Question #43220

A beam of white light is incident from a transparent medium into air at an angle of incidence $\theta_i$. The refractive index of the medium $n$ varies with the wavelength $\lambda$ of light. The angle $\theta_i$ is chosen such that it is exactly the critical angle for a specific wavelength $\lambda_0$, where the refractive index is $n_0$. For wavelengths $\lambda > \lambda_0$, the light is transmitted into the air. In a narrow range of wavelengths near $\lambda_0$, the rate of change of the refractive index is approximately constant, given by $\frac{dn}{d\lambda} = -k$ (where $k > 0$). For a transmitted wavelength $\lambda = \lambda_0 + \Delta \lambda$ (where $0 < \Delta \lambda \ll \lambda_0$), which of the following represents the leading-order approximation for the magnitude of the angular dispersion $\left| \frac{d\delta}{d\lambda} \right|$?