Refraction & Refractive Index

• The absolute refractive index ($n$) of a material is a dimensionless ratio that compares the speed of light in a vacuum ($c$) to its speed in that specific material ($v$).

Formula: $n = \frac{c}{v}$

• Since light travels at its maximum possible speed in a vacuum ($c \approx 3.00 \times 10^8 \text{ m/s}$), the value of $n$ for any physical medium is always greater than or equal to 1.

• For practical calculations, the refractive index of air is typically treated as $1.00$, as light slows down negligibly when passing through it compared to a vacuum.

• Snell's Law provides the mathematical relationship between the angles of incidence and refraction and the refractive indices of the two media involved.

Law: $n_1 \sin \theta_1 = n_2 \sin \theta_2$

• In this equation, $\theta_1$ is the angle in the first medium and $\theta_2$ is the angle in the second medium. Crucially, these angles must always be measured from the normal (the perpendicular line to the surface).

• This relationship implies that the ratio of the sines of the angles is inversely proportional to the ratio of the refractive indices: $\frac{\sin \theta_1}{\sin \theta_2} = \frac{n_2}{n_1}$.

• The direction of bending depends entirely on whether the light is speeding up or slowing down as it crosses the boundary.

• Note that even if the light does not bend (when entering at $0^{\circ}$ to the normal), its speed and wavelength still change according to the refractive index of the new medium.

• Frequency vs. Wavelength: A common misconception is that all properties of light change during refraction. In reality, the frequency is determined by the source and remains constant; only speed and wavelength change proportionally ($v = f\lambda$).

• Optical vs. Physical Density: Students often assume that a physically heavier material must be more optically dense. While often true, optical density refers specifically to the interaction between light and the material's electrons, not its mass per unit volume.

• The 'No Bending' Case: Remember that refraction (the phenomenon of light changing speed) still occurs even if the light enters at $90^{\circ}$ to the surface. The 'bending' is just a visible consequence of that speed change at an angle.