Look at the diagram above. We have 6 interfaces where the ray of light will go from one material to another. The water tank is made from glass with an index of 1.523, the water has an index of 1.33, and the monolith in the center is of some mythical hi-index glass with an index of 1.75. Lets follow the ray of light through the tank from the light to the eye.

1. First the ray goes from air into the glass of the tank. If the angle of incidence is 35 degrees, what is the angle of refraction?

 

 

        () (sin i) = () (sin r)
= 1
          sin i = sin 35 =
= 1.523
          sin r = ?
       (1) (sin 35) = (1.523) (sin r)
       0.5736 = (1.523) (sin r)
       sin r = 0.5736  1.523
       sin r = 0.3766
       r = 22 degrees
[Looking at the line (1) (sin 35) = (1.523) (sin r), you can solve this by punching in: "35" "sin" "" "1.523" "=" "2nd" "sin", and you would have the answer 22.]
 

2. Second, the ray goes from the glass into the water. If the angle of incidence is 22 degrees, what is the angle of refraction? ?

 

 

        () (sin i) = () (sin r)
= 1.523
          sin i = sin 22 =
= 1.33
          sin r = ?
       (1.523) (sin 22) = (1.33) (sin r)
       (1.523) (0.3746) = (1.33) (sin r)
       (1.523) (0.3746)  (1.33) = sin r
       sin r = 0.42897
       r = 25 degrees
 

3. Third the ray travels from the water into the hi-index glass. Suppose I can somehow determine that the angle of refraction is 22 degrees. Then what was the angle of incidence?

 

 

        () (sin i) = () (sin r)
         = 1.33
          sin i = ?
= 1.75
          sin r = sin 22 = ?
       (1.33) (sin i) = (1.75) (sin 22) = (1.75) (0.3746)
       sin i = (1.75) (0.3746)  (1.33)
       sin i = 0.4929
       i = 30
 

4. OK, to leave the monolith the ray is at 0 degrees to the normal -- it is perpendicular to the side. What is the angle of refraction?

 

 

        () (sin i) = () (sin r)
= 1.75
          sin i = sin 0 = ?
= 1.33
          sin r = ?
       (1.75) (sin 0) = (1.33) (sin r)
       sin r = (1.75) (0)  (1.33))
       sin r = 0
       r = 0, which we already knew: If a ray goes from one material to another material perpendicular to the interface, it slows down, but does not change direction.
 

5. This side of the tank was made of something else, not the same glass as the rest of the tank, and I do not know what it's index is. But I manage to determine that the angle of incidence is12 degrees; and then I determine that the angle of refraction is 10 degrees. What is the index of refraction of the new material?

 

 

        () (sin i) = () (sin r)
= 1.33
          sin i = sin 12 = ?
= ?
          sin r = sin 10 = ?
       (1.33) (sin 12) = ( ) (sin 10)
= (1.33) (0.2079)  (0.1736)
= 1.59
 

6. Last, the ray leaves the tank altogether. The angle of incidence is 10 degrees. You found an index in the last problem. So, what is the angle of refraction?

 

 

        () (sin i) = () (sin r)
= 1.59
          sin i = sin 10
=
          sin r = 1
       (1.59) (sin 10) = (1) (sin r)
       sin r = (1.59) (0.1736)
       sin r = 0.2761
       r = 16
 

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