ANSWERS TO THE EXERCISES ON ANGLES
  1. If a ray of light travels from one material to another with an angle of incidence of 32 and an angle of refraction of 26, what is the angle of deviation? Is the ray travelling into the lens or exiting from the lens?

    2.     i = r + d
        i = 32
        r = 26
        d = ?

         32 = 26 + d
        d = 32 - 26
        d = 6.
    Don't take my word for it. Go back to the equation i = r + d and check if d = 6 is true.

    The ray is entering the lens. It looks like the second picture on page 20 of the textbook.
       .

  2. A ray of light crosses an interface and is deviated from its path by 5 degrees. If the angle of refraction is 20 degrees, what was the angle of incidence? Is the ray entering the lens material or exiting from it?

    3.     i = r + d
        i = ?
        r = 20
        d = 5

         i = r + d
        i = 20 + 5
        i = 25
        CHECK IT!
    The ray is again entering the lens material, as in the second picture.


       .

  3. A ray of light travels from one material to another. The angle of incidence is 45 degrees and the angle of refraction is 65 degrees. What is the angle of deviation? Is the ray entering the lens material or exiting from it?

    4.     i = r + d
        i = 45
        r = 65
        d = ?

         i = r + d
        45 - 65 + d
        d = 45 - 65
        d = -20
    The ray is exiting from the lens material into air (or another material which is not as dense).
     
     

  4. A ray is deviated by -10 degrees from its path when it passes from one material into another material. If it was originally travelling at an angle of 29 degrees to the normal, what is its angle of refraction? Is it travelling into the denser material, or is it exiting the denser material?

    5.     i = r + d
        i = 29
        r = ?
        d = -10

         29 = r -10
        r = 29 + 10
        r = 39
    The ray is exiting the densest material.

    .
       .

  5. When a ray of light leaves a lens medium and enters air, it is travelling at an angle of 36 degrees to the normal. Would the angle of incidence be greater than 36 degrees, less than 36 degrees, or equal to 36 degrees? (By the way, I am using the word 'medium' in place of 'material'. In this context they mean the same thing. You could see either term used on a test.)


    6. The ray is going from a dense material to air, so this situation is similar to the third picture on page 20. The angle of incidence is going to be less than 36 degrees.
       .

  6. A ray of light enters a diamond from air, travelling at an angle of 3 degrees from the normal to the surface. If it is deviated from its original path by 2 degrees, what is its angle of refraction?

    7.     i = r + d
        i = 3
        r = ?
        d = 2

         i = r + d
        3 = r + 2
        r = 3 - 2
        r = 1
       .

  7. Because the sides of the diamond are carefully designed, the ray that entered the diamond close to the normal might exit the opposite side at 20 degrees away from the normal. If it is refracted through an angle of 55 degrees, how much has it been deviated?

    8.     i = r + d
        i = 20
        r = 55
        d = ?

         i = r + d
        20 = 55 + d
        d = 20 - 55
        d = -35
       .

  8. If a ray is deviated by -14 degrees, and its angle of refraction is 25 degrees, what was the angle of incidence? Did it go from a faster medium to a slower medium, of from a slower medium to a faster medium?

    9.     i = r + d
        i = ?
        r = 25
        d = -14

         i = r + d
        i = 25 - 14
        i = 11
    It went from slower to faster, or from more dense to less dense.

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