Explanation:
Velocity of light waves in material is
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,v = v\lambda \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 1 \right)\)
Refractive index of material is
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\mu = \frac{c}{v}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 2 \right)\)
where, \(c\) is speed of light in vacuum or
air, \(\,\,\,\,\,\,\,\,\mu = \frac{c}{{v\lambda }}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 3 \right)\)
Given, \(v = 2 \times {10^{14}}\;Hz\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\lambda = 5000\mathop A\limits^ \circ \)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 5000 \times {10^{ - 10}}\;m\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,c = 3 \times {10^8}\;m{s^{ - 1}}\) and
From Eq. (3), we get
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\mu = \frac{{3 \times {{10}^8}}}{{2 \times {{10}^{14}} \times 5000 \times {{10}^{ - 10}}}} = 3\)