Question

define total internal reflection and establish a relation between critical angle and refractive index. answer at least 75 to 100 words​

Answer 1

In Optics, The angle of incidence to which the angle of refraction is 90° is called the critical angle. The ratio of velocities of a light ray in the air to the given medium is a refractive index. Thus, the relation between the critical angle and refractive index can be established as the Critical angle is inversely proportional to the refractive index.

Critical Angle And Refractive Index

The relationship between critical angle and refractive index can be mathematically written as –

SinC=1μab

Where,

C is the critical angle.

μ is the refractive index of the medium.

a and b represent two medium in which light ray travels.

Critical Angle And Refractive Index Formula

Formula SI Unit

Critical angle to Refractive index SinC=1μab degree

Refractive index to Critical angle μab=1sinC No SI unit

Critical angle and refractive index relation derivation

The relationship between critical angle and refractive index can be derived as –

Consider a ray of light,

Let the angle of incidence i be critical angle C

Let the angle of refraction r=90º

Refractive index of the rarer medium be μa

Refractive index of the denser medium be μb

Applying Snells Law

sinisinr=μaμb

⇒μbsinC=μasin900

⇒μbμa=1sinC

Thus, we arrive at formula expressing the critical angle and refractive index relation –

μab=1sinC

Hope you understood the relation and conversion between the Critical Angle and Refractive Index in Optics.