(A) : The radiation force on an absorbing surface is twice that on a reflecting surface. (R) : The radiation force on a reflecting surface is twice that on an absorbing surface.

Options

A. Both 'A' and 'R' are true and 'R' is the correct explanation of 'A'.
B. Both 'A' and ’R' are true and 'R' is not the correct explanation of 'A
C. A' is true and 'R' is false
D. 'A' is false and R' is true

Answer

To solve the question, we need to analyze both the assertion (A) and the reason (R) regarding the radiation force on absorbing and reflecting surfaces.

### Step-by-Step Solution:

1. **Understanding Radiation Force**:
- The radiation force on a surface depends on how the surface interacts with incident electromagnetic radiation. There are two types of surfaces to consider: absorbing surfaces and reflecting surfaces.

2. **Radiation Force on Absorbing Surface**:
- When electromagnetic radiation strikes an absorbing surface, the energy is absorbed, and the radiation force can be calculated using the formula:
\[ F_a = \frac{I}{c} \]
where \( F_a \) is the radiation force on the absorbing surface, \( I \) is the intensity of the radiation, and \( c \) is the speed of light.

3. **Radiation Force on Reflecting Surface**:
- For a reflecting surface, the radiation force is different because the radiation is reflected rather than absorbed. The force on a perfectly reflecting surface is given by:
\[ F_r = \frac{2I}{c} \]
where \( F_r \) is the radiation force on the reflecting surface. This is because the momentum change is double when the radiation is reflected.

4. **Comparing the Forces**:
- From the above equations, we can see that:
\[ F_r = 2 F_a \]
This means the radiation force on a reflecting surface is twice that on an absorbing surface.

5. **Evaluating the Assertion and Reason**:
- **Assertion (A)**: "The radiation force on an absorbing surface is twice that on a reflecting surface." This statement is **false** because we established that the force on a reflecting surface is actually twice that on an absorbing surface.
- **Reason (R)**: "The radiation force on a reflecting surface is twice that on an absorbing surface." This statement is **true** based on our calculations.

6. **Conclusion**:
- Therefore, the assertion (A) is false, and the reason (R) is true. The correct answer is that A is false and R is true.

### Final Answer:
- Assertion (A) is false, and Reason (R) is true.