# Confusion over Snell's law [duplicate]

Does the angle of refraction always have $$n_2$$ as its refractive index? As far as I know, $$\frac{\sin\theta_i}{\sin\theta_r} = \frac{n_2}{n_1}.$$ So I got this question here:

Calculate the critical angle for a flint glass-air ($$n=1.58$$) boundary.

Since the critical angle has an angle of refraction of 90° that is $$\theta_r= 90^\circ$$, but I am confused on what values should I substitute for $$n_2$$ and $$n_1$$. So does the refractive index of the angle of incidence always equal $$n_1$$?

## marked as duplicate by Aaron Stevens, Jon Custer, ZeroTheHero, ahemmetter, John Rennie homework-and-exercises StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Nov 21 '18 at 7:51

• – Stephan Nov 20 '18 at 9:28

To avoid confusion, here is a different way of writing Snell’s law. $$n_1\times\sin(i) = n_2\times\sin(r)$$ Here, $$n_1$$ is the refractive index of the medium in which the incident ray exists $$n_2$$ is the refractive index of the medium in which the refracted ray exists.
So for this question as the light goes from denser to rarer medium, $$n_1$$ would be the refractive index of flint and $$n_2$$ would be that of air.
• @Tfue Yes, if $i$ represents the incident angle. The formula is set up in a nice way to remember it. You just keep things in the same medium on the same side of the equation. It would be even clearer if you wrote it as $$n_i\sin\theta_i=n_r\sin\theta_r$$ – Aaron Stevens Nov 20 '18 at 10:43
• Andrew, many of the students that I taught physics to did NOT like to make a drawing, and I'm not sure why they were so reluctant to do so. Having said that, I note that the subscript "i" in Snell's law represents the incident ray, and the subscript "r" represents the refracted ray. Subscripts "1" and "2" are not as helpful as they could be, so I would recommend that the OP use the equation $n_i sin(\theta_i)=n_rsin(\theta_r)$ – David White Nov 20 '18 at 16:07