An electromagnetic wave of intensity `I` falls on a surface kept in vacuum and exerts radiation pressure `p` on it.Which of the following are true ?

Options

A. Radiation pressure is `I/C` if the wave is totally absorbed
B. Radiation pressure is `I/C` if the wave is totally reflected
C. Radiation pressure is `(2I)/(C)` if the wave is totally reflected
D. Radiation pressure is in the range `(I)/(C) lt p lt (2I)/(C)` for real surfaces

Explanation

To solve the problem, we need to analyze the behavior of electromagnetic waves when they interact with a surface in vacuum. We will consider the scenarios of complete absorption and complete reflection of the wave.

### Step-by-Step Solution:

1. **Understanding Radiation Pressure**:
Radiation pressure \( p \) is defined as the force exerted by electromagnetic waves per unit area on a surface. It can be calculated based on the change in momentum of the waves when they interact with the surface.

2. **Case 1: Total Absorption**:
- When an electromagnetic wave of intensity \( I \) is completely absorbed by the surface, the change in momentum per unit time can be calculated.
- The initial momentum flux (momentum per unit area per unit time) of the incoming wave is \( \frac{I}{c} \), where \( c \) is the speed of light.
- Since the wave is completely absorbed, the final momentum flux is 0.
- Therefore, the change in momentum per unit time is:
\[ \Delta p = \frac{I}{c} - 0 = \frac{I}{c} \]
- Thus, the radiation pressure \( p \) when the wave is totally absorbed is:
\[ p = \frac{I}{c} \]

3. **Case 2: Total Reflection**:
- When the wave is completely reflected, the incoming wave has momentum \( \frac{I}{c} \) and the reflected wave also has momentum \( \frac{I}{c} \) but in the opposite direction.
- The change in momentum per unit time is:
\[ \Delta p = \frac{I}{c} - (-\frac{I}{c}) = \frac{I}{c} + \frac{I}{c} = \frac{2I}{c} \]
- Therefore, the radiation pressure \( p \) when the wave is totally reflected is:
\[ p = \frac{2I}{c} \]

4. **Case 3: Real Surfaces**:
- For real surfaces, they cannot completely absorb or completely reflect the electromagnetic waves. Therefore, the radiation pressure will be in between the two extremes calculated above.
- Hence, for real surfaces, the radiation pressure \( p \) will satisfy:
\[ \frac{I}{c} < p < \frac{2I}{c} \]

### Conclusion:
Based on the analysis:
- Radiation pressure is \( \frac{I}{c} \) if the wave is totally absorbed (True).
- Radiation pressure is \( \frac{2I}{c} \) if the wave is totally reflected (True).
- Radiation pressure is in the range \( \frac{I}{c} < p < \frac{2I}{c} \) for real surfaces (True).

Thus, the correct statements are:
- A: True (Radiation pressure is \( \frac{I}{c} \) if the wave is totally absorbed)
- C: True (Radiation pressure is \( \frac{2I}{c} \) if the wave is totally reflected)
- D: True (Radiation pressure is in the range \( \frac{I}{c} < p < \frac{2I}{c} \) for real surfaces)