Question

The ratio of velocity of light in glass to that in diamond, if R.I of glass and diamond with respect to air are $\dfrac{3}{2}$ and $\dfrac{{12}}{5}$ respectively will be
A. $\dfrac{5}{8}$
B. $\dfrac{8}{5}$
C. $\dfrac{{18}}{5}$
D. $\dfrac{5}{{18}}$

Answer 1

The above problem can be resolved using the concepts and the mathematical relation for the refractive index of any medium. The refractive index of a medium depends on the velocity of light in air and velocity of light in the medium. Moreover, the mathematical relation is then solved by substituting the given values and the fixed standard values to obtain the value of the unknown variable. And the unknown variable being here is the velocity of light in the specific medium, and further required results will be obtained by taking the ratios.

Complete step by step answer:
Given:
The refractive index of glass is, ${\mu _g} = \dfrac{3}{2}$.
The refractive index of diamond is, ${\mu _d} = \dfrac{{12}}{5}$
Then, the velocity of light in glass is,
${v_g} = \dfrac{c}{{{\mu _g}}}$…………………………………….. (1)
Here, c is the velocity of light in the air and its value is $3 \times {10^8}\;{\rm{m/s}}$.
And the velocity of light in diamond is,
${v_d} = \dfrac{c}{{{\mu _d}}}$……………………………………… (2)
Taking the ratio of equation 1 and 2 as,

\dfrac{{{v_g}}}{{{v_d}}} = \dfrac{{c/{\mu _g}}}{{c/{\mu _d}}}\\\ \dfrac{{{v_g}}}{{{v_d}}} = \dfrac{{{\mu _d}}}{{{\mu _g}}} \end{array}$$ Solve by substituting the values in the above equation as, $$\begin{array}{l} \dfrac{{{v_g}}}{{{v_d}}} = \dfrac{{{\mu _d}}}{{{\mu _g}}}\\\ \dfrac{{{v_g}}}{{{v_d}}} = \dfrac{{12/5}}{{3/2}}\\\ \dfrac{{{v_g}}}{{{v_d}}} = \dfrac{{12}}{5} \times \dfrac{2}{3}\\\ \dfrac{{{v_g}}}{{{v_d}}} = \dfrac{8}{5} \end{array}$$ Therefore, the ratio of velocity of light in glass to that of velocity of light in diamond is $$\dfrac{8}{5}$$ and option (B) is correct. **Note:** To resolve the given problem, one must be quite comfortable with the concept and meaning of the refractive index. The idea of refractive index wide includes the comparison of the velocity of light in any medium and the velocity of light in air. These are fundamentals that are taken into consideration to resolve problems of refractive index, such that velocity of light in air is fixed for the problem.