Refraction
of Light

------------------------------------

Joseph F. Alward, PhD
Department of  Physics
University of the Pacific

 

Applets in this eLecture:

A FishEye's View of the World
Internal Reflection Applet
Dispersion through Slab of Glass
Dispersion through Prism

 Ratio of Speed of Light in
 Vacuum to Speed in Various
 Substances
                (l = 589 nm )            
Substance   c/v Substance c/v
Diamond 2.419 Ethyl Alcohol 1.361
Cubic Zirconia   2.21 Ice 1.309
Glass (flint) 1.66 Water   1.333
Glass (crown) 1.52 Air 1.000

 

 

 

  

Index of Refraction
  n = c/v
 The larger the index,

  the smaller the speed of
  light

 

 

 

 

 

 

 

  Index of Refraction                
Substance   Index of
Refraction
      n
Substance Index of
Refraction
      n
Diamond 2.419 Ethyl Alcohol 1.361
Cubic Zirconia   2.21 Ice 1.309
Glass (flint) 1.66 Water   1.333
Glass (crown) 1.52 Air 1.000

 

 

 

 

 

  Reflection and Refraction at an Interface                    

 

 

 

   Refraction:  The Bending of Wavefronts                     

One side of wave front slows down, and the
entire train of fronts twists. Analogy: right
front tire of vehicle enters mud, twisting
vehicle to the right.

 

 

 

 

   Refraction Rules                                                                                      

   Light twists inward when entering medium
   of higher index of refraction

   Light twists outward when entering medium
   of lower index of refraction

  Understanding Refraction                                                                        

 Above: Wheels on axle rolls along a smooth
 sidewalk and onto grass. Which picture
 path is followed?  What happens if the
 motion is reversed?

Right:  One side of wave front slows down,
and the entire train of fronts twists.

 

 

 

   Illustrating Cart Analogy                                             

  Right front wheel slows           Left front wheel slows
  down before left front             down before right front

 

 

 

 

 

  Law of Refraction:  Snell's Law                     

           Right front wheel slows down first.
Snell's Law:  

  n2 sin q2  =    n1 sin q1
 

 

 

 

 

 

 

   Snell's Law Example                                                 
n1 = 1.0 (air)  
n2 = 1.52 (glass)
q1 = 30 degrees
------------------------
n2 sin q2     =    n1 sin q1
1.52 sin q2 = 1.0 sin 30
        sin q2 = 0.33

Put calculator in
Mode Degree


q2 = sin-1 (0.33)
     = 19.3 degrees

 

 

 

 

 

  Rear View Mirror                             

 

 

 

 

 

 

 

  Rear View Mirror Explained                                         

 

 

 

 

 

 

 

  Apparent Depth in Water                                                       

 Light exits into
 medium (air)
 of lower index
 of refraction,
 and turns left.

 

 

 

 

 

  More Apparent Depth                                                                                
Spear-fishing is made more
difficult by the bending of
light.

To spear the fish in the figure,
one must aim at a spot in front
of the fish

 

 

 

  Refraction at Sunset                                                                                 
Why does the sun appear to be
flattened at sunset?
---------------------------------------------------
The sun actually falls below below the
horizon, i.e., it "sets", a few seconds
before we see it set.

 

 

 

 

 

 A Fish-Eye's View     

 

 

   

 

 

                                                      
A FishEye's View of the World
(Excellent applet illustrating refraction)

 

 

 

 

 

 

 

 

 Water on Road Mirage                                

          There's no water on the road; why does it appear so?

 

 

 

 

 

 

 

  The Oasis Mirage                                                  

 

 

 

 

 

   Displacement through a Slab of Glass                               

 Entering and exiting rays are displaced
 from each other, but parallel.

 

 

 

  

 

   Internal Reflection                                              
 All rays reflect internally, but
 the top three rays reflect only
 a small percentage internally;
 most energy leaves the prism.
 
 The fourth and fifth rays are
 reflected 100 % internally.

 

 

 

 

 

 

 

  Internal Reflection                                                        

 Ray 4 is the first to be 100 % reflected; it's angle of incidence is called the critical angle.

 

 

 

 

 

  Crictical Angle Calculation                          

What must be q1 to get q2 = 90 deg ?
Snell's Law

n1 sin q1 =  n2 sin q2
              =  n2 sin 90
    sin q1  =  n2 / n1
------------------------------
Assume water to air:  
 n1 = 1.33              n2 = 1.00
q1  = sin-1 (0.752)
    = 48.8 degrees

qc = critical angle  
     = 48.8 degrees


 

 

 

 Cone of Light                                                                             
Crictical angle for water = 48.8 degrees

 Light within the 48.8 degree cone
 is detected by fish, while nothing in the
 air outside that  cone can be seen.

 The only light reaching the fish outside
 the cone is that light (not shown) which
 is reflected off the bottom of the pool.

 

Internal Reflection Applet

 

 

 

 

 

 

 

  Critical Angle of Diamond                           
n = 2.419

qc = sin-1(1.00/2.419)
    = 24.42 degrees

90.00 - 24.42 = 65.58 degrees

Light outside of 65.58 degree
cone is reflected back inside.

Virtually all light entering the
top face of the diamond is
reflected internally.

 

 

  Optical Fiber                                                                  

 

 

 

 

 

 

  Optical Fiber                                             

 

 

   

 

 

 

 

  Optical Fibers in Medicine                                                                                  

 Arthroscopic Surgery                              Bronchoscope                                 Colonoscope

 

 

  

 

  Index of Refraction vs Color           
v = c/n

The speed of blue light is
less than the speed of
red light
.

Blue light bends more
than red light.

 

 

 The Spectrum of White Light                                           

Note that the shorter wavelengths of light are bent more than the longer; blue more than red.

 

 

 

 

   Applets
1. Dispersion through Slab of Glass

2.  Dispersion through Prism

 

 

 

 

 Refraction in a Raindrop                                                        

 

 

 

 

 

  Forming a Rainbow                                    

 

 

 

  Rainbow                                           

 

  Index Matching