# Do Normal Incidence contradicts the definition of refraction?

Professor told our class that if someone wants to define refraction in words, it can be done as the following, The deviation of light from its path when it passes from one medium to another is called refraction. And i found normal incidence when i putted i = 0° in Snell's law, and found that angle of refraction was also 0°. I think that this contradicts the definition of refraction because in this case the light ray didn't bend.

I think maybe the light ray bend in normal incidence also but it bend downward direction instead of sideways bending.

• Speed can be defined as the distance moved in a unit of time. Would you say the case of zero speed contradicts this definition because the object doesn't move? Commented Oct 25, 2023 at 2:12
• If you really want to be pedantic then you have cited a special case when the deviation has the value zero. This is nothing new as when analysing normal modes some solutions produce a frequency of oscillation of zero and those are still called normal modes.. Commented Oct 25, 2023 at 7:22
• @Farcher Sir what is mode ?
– user380777
Commented Oct 25, 2023 at 7:41
• Normal modes Commented Oct 25, 2023 at 7:51

The crux is how you define the word "deviation." One can think of it as the difference between two angles, or as the ratio between two angles, or something else.

Recall Snell's law, perhaps rearranged, for two media with indices of refraction $$n_1$$ and $$n_2$$: $$\sin \theta_2=\frac{n_1}{n_2}\sin\theta_1.$$ Here, we see that the outgoing angle from the normal, $$\theta_2$$, differs from the incoming angle from the normal, $$\theta_1$$, when $$n_1\neq n_2$$ and, as pointed out correctly, $$\theta_1\neq 0$$.

A more precise language says "that the sine of the light's incident angle gets multiplied by something other than $$1$$ in order to yield the sine of the light's outgoing angle is called refraction." This precise language still has the light's path "deviating" by some $$n_1/n_2$$, but only if we define the "path" as the sine of the angle $$\sin \theta$$ and the "deviation" as a multiplication instead of as a subtraction. Then, we can still say that the "path" is "deviating" but because the "path" is 0 and "deviating" means multiplying then the number doesn't change. Small consolation, you can alternately conclude that your professor was using language that is not 100% correct.

You can take the small-angle approximation, where $$\sin x\approx x$$, to see Snell's law for small angles as $$\theta_2\approx \frac{n_1}{n_2}\theta_1$$. Then this ratio $$\frac{n_1}{n_2}$$ is the same as the ratio between the two angles $$\frac{\theta_2}{\theta_1}$$, so the index of refraction is thereby the "deviation" between the two paths in terms of the ratio of the two paths' angles.

This sort of distinction is important everywhere. Say you take a test and you score "deviates" from your previous scores. You might talk about the deviation in terms of the difference between the scores and you might talk about it in terms of the ratio between the scores, where each will provide different insight. The same goes for an experiment with an expected and measured value. Often the ratio is more informative than the difference, often the ratio of the difference to the actual value is more informative, etc., and it all depends on your problem, but of course you should use precise language whenever possible.

In this case, it does make sense to talk about the path in terms of the sine of the angle, if you watch the light propagate and want to know how far it has propagated along the direction perpendicular to the normal. Whether or not you are happy to refer to the "deviation" as the multiplication of this value by something is up to you, because any time you define deviation in that sense you have to worry about the edge case where your value is $$0$$ and thereby unchanged by multiplication.

• Yes sir but at the end when we multiply 0 with μ1/μ2 we get zero, which means the deviation is zero in case of normal incidence.
– user380777
Commented Oct 25, 2023 at 7:49
• @Galaxy_sprinter agreed. I mean that the "multiplication factor" is not unity, but otherwise it is hard to find a way out for your professor! Commented Oct 25, 2023 at 14:14

Your professor has given the correct definition. Snell's law covers cases of refraction, when the angle of incidence of light at the interface is non-zero, but it also covers the case when the angle of incidence is zero and there is no refraction, just undeviated penetration of the light into the 'new' medium.

Just because Snell's law applies doesn't imply that there is refraction.

• So sir is it correct to say that normal incidence is NOT refraction ?
– user380777
Commented Oct 25, 2023 at 7:35
• Yes; refraction implies bending, and there is no refraction at normal incidence. Commented Oct 25, 2023 at 7:41
• Thanks a lot sir
– user380777
Commented Oct 25, 2023 at 7:42