Reflection and Refraction
Use ray diagrams, law of reflection, refraction, Snell law conceptually, lenses, mirrors, and image formation to describe light behavior.
A lesson of Physics, in Waves, Sound, and Light, about 10 minutes.
By the end of this lesson, you will be able to apply the law of reflection, use Snell's Law for refraction, explain total internal reflection, and describe the behavior of light through lenses and mirrors.
Reflection
Law of Reflection: the angle of incidence equals the angle of reflection, both measured from the normal.
$$\theta_i = \theta_r$$
Specular reflection: smooth surface → clear image (mirror).
Diffuse reflection: rough surface → scattered reflection (paper, walls).
Refraction
When light passes from one medium to another, it bends. This is because light travels at different speeds in different media.
Index of refraction ($n$): $n = c/v$ where $c = 3 \times 10^8$ m/s and $v$ = speed of light in the medium.
Higher $n$ → slower light → more bending.
Snell's Law:
$$n_1\sin\theta_1 = n_2\sin\theta_2$$
Bending direction: light bends toward the normal when entering a denser medium ($n_2 > n_1$); away from normal when entering a less dense medium.
Example 1 — Snell's Law
Light in air ($n = 1.00$) strikes water ($n = 1.33$) at 45°. Find the refraction angle.
$1.00\sin 45° = 1.33\sin\theta_2$
$\sin\theta_2 = 0.707/1.33 = 0.532$
$\theta_2 = 32.1°$ (light bends toward normal)
Total Internal Reflection
When light in a denser medium hits the boundary with a less dense medium at a large enough angle, it is completely reflected back.
Critical angle: $\sin\theta_c = n_2/n_1$ (for $n_2 < n_1$).
Above $\theta_c$: total internal reflection.
Example: Fiber optic cables — light trapped by total internal reflection travels along the fiber; used in internet cables and medical endoscopes.
Lenses
Convex (converging) lens: bends parallel rays to a focal point; used in cameras, eyes, magnifying glasses.
Concave (diverging) lens: spreads rays; used in glasses for nearsightedness.
Thin lens equation: $\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$
$f$ = focal length; $d_o$ = object distance; $d_i$ = image distance.
Magnification: $m = -d_i/d_o$
Summary
Reflection: $\theta_i = \theta_r$ (from normal).
Refraction: $n_1\sin\theta_1 = n_2\sin\theta_2$ (Snell's Law).