**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:

- Light is in the more dense medium heading toward the less dense medium.
- 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

where n_{1} = the index of refraction of the incident
medium

n_{2 } = the index of refraction of the refractive
medium

( n_{2 } > n_{1 })

**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:

where n_{1} = index of refraction value of material 1 (on
one side of the boundary)

n_{2} = 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.

**Additional Readings/Study
Aids:**

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

View Sample Problem Set.

Return to: Set C Overview Page || Audio Help Home Page || Set C Sample Problems

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