Suatu lapisan sabun dengan indeks bias \(\frac 53\) disinari cahaya dengan panjang gelombang 600 nm dengan arah 30o terhadap normal. Berapa tebal minimum lapisan sabun agar terjadi interferensi konstruktif?
Menentukan sudut bias
\begin{equation*}
\begin{split}
\frac {\sin i}{\sin r} & = \frac {n_2}{n_1} \\\\
\frac {\sin 30}{\sin r} & = \frac {\frac 53}{1} \\\\
\frac 53 \:.\: \sin r & = \sin 30 \:.\: 1 \\\\
\frac 53 \:.\: \sin r & = \frac 12 \\\\
\sin r & = \frac {\frac 12}{\frac 53} \\\\
\sin r & = \frac {3}{10}
\end{split}
\end{equation*}
Menentukan \(\cos r\)
\begin{equation*}
\begin{split}
\sin^2 r + \cos^2 r & = 1 \\\\
\left(\frac {3}{10} \right)^2 + \cos^2 r & = 1 \\\\
\frac {9}{100} + \cos^2 r & = 1 \\\\
\cos^2 r & = 1 - \frac {9}{100} \\\\
\cos^2 r & = \frac {91}{100} \\\\
\cos r & = \frac {1}{10} \sqrt{91}
\end{split}
\end{equation*}
Menentukan tebal lapisan sabun
\begin{equation*}
\begin{split}
2 \:.\: n \:.\: d \:.\: \cos r & = \left(n - \dfrac 12 \right) \:.\: \lambda \\\\
2 \:.\: \frac 53 \:.\: d \:.\: \frac {1}{10} \sqrt{91} & = \left(1 - \dfrac 12 \right) \:.\: 600 \:.\: 10^{-9} \\\\
\frac 13 \sqrt{91} \:.\: d & = 300 \:.\: 10^{-9} \\\\
d & = \frac {300 \:.\: 10^{-9}}{\frac 13 \sqrt{91}} \\\\
d & = \frac {900}{\sqrt{91}} \:.\:10^{-9} \text{ m}
\end{split}
\end{equation*}
