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 2 I//c` for real surfaces.

Answer

To solve the problem regarding the radiation pressure exerted by an electromagnetic wave of intensity \( I \) on a surface in vacuum, we need to analyze 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 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. **Momentum Change**:
The momentum \( P \) of electromagnetic waves is related to their intensity \( I \) and the speed of light \( c \). The intensity \( I \) is defined as the power per unit area. The momentum change per unit time for the wave can be expressed as:
\[ \frac{\Delta P}{\Delta t} = \frac{I}{c} \]

3. **Case of Complete Absorption**:
When the wave is completely absorbed by the surface, the change in momentum is equal to the momentum of the incoming wave. Thus, the radiation pressure exerted on the surface is:
\[ p_{\text{absorbed}} = \frac{I}{c} \]

4. **Case of Complete Reflection**:
When the wave is completely reflected, the change in momentum is twice that of the incoming wave because the wave reverses direction. Therefore, the radiation pressure in this case is:
\[ p_{\text{reflected}} = \frac{2I}{c} \]

5. **Range of Radiation Pressure**:
From the above two cases, we can conclude that the radiation pressure \( p \) can vary between:
\[ p_{\text{min}} = \frac{I}{c} \quad (\text{for complete absorption}) \]
\[ p_{\text{max}} = \frac{2I}{c} \quad (\text{for complete reflection}) \]
Thus, the radiation pressure \( p \) lies in the range:
\[ \frac{I}{c} \leq p \leq \frac{2I}{c} \]

### Conclusion:
Based on the analysis, the true statements regarding the radiation pressure \( p \) exerted by the electromagnetic wave of intensity \( I \) are:
- It is equal to \( \frac{I}{c} \) when the wave is completely absorbed.
- It is equal to \( \frac{2I}{c} \) when the wave is completely reflected.
- The radiation pressure varies between these two values.