Show that the momentum $p$ of a photon of electromagnetic radiation with wavelength $\lambda$ is $p = \frac{h}{\lambda}$, where $h$ is the Planck constant.
Use the expression in (a)(i) to show that a photon in free space with momentum $9.5 \times 10^{-28}\,\text{N s}$ is a photon of red light.
A beam of red light with intensity $160\,\text{W m}^{-2}$ is incident normally on a plane mirror, as shown in Fig. 8.1. The momentum of each photon in the beam is $9.5 \times 10^{-28}\,\text{N s}$. All of the light is reflected by the mirror in the opposite direction to its original path. The cross-sectional area of the beam is $2.5 \times 10^{-6}\,\text{m}^2$.
Show that the rate at which photons strike the mirror is $1.4 \times 10^{15}\,\text{s}^{-1}$.
Use the result in (b)(i) to find the pressure exerted on the mirror by the light beam.
The red beam in (b) is replaced by a blue beam of the same intensity. Suggest and explain whether the pressure exerted on the mirror by the blue beam is less than, the same as, or greater than the pressure exerted by the red beam.