Critical Angle a Pair of Media
Snell’s law defines the correlation between the angles of incidence (θ1) and refraction (θ2) and the refractive indices ( n1 and n2 ) of two media:
[ n1sin θ1 = n2sin θ2]
Now, we know that the concept of critical angle is valid when ray moves from denser medium to rarer medium. Since, at critical angle, the refracted ray travels parallel to the media, thus it makes 90° with the normal. Therefore,
θ1 = Critical Angle denoted by C
θ2 = 90°
n1 sin C = n2 sin 90°
Sin C = n2/n1
Hence,
C = sin-1(n2/n1)
By setting θ2 to 90 degrees (since refraction is along the boundary at the critical angle) and substituting n2 = 1 (for air) and putting it in the Snell’s law we get
θ1 = Critical Angle denoted by C
θ2 = 90°
n1 = n
n2 = 1 (air)
n1sin θ1 = n2sin θ2
n × Sin C = 1 × Sin 90
n × Sin C = 1
⇒ Sin C = 1/n
⇒ C = Sin-1(1/n)
How to Find Critical Angle of a Light Ray
The critical angle is a key concept in optics, especially when light interacts with boundaries between two dissimilar materials. It determines the exact angle of incidence at which light will refract along the interface between the materials, instead of entering the second medium.
In this article, how to find the critical angle of a light ray, the formula for critical angle, Snell’s law, finding a critical angle, and solve the problem.
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