# Is it possible for any value of incident angle (except 90°) that the refracted ray goes along the normal (rarer to denser case)?

I was going through the topic critical angle. When light travels from denser to rarer medium & when angle is critical angle, it goes along the surface of separation, i.e. grazing emergence.

Will the ray coincide with normal, when the medium is rarer to denser with a smaller angle of incidence?

If yes, then what will happen when we further decrease the incidence angle?

• if you know the law of diffraction $\sin(a)/\sin(b)=n you can see that a never can be 0 so the angle 0. Commented Apr 15, 2020 at 15:00 • why have you stated except$\frac{\pi}{2}$radians? Did you mean except$0\$? Commented Apr 18, 2020 at 8:33

The answer is that the ray will coincide, but the second part of your question can be answered easily.

By Snell's law,

$$\frac{\sin\left(i\right)}{\sin\left(r\right)}=n_{21}.$$

For the refracted ray to make an angle $$0$$ with the normal, $$\sin(r)=0$$.

If $$\sin(r)$$ becomes zero, for Snell's law to be valid, $$\sin(i)$$ should also be zero (actually, they will be tending to zero), which means you have to shine light perpendicular to the surface.

You obviously can see why we cannot make the angle any smaller than that.

If you know Snell's law of refraction i.e. $$\sin(a)/\sin(b)=n$$, you can see that $$sin(a)$$ never can be $$0$$ unless $$sin(b)$$ is zero. So the angle will be $$0$$ in both media.

You can inverse any way of the light so turn the direction of your light in the last picture around and see, that it is impossible.

• It's refraction, not diffraction. Commented Apr 15, 2020 at 19:31

I like to look at questions like this from the perspective of symmetry. If you look at your second sketch in reverse, you can see that it would require a symmetrical ray to become asymmetrical upon refraction. Symmetries are always preserved in classical physics: there is no reason for a ray to "make a choice" to turn even slightly in any one direction more than another direction.

So the answer is "no", an angled ray will never exit a uniform slab of material in a direction perpendicular to the surface.