A ray of light undergoes total internal reflection while moving from a denser to a rarer medium . Derive the relation connecting critical angle and refractive indices of the two media .

* Total internal reflection is the phenomenon of reflection of light into a denser medium from an interface of the denser medium and the rarer medium.

 * Two essential conditions for total internal reflection: 

 Incident ray should travel in denser medium and refracted ray should travel in rarer medium. 

Angle of incidence (i) should be greater than the critical angle for the pair of media in contact.

 

 Relation between refractive index  (μ) and critical angle (C) 

When, i = c, r = 90°; Applying Snell’s law at A2, we get

μb sin c = μb sin 90° = μa × 1

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Critical angle is the angle of incidence for which the angle of refraction is 900.

Thus, light from the bottom of the water if incident on the air-water interface with an angle greater than the critical angle will be reflected back to the water. For all other angles of incidence light will be refracted to the air.

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