Lesson Plan

Explain refraction as the change in a light ray's direction caused by a change in its speed at a boundary between media

Define the index of refraction n = c/v, compute it, and explain why n is always greater than or equal to one

Apply Snell's law to predict the path of light crossing a boundary and to solve for an unknown angle or index

Predict whether a ray bends toward or away from the normal based on the relative indices of the two media

Explain total internal reflection and calculate the critical angle from θ_c = sin⁻¹(n₂/n₁) for n₁ > n₂

Describe applications of refraction and total internal reflection, including dispersion, rainbows, diamonds, corner reflectors, and fiber optics

16.2

"We define the index of refraction, n, of a material to be $n = \frac{c}{v}$, where v is the observed speed of light in the material. Because the speed of light is always less than c in matter and equals c only in a vacuum, the index of refraction (plural: indices of refraction) is always greater than or equal to one." "The exact mathematical relationship is the law of refraction, or Snell's law, which is stated in equation form as $n_1 \sin\theta_1 = n_2 \sin\theta_2$." "If the incident angle, $\theta_1$, is greater than the critical angle, then all the light is reflected back into medium 1, a condition called total internal reflection." "The critical angle, $\theta_c$, for a given combination of materials is thus $\theta_c = \sin^{-1}\left(\frac{n_2}{n_1}\right)$, for n₁ > n₂." "Total internal reflection, coupled with a large index of refraction, explains why diamonds sparkle more than other materials. The critical angle for a diamond-to-air surface is only 24.4°."