Is it true to say no refraction takes place when a ray comes along normal drawn to interface?

Question

Many books and websites in our country say that there are two conditions for no refraction of light:

1. If index of Refraction of media on both sides is same.
2. If the ray of light falls normally on the interface.

Now the question arises if a ray enters a different medium normally surely its speed (or wavelength ) changes although it doesn't bend . How can we say this is a case of no refraction? I had consulted books authored by Paul Tipler Gene Mosca Sears zemansky Halliday Resnick and no book says Bending of light is called refraction. Resnick Halliday says: ""Travel of light through an interface is called refraction and the light is said to be refracted.Unless an incident beam of light is perpendicular to surface, refraction changes light's direction of travel "" From this can we conclude that Bending of light is a consequence of refraction but Bending of light itself is not refraction.

Answer 1

From an incident angle $\alpha$, we can deduce refraction angle $\beta$ using Snell law as : $$ \beta = \sin^{-1}\left(\sin \alpha \cdot \left[ \frac {n_\alpha}{n_\beta} \right] \right)$$

This equation shows that : $$ \beta = \alpha ,~\text{when} \begin{cases} {n_\alpha}={n_\beta},\\ \alpha = 0\\ \end{cases} $$

First case is when there's no refractive index differences between pair of media, obviously then light travels in the same(or analogous) media undisturbed. Second case is when incident angle is zero radians (when light rays goes parallel to surface normal), then it doesn't matter what kind of media you will plug-in (what ratio of ${n_\alpha}/{n_\beta}$ will be),- you will always get zero output angle.

So for the refraction law to work we need $${n_\alpha} \ne{n_\beta} ~\land~ \alpha \ne 0$$ composite condition.

Another way to see that Snell's law is undefined when $\alpha = 0$ is try to solve limit :

$$ \lim _{\alpha,\beta \to 0} {\frac {\sin \alpha}{\sin \beta} \approx \frac {\alpha}{\beta} = \frac 00 = \text{indeterminate form }}, $$

that is,- in this case you can't say from a Snell's law what type of media's in light travel path were involved.