Physics / Unit 8: Light and Optics
8.4 Refraction
Notes
Refraction is the bending of light as it passes from one material to another, because its speed changes.
- Index of refraction: $\displaystyle n = \frac{c}{v}$. Air $\approx 1.00$, water $= 1.33$, glass $\approx 1.5$, diamond $= 2.42$.
- Snell's law: $n_1\sin\theta_1 = n_2\sin\theta_2$, with angles measured from the normal.
- Going into a higher $n$ (slower) material, light bends toward the normal; into a lower $n$, it bends away.
- Total internal reflection: going from higher $n$ to lower $n$ beyond the critical angle $\theta_c$, where $\displaystyle \sin\theta_c = \frac{n_2}{n_1}$, all light reflects. Fiber optics use this.
- Example: light in air hits water at $30^\circ$: $\displaystyle \sin\theta_2 = \frac{1.00 \times 0.5}{1.33} = 0.376$, so $\theta_2 \approx 22^\circ$.
Practice
Light travels through a glass with $n = 1.5$. What is its speed in the glass?
$\displaystyle v = \frac{c}{n} = \frac{3.0 \times 10^8}{1.5} = 2.0 \times 10^8 \text{ m/s}$.
A light ray passes from air into water at an angle. How does it bend?
Water has a higher index, so light slows and bends toward the normal.
What is the critical angle for light going from glass ($n = 1.5$) into air?
$\displaystyle \sin\theta_c = \frac{1.0}{1.5} = 0.667$, so $\theta_c \approx 42^\circ$.
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