Critical Angle can be described as the angle of incidence that offers an angle of refraction of 90 degrees. Remember that the critical angle is defined as an angle of incidence value. The critical angle will be 48.6 degrees for water-air boundaries and 61.0 degrees for crown glass-water boundary.
The real value of the critical angle depends completely on the combination of materials that are available on each side of the boundary. Let us consider two different medium
- Incident medium
- Refractive medium
Critical angle = Θi that gives a Θr value of 90-degrees
According to Snell’s Law equation, a generic equation for finding the critical angle can be derived easily.
Solved Examples
Example 1
Find the critical angle for the crown glass-air boundary
The solution to the problem requires the use of the above equation for the critical angle.
Θcrit = sin-1 (nr/ni)
nr=refractive index of glass=1.52
ni=refractive index of air=1.000
Θcrit = sin-1 (1.000/1.52) = 41.1 degrees
Example 2
Find the critical angle for the diamond-air boundary.
The solution to the problem requires the use of the above equation for the critical angle.
nr=refractive index of diamond=2.42
ni=refractive index of air=1.000
Θcrit = sin-1 (nr/ni)
Θcrit = sin-1 (1.000/2.42) = 24.4 degrees
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