The refractive index of air with respect to glass is \( \displaystyle\frac{2}{3} \). The refractive index of diamond with respect to air is 2.4. What will be the refractive index of glass with respect to diamond?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0.625
The relative refractive index of medium 2 with respect to medium 1 is the ratio of their absolute refractive indices, \( n_{21} = n_2/n_1 \). Taking air as \( n_{\mathrm{air}} = 1 \):
Air with respect to glass:
\( \displaystyle n_{\mathrm{air,\,glass}} = \frac{n_{\mathrm{air}}}{n_{g}} = \frac{2}{3} \;\Rightarrow\; n_{g} = \frac{3}{2} = 1.5 \)
Diamond with respect to air:
\( \displaystyle n_{\mathrm{diamond,\,air}} = \frac{n_{d}}{n_{\mathrm{air}}} = 2.4 \;\Rightarrow\; n_{d} = 2.4 \)
Glass with respect to diamond:
\( \displaystyle n_{\mathrm{glass,\,diamond}} = \frac{n_{g}}{n_{d}} = \frac{1.5}{2.4} = 0.625 \)