Index of refraction

Printed on the AP Physics 2 sheet, and the CED's phrasing is that $n$ is inversely proportional to the speed of light in the medium. It has no units: it is a speed divided by a speed.

Never less than 1, because light cannot outrun $c = 3.00 \times 10^8$ m/s. Vacuum sits at exactly 1, air is close enough to 1 that problems treat it as 1, water is about 1.33 and ordinary glass around 1.5. A larger $n$ means slower light, and slower light means a stronger bend.

Two consequences follow straight from the definition.

• $v = c/n$, so light travels at about $2.0 \times 10^8$ m/s in glass of index 1.5.
• $\lambda_{\text{medium}} = \lambda_0 / n$, because the frequency is set by the source and cannot change at a boundary. This is the factor that makes thin-film interference work.

The index is the quantity Snell's law compares across a boundary, so what matters for a bend is never one index but the ratio of the two. The same ray of light bends toward the normal entering glass from air and away from it going back out.

Careful with the word denser. An optically denser medium is one with a higher $n$, and that has no necessary connection to mass density. Topic 13.3 carries the worked cases.