Question

The wavelength of monochromatic light is $5000\stackrel{o}{A}$ in air what will be its wave number in a medium of refractive index $1.5$?

• A. $3\times {10}^6{m}^{-1}$.
• B. $5\times {10}^6{m}^{-1}$.
• C. $2\times {10}^6{m}^{-1}$.
• D. $9\times {10}^6{m}^{-1}$.

Answer 1

The correct option is A $3\times {10}^6{m}^{-1}$.

From Snell's law we get refractive index of medium with respect to air$=\frac{v_a}{v_m}$

$\frac{v_a}{v_m}=\frac{\frac{{\lambda }_a}{t}}{\frac{{\lambda }_m}{t}}=1.5$ assuming time to be equal we get,

${\lambda }_m=\frac{5\times {10}^{-7}}{1.5}$

Now as asked in the question for wave number the above equation will become,

$\frac{1}{{\lambda }_m}=\frac{1.5}{{10}^{-7}\times 5}=3\times {10}^{-6}{m}^{-1}$