Done reading? We are now going to start a procedure that will continue for the rest of the semester. I will give you a problem, work it out, then give you some more. As you finish them you click on a link that takes you to the answers, so you can see if you did them right.

Does the subject seem too easy, and you know how to do these? Makes perfect sense when I do them, doesn't it? No?

Well, for those few of you who said yes, I have a secret for you. You can just go to the answers and say, "yes, that is what I would have gotten if I had done the problem." And you might even be right. But we will not KNOW until the test comes, will we? And you know what? If it IS that easy, it would only take you a minute to actually do the exercises and then you would really know that you understand this. If you do not do them, the only person who will know is you. And the only person who will be cheated of the experience that you are spending time and money on is you. So, DO IT FIRST, CHECK IT SECOND!!!!!

For those of you who do not find this part obvious, do, say, try the first two exercises, then click on my answers. If you answers are different from mine, read them over, come back, and try the next two. Hopefully, by the time we have done a few this way, you will understand how to do them.

When you get to the end of the exercises, if you do not understand what I have been doing, Call your instructor!

That's it. I'm through preaching. [For the moment.]

So, here is the first exercise:

1. The ray of light (remember, this is the path of one lonely photon) travels from air into crown glass (that is the clear glass that we used to make all of our lenses of) and impacts the surface of the glass at an angle of 15 degrees to the normal to the surface. If it is refracted through an angle of 10 degrees, how much was it deviated from its original path?

OK, another bit of lecture. The way to do word problems is this:

• Read the problem through once, and decide what types of information it is giving you. In this case, it is talking about angles of incidence, refraction and deviation.
• Decide what formula(s) you will probably be using. In this case, i = r + d.
• Write down the formula. Write down a list of the unknowns.
 i = r + d
i =
r =
d =
• Read the question phrase by phrase, and write down what each phrase is telling you.
 
• "The ray of light travels from air into crown glass and impacts the surface of the glass at an angle of 15 degrees to the normal to the surface."

     i = 15.
• "If it is refracted through an angle of 10 degrees, "

    r = 10.
• "how much was it deviated from its original path?"

    d = ?.
Always make sure that you know what the question is!  Many times you will save time and frustration by identifying the question before you do a lot of work!

So now we have:
i = r + d
i = 15
r = 10
d = ?

• Now you substitute the values of the letters in the equation;

i = r + d
15 = 10 + d
d = 15 - 10
d = 5
And that is the answer!.
   .
2. When the ray of light leaves the crown glass, its angle with the normal to the surface is only 8 degrees. If it has an angle or refraction of 12 degrees, what is the angle of deviation when it leaves the glass?
• OK, read it through. Done.
• What is it talking about? Angles of refraction, incidence and deviation.
• What formula do we use for these items?

i = r + d
i =
r =
d =
• Going phrase by phrase, fill in the unknowns.

i = 8
r = 12
d = ?
• Substitute into the equation and solve.

i = 8
r = 12
d = ?

i = r + d
8 = 12 + d
d = 12 - 8
d = -4

 [Notice that you can always check to see if you did the algebra right by going back to the original equation.
i = 8
r = 12
d = -4

i = r + d
8 = 12 - 4
8 = 8. Yup, it checks out OK.

What does a negative deviation mean? That the ray went from a more dense material to a less dense material. Did it?

1. If a ray of light is incident on a material at an angle of 18 degrees, and it is deviated by 7 degrees, what is its angle of refraction?

     i = r + d
    i = 18
    r = ?
    d = 7

    18 = r + 7
    r = 18 - 7
    r = 11

 Right?
   .

2. If a ray leaves a material with an angle of refraction of 20 degrees and an angle of deviation of -7 degrees, what was its angle of incidence?

     i = r + d
    i = ?
    r = 20
    d = -7

     i = 20 + (-7)
    i = 20 - 7
    i = 13

CHECK:
    i = r + d
    i = 13
    r = 20
    d = -7

    13 = 20 -7
    13 = 13
   .

3. If a ray of light travels from one material to a second material with an angle of incidence of 35 degrees, and the ray is deviated by 18 degrees, what is the angle of refraction?

     i = r + d
    i = 35
    r = ?
    d = 18

    35 = r + 18
    r = 35 - 18
    r = 17
 

Ready to try some?

Do the first two. Make a drawing, decide if r is smaller or bigger than i. If r is smaller, the ray is ENTERING the lens material. If r is bigger, the ray is EXITING the lens material. After you try the first two, click on the answers, and only look at those two. Then click the back button, try the next two, and check again.

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 traveling into the lens or exiting from the lens?

    i = r + d
    i =
    r =
    d =
   .
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?

    i = r + d
    i =
    r =
    d =

Click here - all of the answers are there, so only look at the first two.
   .

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?

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

    i = r + d
    i =
    r =
    d =

click here to continue checking the answers.
   .

5. When a ray of light leaves a lens medium and enters air, it is traveling 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.)

You start writing the formula and unknowns out. It will actually help you to memorize the formula to write it all out: Honest!
  .

6. A ray of light enters a diamond from air, traveling 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. Because the sides of the diamond are carefully designed, the ray that entered the diamond close to the normal exits 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. 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?

Now do the exercises on page (21 / 27) in the Optical Formulas book, and check those answers in the back of the book.