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ucph>Tommy: Created page with " =====Question 1===== Knowing that momentum must be conserved across the interface, derive Snell's Law. {{hidden begin|toggle=right|title=Solu..."

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Created page with " =====Question 1===== Knowing that momentum must be conserved across the interface, derive Snell's Law. {{hidden begin|toggle=right|title=Solu..."

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=====Question 1=====
Knowing that momentum must be conserved across the interface, derive Snell's Law.

{{hidden begin|toggle=right|title=Solution|titlestyle=background:#ccccff}}
The momentum of the neutron is given by the wavevector through the de Broglie relation
\begin{equation}
{\bf{p}}=\hbar\bf{k}.
\end{equation}
The only components of the momentum to change on reflection/refraction are those normal to the interface, i. e. \( q_z\).
The components of the momentum perpendicular to the interface normal are unchanged across the interface. Thus,
\begin{equation}
k_i\cos\theta_i = k_r\cos\theta_r = k_t\cos\theta_t.
\end{equation}
or more generically:
\begin{equation}
k_1\cos\theta_1 = k_2\cos\theta_2.
\end{equation}

[[Neutron reflectivity#label-reflectivityeq:n|This equation]] from the [[Neutron reflectivity]] page, \(n_m=\frac{\lambda_0}{\lambda_m}=\frac{k_m}{k_0}\),
gives the relation between the refractive index and the wavenumber. Substituting this into the equation above gives Snell's Law:
\begin{equation}
n_1\cos\theta_1 = n_2\cos\theta_2.
\end{equation}

{{hidden end}}

Problem: Snell's Law - Revision history

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ucph>Tommy: Created page with " =====Question 1===== Knowing that momentum must be conserved across the interface, derive Snell's Law. {{hidden begin|toggle=right|title=Solu..."