Refraction by yaoyufang

VIEWS: 5 PAGES: 40

									         Refraction
What does light do when it changes from one
       medium to another medium?
    Introduction to Refraction
• Light changes mediums all the time!

  – Remember: a medium is the substance light
    travels through.

  – Example: Light can change mediums by traveling
    from air into water.
     • Air is the old medium
     • Water is the new medium
      Basics of Refraction
• When light changes mediums, it
  changes its speed!

• When light changes its speed it bends.

• Refraction = the bending of light as it
  passes from one medium into another
  medium.
    Examples of Refraction
   Here is a laser passing from air into glass.




We would expect that the path of the laser would remain unchanged, but
       since the laser light enters a new medium (glass), it bends.
     Examples of Refraction
    Here is a pencil sitting in a glass of water.




We would expect the pencil to appear straight, but since the light bends in
                  the water, the pencil appears distorted.
   Examples of Refraction
        Ever tried to catch a fish?




We would expect to find the fish exactly where
   we see them in the water, but since light
 bends when moving from the water to the air,
   the fish are not where they appear to be.
       Refraction Definitions
• Since the light is bending when it enters a
  new medium our goal will be to figure out how
  much it bends.

• To find out how much the light bends we will
  measure two angles:

  – Angle of Incidence: the angle the light was at in
    the old medium.
     • Denoted by the symbol theta: I the “I” means “Incident”

  – Angle of Refraction: the angle the light is at in
    the new medium.
     • Denoted by the symbol theta: r where the “r” means
       “refraction”
        Refraction Definitions
• We will measure both angles with respect to
  the Normal Line.

• Normal Line = the line that is perpendicular to the
  boundary of the two mediums.

• For example: in the diagram below, the Normal line
  is shown in blue.



         New Medium


         Old Medium                       Normal Line
       Diagram of Refraction

                 •The white space is the old medium.

                 •The box is the new medium.

New Medium       •A light ray travels from the old
                 medium into the new medium.

                 •The light ray in the old medium is
                 shown by a black arrow.

                 •The light ray in the new medium is
Old Medium       shown by the black arrow in the
                 new medium.

                 •The blue line represents the
                 NORMAL LINE.
       How Refraction Works
                 •What happens in the diagram: A
                 light ray travels from the old
                 medium to the new medium.

                 •We would expect the light ray to
                 continue on a straight path through
                 the new medium (shown by red
New Medium       dotted arrow).

                 •But the light ray doesn’t keep
                 going straight!

                 •It bends! The actual path of the
Old Medium       light ray is shown by the black arrow
                 in the new medium.

                 •The reason it bends to a new angle
                 is that the light travels at a different
                 speed in the new medium.
       How Refraction Works
                   How much does the light bend?

                  •In order to find out, we need to
                  measure the angles the light rays
             r   make with the Normal line!

New Medium        •Angle of incidence: I is in blue


                  •Angle of refraction: r is in red
       i
                  •It is important to note that in this
                  example diagram, the light ray bent
Old Medium        towards the Normal Line.

                  •In other cases, the light ray could
                  bend away from the Normal Line.
Relationship Between Angles
      and the Mediums

• There is a relationship between the
  angles the light bends at and the
  mediums it passes through.

• This relationship is called Snell’s Law
                     Snell’s Law
Snell’s Law is:
                  ni(sin I) = nr (sin r)

n = the Index of Refraction of the medium (this is
  just a naked number)
I = the Angle of Incidence
      • This is the angle of the light ray in the old medium

r = the Angle of Refraction
      • This is the angle of the light ray in the new medium

“sin” = Sine, (pronounced like “sign”) is a calculator
  operation you can do with the two angles.
How to Find the Sine (“sin”) of
          an Angle
Taking the Sine of an angle is a mathematical
  operation we can do using a calculator.

On Calculator: Press the “sin” button, then
 type in the angle, then press “Enter.”

