Snell's Law Application:
- The angle of refraction at the prism's second face equals the critical angle, \( C \), leading to:\[\sin C = \frac{n_{\text{medium}}}{n_{\text{prism}}}\]- For an equilateral prism, the internal angle of incidence is:\[r = \frac{A}{2} = \frac{60^\circ}{2} = 30^\circ\]- The critical angle \( C \) is defined as:\[\sin C = \frac{1}{n}\]Given \( C = 60^\circ \):\[\sin 60^\circ = \frac{n_{\text{medium}}}{n_{\text{prism}}}\]\[\frac{\sqrt{3}}{2} = \frac{n_{\text{medium}}}{n_{\text{prism}}}\]\[n_{\text{medium}} = \frac{\sqrt{3}}{2} n_{\text{prism}}\]Consequently, the refractive index of the medium is \( \frac{\sqrt{3}}{2} n_{\text{prism}} \).