Question

The index of refraction of a sugar solution in water is about 1.5, while the index of refraction of air is about 1. What is the critical angle for the total internal reflection of light traveling in a sugar solution surrounded by air

Answer 1

Answer:

The critical angle is  $i = 41.84 ^o$

Explanation:

From the  question we are told that

    The index of refraction of the sugar solution is  $n_s = 1.5$

   The  index of refraction of air is  $n_a = 1$

Generally from Snell's  law

      $\frac{sin i }{sin r } = \frac{n_a }{n_s }$

Note that the angle of incidence in this case is equal to the critical angle

Now for total internal reflection the angle of reflection is $r = 90^o$

So  

      $\frac{sin i }{sin (90) } = \frac{1 }{1.5 }$

      $i = sin ^{-1} [\frac{ (sin (90)) * 1 }{1.5} ]$

      $i = 41.84 ^o$