Critical Angle Formula

Critical Angle Formula

The Critical Angle is an angle of incidence that offers a 90-degree angle of refraction. It is important to remember that the critical angle is defined as an angle of incidence value. For water-air boundaries, the critical angle is 48.6 degrees, and for crown glass-water boundaries, it is 61.0 degrees.

Critical Angle Formula

Refraction, reflection, and other phenomena are common in optical science. The refraction event occurs when the propagation direction of light changes owing to a change in the medium through which it is transmitted. When light enters a denser media from a rarer medium, its direction changes, and the light beam bends towards the normal. This normal line is an imaginary perpendicular line drawn at light’s point of contact. This article discusses an essential measurement in this respect. It is a crucial angle. Let’s study the critical angle formula with examples.

Concept of Critical Angle

The critical angle of a substance when a light beam is sent from it to vacuum is critical because it determines whether entire internal reflection occurs. It’s also necessary for your physics exam.

The critical angle in optics is a certain angle of incidence. Beyond this angle, there will be total internal reflection of light. When a light beam encounters a material with a lower refractive index, its trajectory deviates from that of the normal path. As a result, the ray’s angle of departure always exceeds its angle of incidence. This form of reflection is known as internal reflection.

Light moves from a media with a higher refractive index ($$n_1$$) to a medium with a lower refractive index ($$n_2$$). Here, the angle of refraction is greater than the angle of incidence. Because of the difference in refractive index, the beam bends towards the surface.

The critical angle is thus defined as the angle of incidence that results in a 90-degree angle of refraction. It should be noted that the crucial angle is the angle of incidence value. The water-to-air limit has a critical angle of 48.6 degrees. The crucial angle at the glass-to-crown water exceed is 61.0 degrees. The critical angle’s exact value is determined by the materials present on both sides of the boundary.

The Formula for Critical Angle

Let us consider two different media. The critical angle is that of $$θ_{cric}$$ which gives a value of exactly 90 degrees. If these values are substituted in the Snell’s Law equation, we will get a generic equation that will be used to predict the critical angle.

Therefore, The equation is:

$$\theta_{cric} = \sin^{-1}\frac{n_r}{n_i}$$

Where,

Solved Examples on Critical Angle

Example 1: A ray of light strikes from a medium with n = 1.67 on a surface of separation with the air with n = 1. Calculate the value of a critical angle.

Solution :

Given the indices for both the means.

We know the formula,

$$\theta_{cric} = \sin^{-1}\frac{n_r}{n_i}$$

$$\theta_{cric} = \sin^{-1}\frac{1}{1.67}$$

Therefore,

$$\theta_{cric}=0.064rad$$