Consider light travelling from a medium 
to medium 
separated by a plane interface. If the light undergoes total internal reflection during its travel from medium 
to 
and the speed of light in media 
and 
are 
and 
, respectively, then the value of critical angle is :
Text Solution
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The refractive index of a medium is inversely proportional to the speed of light in that medium, given by
.
For light travelling from medium 
to medium 
, the critical angle 
is defined when light travels from a denser to a rarer medium.
Given speeds are 
and 
.
The refractive indices are 
and 
.
The critical angle 
is given by 
.
Substituting the values: 
.
To find the value in terms of 
, we use the trigonometric identity for a right-angled triangle where perpendicular 
and hypotenuse 
.
The base 
.
Thus, 
.
Therefore, 
.
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