On iPod or Cell Phone: Type in your angle,
 then press the “sin” button, then press “=.”
  Practice Finding the Sine of
           an Angle!
• Find (sin 30˚)
                    Answer = 0.50
• Find (sin 90˚)
                     Answer = 1.0
• Find (sin 45˚)
                    Answer = 0.70
         Back to Snell’s Law!
Snell’s Law is:

                  ni(sin I) = nr (sin r)

       What does this equation mean?

It means that if we know the index of refraction (n) for
    both mediums, and the angle of incidence (i), we
     can calculate how much the light will bend in the
                    new medium (r) !!!
    How to Use Snell’s Law
 There are two types of refraction problem that
        you will need to learn how to solve:

1. Using Snell’s Equation to find ni or nr

2. Using Snell’s Equation to find i or r


 Take notes on the steps to solve each type
                  of problem!
             Type 1: Finding n
The Problem: If light passes from air (n = 1.0) into water with
  an angle of incidence of 36˚, and bends to an angle of 26.2˚,
  what is the index of refraction (nr ) of water?

               Step 0: What are we solving for?


                  We are solving for nr
             Type 1: Finding n
The Problem: If light passes from air (n = 1.0) into water with
  an angle of incidence of 36˚, and bends to an angle of 26.2˚,
  what is the index of refraction (nr ) of water?

         Step 1: Draw a picture of what is happening!

                                    26.2˚
                   Water
                   nr = ?

                   Air
                   ni = 1.0   36˚
             Type 1: Finding n
The Problem: If light passes from air (n = 1.0) into water with
  an angle of incidence of 36˚, and bends to an angle of 26.2˚,
  what is the index of refraction (nr ) of water?

          Step 2: Write out the Snell’s Law equation.


                   ni(sin I) = nr (sin r)
              Type 1: Finding n
The Problem: If light passes from air (n = 1.0) into water with
  an angle of incidence of 36˚, and bends to an angle of 26.2˚,
  what is the index of refraction of water?

       Step 3: List out what you know from the problem.


                      ni = 1.0 i = 36˚
                      nr = ?   r = 26.2˚
              Type 1: Finding n
The Problem: If light passes from air (n = 1.0) into water with
  an angle of incidence of 36˚, and bends to an angle of 26.2˚,
  what is the index of refraction of water?

Step 4: Fill in the Snell’s Law Equation ni(sin I) = nr (sin r)



               (1.0)(sin 36˚) = nr (sin 26.2˚)
               Type 1: Finding n
The Problem: If light passes from air (n = 1.0) into water with
  an angle of incidence of 36˚, and bends to an angle of 26.2˚,
  what is the index of refraction of water?

                Step 5: Solve the equation for n!

 To get nr by itself, we will divide both sides of the equation by
                               (sin 26.2˚)

               (1.0)(sin 36˚) = nr (sin 26.2˚)
                 (sin 26.2˚)         (sin 26.2˚)
              Type 1: Finding n
The Problem: If light passes from air (n = 1.0) into water with
  an angle of incidence of 36˚, and bends to an angle of 26.2˚,
  what is the index of refraction of water?

               Step 5: Solve the equation for n!

The (sin 26.2˚) will be canceled out on the right side, leaving nr
                             by itself.

               (1.0)(sin 36˚) = nr (sin 26.2˚)
                 (sin 26.2˚)        (sin 26.2˚)
              Type 1: Finding n
The Problem: If light passes from air (n = 1.0) into water with
  an angle of incidence of 36˚, and bends to an angle of 26.2˚,
  what is the index of refraction of water?

                Step 5: Solve the equation for n!

 Now all we have to do is plug the left side of this equation into
    our calculator. Try it on your own! Don’t forget to include
                           parentheses!!!!
                      (1.0)(sin 36˚) = nr
                        (sin 26.2˚)

           You should find that nr = 1.33
Problem Solved!!



   nr = 1.33
               Type 2: Finding 
The Problem: A light ray passes from air (n = 1.0) at an angle
  of incidence of 26˚, into a sapphire (n = 1.77). What is the
  angle of refraction (r)in sapphire?

