Critical Angle

The angle of incidence in the denser medium at which angle of reflection is 90° is called critical Angle.

            Formation of critical angle

Let see in case of total internal reflection 

When a ray of light passes from denser to rarer medium, the refracted ray bends away from the normal. Hence, the angle of refraction is greater than the angle of incidence. Gradually if the angle of incidence increases, angle of refraction also increases. At a particular angle of incidence, the refracted ray just grazes the refracting surface making the angle of refraction is equal to 90°. This angle of incidence in the denser medium is called ‘critical angle’. If the angle of incidence is further increased, the ray does not undergo refraction, it gets reflected into the same optically denser medium. This is known as total internal reflection.

Relation between Critical Angle and Reflective Index

Consider a ray of light PQ travelling from denser medium to rarer medium. Let the ray be incident at the critical angle. the angle of refraction will be equal to 90°.

A ray PQ refracting from denser to rare medium

From Snell’s Law,

$^1μ_2 = \dfrac{sin i}{sin r}$  → eq (1)

But i = c and r = 90°

$^1μ_2 = \dfrac{sin c}{sin 90}$

$^1μ_2 = \dfrac{sin c}{1}$

$(∴ sin 90 = 1) ⇒ \dfrac{μ_2}{μ_1}= sin\sqrt{C}$

[$^1μ_2 = \dfrac{μ_2}{μ_1}$ from relative reflective index]

If the second medium is air, then, $μ_2 = 1 and μ_1 = μ ⇒ μ = \dfrac{1}{sin}.$

Critical angle of different materials

The critical angle varies depending on the combination of materials involved. Here are some common examples of critical angles for specific material interfaces:

1. Air to Water: The critical angle for the interface between air and water is approximately 48.8 degrees.

2. Air to Glass: The critical angle for the interface between air and standard crown glass is approximately 41.8 degrees.

3. Water to Glass: The critical angle for the interface between water and standard crown glass is approximately 61.0 degrees.

4. Glass to Diamond: The critical angle for the interface between glass and diamond is approximately 24.4 degrees.

These values are approximate and can vary depending on the specific properties and refractive indices of the materials involved. It’s important to note that these examples assume light traveling from a medium with a higher refractive index to a medium with a lower refractive index. If the order of the media is reversed, the critical angle will be different.

If you have a specific material combination in mind, I can try to provide the corresponding critical angle for that particular interface.