Question

The speeds of light in water and glass are respectively \( 2.25 \times 10^8 \, \text{m/s} \) and \( 2.0 \times 10^8 \, \text{m/s} \). Calculate the following refractive indices:
(i) The glass relative to water.
(ii) The glass relative to air.

Hint:

The greater the refractive index, the slower light travels in that medium. Always use the ratio of light speeds to find relative refractive indices.

Answer 1

Step 1: Formula for refractive index.
The refractive index of one medium with respect to another is given by \[ n_{21} = \frac{v_1}{v_2} \] where \( v_1 \) and \( v_2 \) are the speeds of light in the two media.
(i) Refractive index of glass relative to water:
Let \( v_{\text{water}} = 2.25 \times 10^8 \, \text{m/s} \) and \( v_{\text{glass}} = 2.0 \times 10^8 \, \text{m/s} \). \[ n_{\text{glass/water}} = \frac{v_{\text{water}}}{v_{\text{glass}}} = \frac{2.25 \times 10^8}{2.0 \times 10^8} = 1.125 \] Hence, refractive index of glass relative to water = \( 1.125 \).
(ii) Refractive index of glass relative to air:
The speed of light in air is approximately \( 3.0 \times 10^8 \, \text{m/s} \). \[ n_{\text{glass/air}} = \frac{v_{\text{air}}}{v_{\text{glass}}} = \frac{3.0 \times 10^8}{2.0 \times 10^8} = 1.5 \] Thus, refractive index of glass relative to air = \( 1.5 \).
Step 2: Conclusion.
\[ \boxed{n_{\text{glass/water}} = 1.125, n_{\text{glass/air}} = 1.5} \]