Answer:
The value is [tex]c = 51.38 ^o[/tex]
Explanation:
From the question we are told that
The angle of incidence is [tex]\theta_i = 30^o[/tex]
The angle of refraction is [tex]\theta_r = 23^o[/tex]
Generally at the point where the light enters the material , from Snell's law we have that
[tex]n = \frac{sin (\theta_i)}{sin (\theta_{r})}[/tex]
Here n is the refractive index of the material
=> [tex]n = \frac{sin (30)}{sin (23)}[/tex]
=> [tex]n = 1.28[/tex]
Generally for total internal reflection , the critical angel is evaluated using Snell law as follows
[tex]n = \frac{sin (90)}{sin (c)}[/tex]
=> [tex]1.28 * sin (c) = sin(90)[/tex]
=> [tex]c = sin^{-1} [0.7813 ][/tex]
=> [tex]c = 51.38 ^o[/tex]
