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\begin{document}
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{\newpage
\clearpage
\samepage \( n^{2}=(\frac{ck}{\omega })^{2}=1+\frac{\omega _{p}^{2}}{\omega _{0}^{2}-\omega ^{2}} \)
}

{\newpage
\clearpage
\samepage \( \omega _{p}^{2}=\frac{4\pi Ne^{2}}{m} \)
}

{\newpage
\clearpage
\samepage \( f_{p}=\frac{\omega _{p}}{2\pi }\simeq 10^{4}(\frac{N}{cm^{-3}})^{\frac{1}{2}}Hz \)
}

{\newpage
\clearpage
\samepage \( \omega <\omega _{0} \)
}

{\newpage
\clearpage
\samepage \( w>\omega _{0} \)
}

{\newpage
\clearpage
\samepage \( \omega _{0}=0 \)
}

{\newpage
\clearpage
\samepage \( n^{2}=1-(\frac{\omega _{p}}{\omega })^{2} \)
}

{\newpage
\clearpage
\samepage \( \omega <\omega _{p} \)
}

{\newpage
\clearpage
\samepage \( n^{2}\simeq 1+\frac{\omega _{p}^{2}}{\omega _{0}^{2}} \)
}

{\newpage
\clearpage
\samepage \( (\frac{\omega }{\omega _{0}})<<1 \)
}

{\newpage
\clearpage
\samepage \( n^{2}-1 \)
}

{\newpage
\clearpage
\samepage \( =\frac{4\pi Ne^{2}}{m\omega _{0}^{2}}\simeq \frac{4\pi a^{2}_{0}\hbar ^{2}}{a^{3}me^{2}}\simeq \frac{4\pi a_{0}^{3}}{a^{3}} \)
}

{\newpage
\clearpage
\samepage \( \begin{array}{cccc}
water & glass & diamond & air\\ 
1.3 & 1.5 & 2.4 & 1+3*10^{-4}
\end{array}
 \)
}


\end{document}