What are Critical Angles?

Hana Elgaweesh
2 days ago
3 min read

Edmonton, AB

Have you ever placed a pencil in a glass of water and noticed that it appears bent rather than straight? It might look like magic, but this phenomenon is actually due to the science of refraction.

Before learning about critical angles, there are a few terms you need to be familiar with. The first one is medium. A medium is the material that waves travel through. It could be glass, water, diamond, or air, along with various other substances. Another important word is refraction. When light travels through different mediums, its speed changes. This change in speed causes the light to bend, which is known as refraction. This is the magic behind the illusion of the bending pencil in water. The next term you need to know is the index of refraction. The index of refraction measures the optical density of a material, meaning how difficult it is for light to travel through a medium. The index of refraction is represented by n. The higher the n value is, the more it is difficult for light to travel through it. Air travels the fastest through air, which has a n value of 1. Therefore, the index of refraction can not be lower than 1. The ray that comes towards a surface is called the incident ray and the ray that is refracted in a surface is called the refracted ray.

When a material is more dense, light travels slower, and when a material is less dense, light travels faster.

rays, lights, medium, physics, emr, electromagnetic radiation, refraction, snell's law, index of refraction, total internal reflection, critical angles — Refraction angle from less dense to more dense.

When light travels from a less dense medium to a more dense medium, as shown to the left, the refracted ray bends towards the normal line. Think of it like this: if someone goes from doing less to doing more—you’d naturally feel closer to them, just like the light ray bends closer to the normal.

When light travels from a more dense medium to a less dense medium, as shown to the left, the refracted ray bends away from the normal line. Think of it like this: if someone goes from doing more to doing less, you’d feel yourself moving further away from them—just like the light ray bends away from the normal.

Now, after learning the basics of refraction, you can learn about critical angles. A critical angle is the angle of incidence that creates an angle of refraction of 90°, and Snell’s equation is used to calculate it. When light travels from a more dense medium to a less dense medium, the refracted ray travels away from the normal. If we continued to increase the incident angle, eventually the refracted ray reaches 90° and becomes parallel to the surface. Therefore, critical angles always happen when the ray travels from a more dense medium to a less dense medium, and never the opposite.

Snell’s Law equation states that n₁ sin (θ₁) = n₂ sin (θ₂) where n₁ and θ₁ refer to the refractive index of the first medium and the angle of incidence and n₂ and θ₂ refer to the refractive index of the second medium and the angle of refraction (which is 90° for finding critical angles). Since critical angles exist only when rays travel from more dense to less dense mediums, the value of n₂ has to be lower than the value of n₁.

Angles are measured with respect to the normal line (dotted line).

What happens if the angle of incidence goes beyond the critical angle? Well, remember, the critical angle is the angle of incidence that causes the angle of reflection to become parallel to the surface. If the angle of incidence gets larger than the critical angle, total internal reflection kicks in, meaning the refracted ray doesn’t escape, and instead reflects back into the medium, and no refraction occurs.