$A$ beam of light has a small wavelength spread $\delta \lambda$ about a central wavelength $\lambda$. The beam travels in vacuum until it enters a glass plate at an angle $\theta$ relative to the normal to the plate,as shown in the figure. The index of refraction of the glass is given by $n(\lambda)$. The angular spread $\delta \theta'$ of the refracted beam is given by

• A
  $\delta \theta' = \left| \frac{1}{n} \delta \lambda \right|$
• B
  $\delta \theta' = \left| \frac{dn(\lambda)}{d\lambda} \delta \lambda \right|$
• C
  $\delta \theta' = \left| \frac{\tan \theta'}{n} \frac{dn(\lambda)}{d\lambda} \delta \lambda \right|$
• D
  $\delta \theta' = \left| \frac{\sin \theta}{\sin \theta'} \frac{\delta \lambda}{\lambda} \right|$