Resource Lesson
Snell's Law: Derivation
Printer Friendly Version
Consider three incident rays of light encountering an interface between two media. In this example, the second medium is the slower medium and the rays are refracted towards the normal - note that angle A is greater than angle B in the diagram.
Since all rays are perpendicular to their respective wavefronts,
Since all normals are perpendicular to their respective interfaces,
Therefore,
and
so we can now examine the following new relationships:
where L is the distance along the interface between points P
_{1}
and P
_{2}
as shown in the diagram below.
Solving each equation for L yields:
Therefore
If d
_{1}
and d
_{2}
represent the distances traveled in the respective mediums during the same amount of time, then we can replace them with the expressions
But v
_{1}
and v
_{2}
represent the speed of the waves in each medium and can be replaced with the expressions
where n
_{1}
and n
_{2}
are the respective indices of refraction and c is the speed of light.
At this junction, we can now write
Canceling the common terms (c and t) yields
Or, as
Snell's Law
is more commonly expressed:
Notice that Snell's Law shows that the index of refraction and the sine of the angle of refraction are inversely proportional - that is, as the refractive index gets larger [n
_{2}
> n
_{1}
] the sine of the refracted angle gets smaller [sinθ
_{2}
< sinθ
_{1}
], since the product of the two terms must remain a constant.
Related Documents
Lab:
Labs -
A Simple Microscope
Labs -
Blank Ray Diagrams for Converging Lenses
Labs -
Blank Ray Diagrams for Converging, Concave, Mirrors
Labs -
Blank Ray Diagrams for Diverging Lenses
Labs -
Blank Ray Diagrams for Diverging, Convex, Mirrors
Labs -
Determining the Focal Length of a Converging Lens
Labs -
Index of Refraction: Glass
Labs -
Index of Refraction: Water
Labs -
Least Time Activity
Labs -
Man and the Mirror
Labs -
Man and the Mirror: Sample Ray Diagram
Labs -
Ray Diagrams for Converging Lenses
Labs -
Ray Diagrams for Converging Mirrors
Labs -
Ray Diagrams for Diverging Lenses
Labs -
Ray Diagrams for Diverging Mirrors
Labs -
Reflections of a Triangle
Labs -
Spherical Mirror Lab
Labs -
Student Lens Lab
Labs -
Target Practice - Revised
Resource Lesson:
RL -
A Derivation of Snell's Law
RL -
Converging Lens Examples
RL -
Converging Lenses
RL -
Demonstration: Infinite Images
RL -
Demonstration: Real Images
RL -
Demonstration: Virtual Images
RL -
Dispersion
RL -
Diverging Lenses
RL -
Double Lens Systems
RL -
Lensmaker Equation
RL -
Mirror Equation
RL -
Properties of Plane Mirrors
RL -
Refraction of Light
RL -
Refraction Phenomena
RL -
Snell's Law
RL -
Spherical Mirrors
RL -
Thin Lens Equation
Review:
REV -
Drill: Reflection and Mirrors
REV -
Mirror Properties
REV -
Physics I Honors: 2nd 9-week notebook
REV -
Physics I: 2nd 9-week notebook
REV -
Spherical Lens Properties
Worksheet:
APP -
Enlightened
APP -
Reflections
APP -
The Librarian
APP -
The Starlet
CP -
Lenses
CP -
Plane Mirror Reflections
CP -
Refraction of Light
CP -
Snell's Law
CP -
Snell's Law
NT -
Image Distances
NT -
Laser Fishing
NT -
Mirror Height
NT -
Mirror Length
NT -
Reflection
NT -
Underwater Vision
WS -
An Extension of Snell's Law
WS -
Basic Principles of Refraction
WS -
Converging Lens Vocabulary
WS -
Diverging Lens Vocabulary
WS -
Lensmaker Equation
WS -
Plane Mirror Reflections
WS -
Refraction and Critical Angles
WS -
Refraction Phenomena
WS -
Refraction Through a Circular Disk
WS -
Refraction Through a Glass Plate
WS -
Refraction Through a Triangle
WS -
Snell's Law Calculations
WS -
Spherical Mirror Equation #1
WS -
Spherical Mirror Equation #2
WS -
Spherical Mirrors: Image Patterns
WS -
Thin Lens Equation #1: Converging Lenses
WS -
Thin Lens Equation #2: Converging Lenses
WS -
Thin Lens Equation #3: Both Types
WS -
Thin Lens Equation #4: Both Types
WS -
Two-Lens Worksheet
WS -
Two-Mirror Worksheet
TB -
27B: Properties of Light and Refraction
TB -
Refraction Phenomena Reading Questions
PhysicsLAB
Copyright © 1997-2023
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton