ChemPhys 173/273

Unit 2: Refraction and Lenses

Problem Set C

Overview:

Problem Set C targets your understanding of total internal reflection and your ability to use the critical angle equation to determine the critical angle at a boundary. Most of the 15 problems involve straightforward calculations for gaining familiarity with the equation. A few of the problems in the latter half of the set involve some complex analysis and ray tracing in order to determine the answer.

Total Internal Reflection and Critical Angle:

Upon reaching a boundary, a light ray will undergo partial reflection and partial transmission. The transmitted light will change its direction whenever it approaches the boundary at any angle of incidence other than 0 degrees. The reflected ray simply reflects according to the law of reflection; that is, the angle of reflection is equal to the angle of incidence. There are instances however when the incidence light does not follow the usual rule of partial reflection and partial transmission. In such instances, all the light which approaches the boundary will undergo reflection and stay within the original medium. This phenomenon is referred to as total internal reflection and occurs whenever the following two criteria are met:

1. Light is in the more dense medium heading toward the less dense medium.
2. Light is approaching the boundary at an angle of incidence which is greater than a critical angle value.

The critical angle is the angle of incidence that causes light to refract along the boundary at an angle of refraction of 90 degrees. Since 90 degrees is the largest possible angle of refraction, an incident ray with an angle of incidence greater than the critical angle cannot refract. Such a light ray will only reflect and stay within the original medium. Using Snell's law, one can show that the critical angle can be calculated from the index of refraction values of the two media on both sides of the boundary. The formula is

critical = sin-1 ( n2 / n1 )

where n1 = the index of refraction of the incident medium

n2 = the index of refraction of the refractive medium

( n2 > n1 )

Refraction and Snell's Law:

A light ray will undergo refraction (a change in direction of its path) at a boundary between two materials whenever it approaches the boundary at an angle of incidence other than zero degrees. This refraction occurs in a rather predictable manner as expressed by the Snell's law equation:

n1 • sin ( 1 ) = n2 • sin ( 2 )

where n1 = index of refraction value of material 1 (on one side of the boundary)

n2 = index of refraction value of material 2 (on the opposite side of the boundary)

1 = angle of refraction of material 1 (on one side of the boundary)

2 = angle of refraction of material 2 (on the opposite side of the boundary)

Knowing the index of refraction values of the two materials on opposite sides of the boundary and the angle of incidence allows one to make a calculation of the angle of refraction. In a similar manner, knowing the two angles which a light ray makes with the normal line for both sides of the boundary and knowing one of the index of refraction values of the two materials allows one to determine the second index of refraction value.

The following pages from The Physics Classroom tutorial may serve to be useful in assisting you in accomplishing the above tasks.

Total Internal Reflection | Critical Angle | Snell's Law | Ray Tracing

View Sample Problem Set.

 Problem Description Audio Link 1 Routine calculation of the critical angle. 2 Routine calculation of the critical angle. 3 Routine calculation of the critical angle. 4 Routine calculation of the critical angle. 5 Routine calculation of the critical angle. 6 Routine calculation of the critical angle. 7 A two-step problem involving the determination of n for an unknown followed by a critical angle calculation. 8 A two-step problem involving the determination of n for an unknown followed by a critical angle calculation. 9 A two-step problem involving the determination of a critical angle. 10 Use of the critical angle to determine an index of refraction value. 11 Routine calculation of the critical angle. 12 Routine calculation of the critical angle. 13 Routine calculation of the critical angle. 14 A complex, multistep analysis of the path of light through a prism; requires the dual usage of Snell's law and the crit equation. 15 A complex analysis of the path of light through three layers using Snell's law.

Audio Help for Problem: 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 || 10 || 11 || 12 || 13 || 14 || 15

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