CATAGORY: Sound & Waves
QUESTION: Light moves from flint glass into water at an angle of
incidence  of 28.7 degress;
(a) What is the angle of refraction?
(b) At what angle would light have to be incident to give an angle of
refraction of 90.0 degrees?


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Part A

We will call the angle of incidence i and the angle of refraction r.
Applying snells law 

(1)               n(i)sin(i) = n(r)sin(r)

Where n(i) and n(r) are index of refraction for mediums the incident (i)
and refracted (r) rays are traveling in. n(i) = 1.58 (light flint glass)
n(r) = 1.33 (water).  Substituting the n's and i =28.7 degrees into 
equation (1) gives

               1.58 sin(28.7) = 1.33 sin(r)
               
solving for sin(r)

               sin(r) = 1.58 sin(28.7) / 1.33
               
               so 
               
               sin(r) = .570

             ***********************
             *                     *
             *  r = 34.8 (degrees) *              
             *                     * 
             ***********************


Part B

when r = 90 degrees sin(r) = 1.0 so snells law becomes

(2)               n(i)sin(i) = n(r)

So                sin(i) = n(r)/n(i)

Substituting the n values gives

                  sin(i) = 1.33/1.58 = .842
                  
             ***********************
             *                     *
             *  i = 57.3 (degrees) *              
             *                     * 
             ***********************                  
                  

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