Momentum Transfer to a Perfectly Reflecting Surface

When radiation of energy E falls normally on a perfectly reflecting surface, the momentum transferred to the surface can be calculated using the principles of electromagnetic radiation and the law of conservation of momentum.

1. Reflection of Electromagnetic Radiation
- When electromagnetic radiation, such as light or other forms of radiation, falls on a surface, it can be reflected, transmitted, or absorbed.
- In the case of a perfectly reflecting surface, the radiation is fully reflected, meaning none of the energy is absorbed or transmitted.

2. Conservation of Momentum
- According to the law of conservation of momentum, the total momentum before and after an event remains constant, provided no external forces act on the system.
- In this case, the system consists of the radiation falling on the surface, and the surface itself.

3. Momentum of Electromagnetic Radiation
- Electromagnetic radiation carries momentum, even though it has no mass.
- The momentum of radiation is given by the equation p = E/c, where p is the momentum, E is the energy, and c is the speed of light in vacuum.
- This equation is derived from the principles of special relativity and the wave-particle duality of light.

4. Calculation of Momentum Transfer
- When the radiation falls normally on the perfectly reflecting surface, the momentum of the radiation before reflection is p = E/c.
- After reflection, the radiation is fully reflected, so the momentum of the reflected radiation is -E/c (the negative sign indicates the reversal of direction).
- The change in momentum is then given by Δp = (-E/c) - (E/c) = -2E/c.
- However, since the momentum is a vector quantity, the magnitude of the change in momentum is 2E/c.

Therefore, the momentum transferred to the perfectly reflecting surface is 2E/c. This means that for every unit of energy E, the surface receives a momentum transfer of 2/c units.

Hence, the correct answer is option 'B': 2E/cc.