Question

If an electromagnetic wave is totally reflected, the radiation pressure in terms of average Poynting vector S\(_{av}\) is:

• A. \(\frac{S_{av}}{2c}\)
• B. \(\frac{2S_{av}}{c}\)
• C. \(\frac{S_{av}}{c}\)
• D. \(\frac{S_{av}}{c^2}\)

Hint:

Remember the two cases for radiation pressure: - **Perfect Absorption:** \(P_{rad} = S_{av}/c\) - **Perfect Reflection:** \(P_{rad} = 2S_{av}/c\) This is analogous to the impulse imparted by a particle: a particle that bounces back imparts twice the impulse of a particle that sticks.

Answer 1

The Correct Option is B

Step 1: Relate the Poynting vector to momentum. The average Poynting vector \(S_{av}\) represents the average energy flux (energy per unit area per unit time) of an electromagnetic wave. The momentum flux (momentum per unit area per unit time) is given by \(\frac{S_{av}}{c}\). This momentum flux is equal to the radiation pressure exerted by the wave when it is completely absorbed.
Step 2: Consider the case of total reflection. When the wave is totally reflected, its momentum is reversed. - The initial momentum arriving per unit area per unit time is \(\frac{S_{av}}{c}\). - The final momentum leaving per unit area per unit time is \(-\frac{S_{av}}{c}\). The change in momentum per unit area per unit time is the difference between the final and initial momentum fluxes: \[ \Delta (\text{momentum flux}) = \left(-\frac{S_{av}}{c}\right) - \left(\frac{S_{av}}{c}\right) = -\frac{2S_{av}}{c} \]
Step 3: Determine the pressure on the surface. The radiation pressure on the surface is the force per unit area, which is equal to the magnitude of the change in momentum per unit area per unit time transferred to the surface. \[ P_{rad} = \left| \Delta (\text{momentum flux}) \right| = \frac{2S_{av}}{c} \]