \frac{1}{6} \), we need a common denominator. The least common multiple of 3 and 6 is 6.
- Convert \( \frac{1}{3} \) to sixths:
\[ \frac{1}{3} = \frac{2}{6} \]
- Now substitute:
\[ \frac{2}{6} + A + \frac{1}{6} = 1 \]

4. **Simplify the Equation:**
Combine the fractions on the left side:
\[ \frac{2}{6} + \frac{1}{6} = \frac{3}{6} \]
So the equation becomes:
\[ \frac{3}{6} + A = 1 \]

5. **Isolate the Absorptive Power (A):**
To find \( A \), subtract \( \frac{3}{6} \) from both sides:
\[ A = 1 - \frac{3}{6} \]
Convert 1 to sixths:
\[ 1 = \frac{6}{6} \]
Thus:
\[ A = \frac{6}{6} - \frac{3}{6} = \frac{3}{6} \]

6. **Simplify the Result:**
Simplifying \( \frac{3}{6} \) gives:
\[ A = \frac{1}{2} \]

### Final Answer:
The absorptive power (A) of the surface is \( \frac{1}{2} \).