✔ 最佳答案
Let n1, n2 and n3 be the refractive indices (折射率) of the three media(介質) 1, 2 and 3 respectively.
Apply Snell's Law from media 1 to 2,
(n1).sin(i) = (n2).sin(r)
i.e. sin(i)/sin(r) = n2/n1
where i is the incident angle (入射角) at medium 1 and r is the refractive angle (折射角) at medium 2
Because from the diagram, angle i > angle r
hence, n2 > n1
Apply Snell's Law from media 2 to 3, because total internal reflection (全內反射) occurs,
(n2).sin(c) = (n3).sin(90) where c is the critical angle (臨界角)
hence, sin(c) = n3/n2
i.e. n3 < n2 (because sin(c) < 1)
But from geometry, angle r = angle c (alternate angles are equal)
hence, n3 = (n2).sin(c) = (n2).sin(r) = (n1).sin(i)
i.e. sin(i) = n3/n1
or n3 < n1 (because sin(i) < 1)
Therefore, the three refractive indices, from smallest to highest, are
n3 < n1 < n2