Critical Angle: Meaning And Its Formula

In the study focus has been given to determining the concept that lies behind the occurrence of “critical angles”. It is quite well known to us that when light passes through one medium to another the speed with which the light travels changes consequently depending on the material it passes through. The true fact behind this is that speed associated with the wave gets affected due to the thickness or better to call the density of the material it passes through. “Critical angle” occurs when the speed of the light increases as it passes from one material to another, thereby, creating an angle of refraction that is greater than the angle of incidence.

Understanding the meaning of critical angle in Physics

In order to better understand the concept associated with the “critical angle”, it is our prime requirement to have proper knowledge of the incidence angle as well as the refraction angle”. Delving into the study it is noticed that, incidence angle is defined as the angle that is formed between the incident ray and that of the normal ray. On the other hand, the refraction angle is determined as the angle that is formed between the “normal drawn at a point” to that of the refracted angle to the interface where the refraction is generated. Notions of incidence angle and refraction angle together form an intricate connection that determines the interesting situation of the occurrence of critical angles.

Definition Critical angle

In the field of optics, it is noted that when the refraction angle is 90 degrees to the incidence angle, at that very moment the critical angle is formed. In determining the “critical angle”, one needs to get aware of the term “total internal reflection”. The term “total internal reflection” refers to a complete reflection associated with the ray of light in the mediums of glass or water from the nearby medium and returns to the previous medium. Critical angle occurs in two special cases, one, when the ray of light within the dense medium travels to quite a less dense medium. Another condition at which “critical angle” occurs is when the incidence angle associated with the ray of light is greater than that of the stated “critical angle”. 

Derivation of Critical angle formal 

From the “Snell’s Laws of the equation”, the derivation of the “critical angle” is formed. First, consider that, there lies two different mediums, one named medium of incidence (i) and refractive medium denoted by (r), and their critical angle is denoted by “Θi” which provides a value of “Θr” as 90 degrees. According to the “Snell’s Laws of equation”, the formula thus derives as follows, ni *• sine(Θi) = nr • sine (Θr)

ni • sine(Θcrit) = nr • sine(90 degrees)

ni • sine(Θcrit) = nr

sine(Θcrit) = nr/ni

Θcrit= sine-1 (nr/ni) = invsine (nr/ni)

Calculation of critical angle 

In calculating the value of “critical angle”, one needs to consider tables associated with the refractive indices. For example the “critical angle” denoted for “crown glass” to “boundary of water”, then the critical angle will be, “Θcrit = sin-1 (nr/ni) = invsine (nr/ni); Θcrit = sin-1 (1.000/1.52) = 41.1 degrees”.

An interesting fact can be noted that the critical angle that is formed between the air boundary and that of the diamond is quite small in number, as the ray of light gets trapped within the cyst of the diamond and therefore, provides the fact of sparkling of the diamond. 

Definition of total internal reflection

The term “total internal reflection” is crucial in understanding the mechanisms associated with the field of optics. The ray of light reaching the interface makes a total reflection, which successively occurs at the time of travelling to a less dense medium and exceeds the stated critical angle. 

Conclusion  

In conducting the study it can be easily acknowledged that in order to get a vivid picture of concepts associated with the critical angle an individual needs to under the basic concepts of incidence, reflection and as well as refraction. The study has successively explored the definition of the term critical angle and its formula. Furthermore, derivation of the formula has been provided that will help in further calculation of the critical angle for two given mediums, through which the light is travelling. In addition to this, importance needs to be given to the tables associated with refractive indices, which are crucial in effectively calculating the critical angles.