Refractive Index

Light changes direction when it moves from one transparent material to another because its speed changes. This bending is called refraction. The refractive index tells us how strongly a material slows and bends light.

Key terms

• Normal: a line drawn at right angles (90°) to the surface at the point where the ray meets it.
• Angle of incidence (i): the angle between the incoming ray and the normal.
• Angle of refraction (r): the angle between the refracted ray and the normal inside the second material.

What is refractive index?

It measures how much a material slows light. Bigger refractive index means light slows down more and bends more towards the normal.

Speed definition (air/vacuum to a material): $n = \dfrac{c}{v}$, where $c$ is the speed of light in air/vacuum and $v$ is the speed in the material.

Angle definition (air to a material): $n = \dfrac{\sin i}{\sin r}$.

General form (between any two media): $n_1 \sin i = n_2 \sin r$.

How light bends

• Into higher n (e.g. air to glass): bends towards the normal ($r < i$).
• Into lower n (e.g. glass to air): bends away from the normal ($r > i$).

Measuring n in the lab

Shine a narrow ray into a rectangular glass block. Draw the normal at the entry point. Measure $i$ and $r$ with a protractor. Calculate $n = \sin i / \sin r$. Repeating for several angles and plotting $\sin i$ (y-axis) against $\sin r$ (x-axis) gives a straight line with gradient equal to $n$.

Link to critical angle

For light trying to leave a material into air, there is a largest inside angle (the critical angle, $c$) where the refracted ray just skims the surface. The refractive index links to it by: $n = \dfrac{1}{\sin c}$.

Everyday uses

• Lenses and cameras rely on precise refractive indices to focus images.
• Optical fibres guide light using high $n$ cores and total internal reflection for telecommunications.