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Applications of refractive index

Answer Text:
Applications of refractivec index
Total internal reflection:
-This occurs when light travels from a denser optical medium to a less dense medium. The refracted ray moves away from the normal until a critical angle is reached usually `90^0` where the refracted ray is parallel to the boundary between the two media. If this critical angle is exceeded total
internal reflection occurs and at this point no refraction
occurs but the ray is reflected internally within the denser medium.
Relationship between the critical angle and refractive index.
Consider the following diagram

From Snell’s law
`\ _gn_w` = `sin C/sin 90^0`,but `\ _an_g` =
`1/(\ _gn_a)` since sin `90^0` = 1
Therefore `\ _an_g`= `1/sin C`,
hence sin C=`1/n` or n=`1/sinC`
Example
Calculate the critical angle of diamond given that its refractive index is 2.42
Solution
Sin `C= 1/n=1/ 2.42`=
0.4132= 24.40