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

 Applets in this eLecture:

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)

 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.

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