               Step 0: What are we solving for?


                 We are solving for r
               Type 2: Finding 
The Problem: A light ray passes from air (n = 1.0) at an angle
  of incidence of 26˚, into a sapphire (n = 1.77). What is the
  angle of refraction (r)in sapphire?

  Step 1: Draw a picture of what’s happening in the problem!

                              r = ?
                Sapphire
                n = 1.77

                Air
                n = 1.0 ˚
               Type 2: Finding 
The Problem: A light ray passes from air (n = 1.0) at an angle
  of incidence of 26˚, into a sapphire (n = 1.77). What is the
  angle of refraction in sapphire?

          Step 2: Write out the Snell’s Law Equation.


                  ni(sin I) = nr (sin r)
              Type 2: Finding 
The Problem: A light ray passes from air (n = 1.0) at an angle
  of incidence of 26˚, into a sapphire (n = 1.77). What is the
  angle of refraction in sapphire?

                Step 3: List out what you know.


                    ni = 1.0 i = 26˚
                    nr = 1.77 r = ?
               Type 2: Finding 
The Problem: A light ray passes from air (n = 1.0) at an angle
  of incidence of 26˚, into a sapphire (n = 1.77). What is the
  angle of refraction in sapphire?

            Step 4: Fill in the Snell’s Law equation.


               (1.0)(sin 26˚) = (1.77)(sin r)
                Type 2: Finding 
The Problem: A light ray passes from air (n = 1.0) at an angle
  of incidence of 26˚, into a sapphire (n = 1.77). What is the
  angle of refraction in sapphire?

  Step 5: Solve for (sin r). To get (sin r) by itself, divide both
                            sides by 1.77.


                (1.0)(sin 26˚) = (1.77)(sin r)

                     (1.77)              (1.77)
               Type 2: Finding 
The Problem: A light ray passes from air (n = 1.0) at an angle
  of incidence of 26˚, into a sapphire (n = 1.77). What is the
  angle of refraction in sapphire?

Step 5: Solve for (sin r). The 1.77 will cancel out from the right
                        side of the equation.


               (1.0)(sin 26˚) = (1.77)(sin r)

                    (1.77)              (1.77)
              Type 2: Finding 
The Problem: A light ray passes from air (n = 1.0) at an angle
  of incidence of 26˚, into a sapphire (n = 1.77). What is the
  angle of refraction in sapphire?

                 Step 5: Now we are left with:


                  (1.0)(sin 26˚) = (sin r)
                       (1.77)
              Type 2: Finding 
The Problem: A light ray passes from air (n = 1.0) at an angle
  of incidence of 26˚, into a sapphire (n = 1.77). What is the
  angle of refraction in sapphire?

      Step 5: Plug this into your calculator to find (sin r):


                   (1.0)(sin 26˚) = (sin r)
                        (1.77)


           You should find that (sin r) = 0.247
              Type 2: Finding 
The Problem: A light ray passes from air (n = 1.0) at an angle
  of incidence of 26˚, into a sapphire (n = 1.77). What is the
  angle of refraction in sapphire?

Step 6: Right now we’ve got (sin r). We need to find what r is.
  Use the inverse sine button “sin-1” to cancel out the sin and
  find out what r is.

                    sin-1 (0.247) = ________



          You should find that r = 14.33˚
Problem Solved!!


  r = 14.33˚
What is Refraction Good For?
Lots of things! For example:

  Rainbows work by refracting sunlight through water
                        drops.




   For more details ask Miss Byrne for her Rainbow
                       workshop!
What is Refraction Good For?
Another example:
 Fiber Optics are clear cables used to transfer data!
   These cables revolutionized phone lines and high
                    speed internet!




 For more details ask Miss Byrne for her Fiber Optics
                       workshop!
         Now You Try!
You are now ready to finish Homework
         10 and Homework 11!

Use these slides and the notes you took
     from them to help you solve the
          homework problems.

								
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