Critical Angle: Vacuum vs. Air Refraction

[Cheman]

Critical angle...

Is the formula:

sin(critical angle) = 1/ mu, only true light is moving from one medium into air/ a vacuum?

Thanks in advance.

 

[Doc Al]

Correct. (Assuming "mu" is the index of refraction.) To generalize it to any two media (as long as $n_2 < n_1$) go to Snell's law: $n_1 \sin \theta_1 = n_2 \sin \theta_2$. The critical angle arises when $\sin \theta_2 = 1$, thus:
$$\sin \theta_{cr} = \frac {n_2}{n_1}$$

When the second medium is air or vacuum, $n_2 = 1$.

 

[sir-pinski]

The formula for critical angle, sin(critical angle) = 1/ mu, is true for any situation where light is moving from a medium with a higher refractive index (mu) to a medium with a lower refractive index. This includes cases where light is moving from a medium into air or a vacuum. The critical angle is the angle at which light is refracted at a 90 degree angle, and any angle greater than the critical angle will result in total internal reflection. This is why it is often used in fiber optics, where light travels through a medium with a higher refractive index (such as glass) and then into air or a vacuum. In this case, the critical angle is crucial in determining the maximum angle at which light can enter the fiber before it is reflected back. So, in short, the formula for critical angle is applicable in both situations, whether light is moving from a medium into air or a vacuum.