Total Internal Reflection Formula

Consider the case below. A beam of light travels from a watery medium to one of air. The light ray will be refracted at the point where the two mediums meet. The refracted light beam bends away from the normal as it passes from a medium with a higher refractive index to one with a lower refractive index.

• The incident beam of light is refracted in such a way that it travels over the water’s surface at a certain angle of incidence.
• The critical angle is the angle of incidence at which something happens. The refraction angle is 90° here.
• The incident ray is reflected back to the medium when the angle of incidence is larger than the critical angle. This event is referred to as total internal reflection.

The formula for total internal reflection is stated as:

n₁ ⁄ n₂ = sin θ₁ ⁄ sin θ₂

where,

• θ₁ is the angle of incidence,
• θ₂ is the angle of refraction,
• n₁ is the denser medium, &
• n₂ is the rarer medium.

Critical Angle

Critical angle is defined as the largest angle of incidence for which refraction of light inside the medium still can be possible. Therefore, the angle of incidence, when the angle of refraction is 90 degrees and the ray which is refracting to total internal refraction is called the critical angle. 

Mathematically, the critical angle for a total internal reflection is defined as,

θ_c = sin⁻¹(n₂ ⁄ n₁)

where, 

• θ_c is the critical angle.
• n₁ is the denser medium, &
• n₂ is the rarer medium.

In Physics, total internal reflection is the complete reflection of a light ray within the medium (air, water glass, etc). For example, the total internal reflection of rays of light takes place in a Diamond. Since Dimond has multiple reflecting surfaces through which the Total internal reflection takes place. The total internal reflection occurs when light travels from a denser medium to a less dense medium and the angle of incidence must be greater than the critical angle. The phenomenon of total internal reflection has a wide application in optical devices such as telescopes, binoculars, periscopes, etc. Read more about the concepts of Total Internal Reflection like Total Internal Reflection of Light, definition, critical angle, and total internal reflection, examples, and FAQs, here in this article!