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 2 `I//c` if the wave is totally reflected.
D. Radiation pressure is in the range `I//cltplt2I//c` for real surfaces.

Explanation

To solve the problem regarding the radiation pressure exerted by an electromagnetic wave of intensity \( I \) on a surface in vacuum, we can analyze the situation based on the principles of momentum transfer and the behavior of electromagnetic waves upon absorption and reflection.

### Step-by-Step Solution:

1. **Understanding Radiation Pressure**:
- Radiation pressure \( P \) is defined as the force per unit area exerted by electromagnetic waves on a surface. It can be derived from the change in momentum of the wave when it interacts with the surface.

2. **Case 1: Total Absorption**:
- When the electromagnetic wave is totally absorbed by the surface, the momentum change per unit area per unit time is given by:
\[ P = \frac{I}{c} \]
- Here, \( I \) is the intensity of the wave and \( c \) is the speed of light. The momentum of the absorbed wave contributes to the radiation pressure.

3. **Case 2: Total Reflection**:
- When the wave is totally reflected, the momentum change is different. The momentum of the incoming wave is \( \frac{I}{c} \) and the momentum of the reflected wave is also \( \frac{I}{c} \) but in the opposite direction.
- Therefore, the total change in momentum per unit area per unit time is:
\[ P = \frac{I}{c} - (-\frac{I}{c}) = \frac{I}{c} + \frac{I}{c} = \frac{2I}{c} \]

4. **Case 3: Real Surfaces**:
- For real surfaces that are neither perfect absorbers nor perfect reflectors, the radiation pressure will fall between the two extremes:
\[ \frac{I}{c} < P < \frac{2I}{c} \]

5. **Conclusion**:
- From the analysis, we can conclude the following:
- 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 for real surfaces lies in the range \( \frac{I}{c} < P < \frac{2I}{c} \). (True)

### Final Statements:
- The statements regarding radiation pressure are true:
1. Radiation pressure is \( \frac{I}{c} \) if the wave is totally absorbed. (True)
2. Radiation pressure is \( \frac{2I}{c} \) if the wave is totally reflected. (True)
3. Radiation pressure is in the range \( \frac{I}{c} < P < \frac{2I}{c} \) for real surfaces. (True)