The total momentum of incident and reflected radiation can be expressed by which formula?

The correct answer, M = 2E/C, is based on the principles of conservation of momentum and the behavior of photons in reflecting surfaces.

When a photon strikes a reflective surface and is reflected, it imparts momentum to that surface. A photon has energy E, and since the momentum p of a photon is given by the relationship p = E/c, where c is the speed of light, we can calculate the momentum involved.

When the photon hits the surface and is reflected, there is a change in momentum equal to twice the momentum of the photon. This happens because the momentum vector of the photon reverses direction upon reflection. Therefore, the total momentum contributed by one photon upon reflection becomes:

• The momentum before reflection is E/c in the direction of the incoming photon.

• The momentum after reflection is also E/c but in the opposite direction.

The change in momentum for one photon is:

Initial momentum (E/c) + Final momentum (-E/c) = E/c - E/c = -2(E/c).

If we consider both the incident and the reflected photons, the total momentum is effectively the momentum of the incident photon plus the momentum of the reflected photon:

Total momentum = E/c (incident) + E/c (ref