Question

Light enters a transparent material from air at 30.0° to the normal. It continues within the material at the angle of refraction of 23.0°. What is the critical angle for total internal reflection when this material is surrounded by air?

Answer 1

Answer:

The value is $c = 51.38 ^o$

Explanation:

From the question we are told that

    The angle of incidence is  $\theta_i = 30^o$

    The angle of refraction is  $\theta_r = 23^o$

     

Generally at the point where the light enters the material ,  from Snell's law  we have that

          $n = \frac{sin (\theta_i)}{sin (\theta_{r})}$

Here  n is the refractive index of the material

=>       $n = \frac{sin (30)}{sin (23)}$  

=>       $n = 1.28$  

Generally for total internal  reflection , the critical angel is evaluated using Snell law as follows

          $n = \frac{sin (90)}{sin (c)}$

=>       $1.28 * sin (c) = sin(90)$  

=>      $c = sin^{-1} [0.7813 ]$

=>    $c = 51.38 ^o$