Question #43144

A polychromatic light beam is incident normally on the first refracting face of a thin prism in a vacuum. The prism has a very small refracting angle $\theta_0$. The refractive index of the prism material varies with the wavelength $\lambda$ of the light as $n(\lambda) = 1 + \frac{\alpha}{\lambda^2}$, where $\alpha$ is a positive constant. The incident beam has a constant photon number distribution $\frac{dN}{d\lambda} = k$ (where $N$ is the number of photons per unit time) in the wavelength range $\lambda_0 \le \lambda \le 2\lambda_0$, and zero outside this range. If the total power of the incident beam is $P_0$, determine the magnitude of the net transverse force exerted by the light beam on the prism. (Assume the prism absorbs no light and the angle of deviation is small enough that $\sin \delta \approx \delta$).