Refraction and Lenses - Detailed Help

Assignment RL5: Total Internal Reflection

Objectives:
  • The student should be able to use an understanding of boundary behavior of light to predict the effect of changing incident angle upon the brightness and relative amount of energy in the reflected and refracted light.
  • The student should be able to identify the two prerequisites for the occurrence of total internal reflection and apply these to determine whether or not it could occur in any given situation.

 

Reading:

The Physics Classroom, Refraction and Lenses Unit, Lesson 3, Part a

The Physics Classroom, Refraction and Lenses Unit, Lesson 3, Part b

 

 

Total internal reflection can most accurately be described as ____.


Definition of Total Internal Reflection:

Total internal reflection (TIR) is the phenomenon which occurs when all the light which is approaching a boundary with a transparent medium undergoes reflection and remains within the original medium.

What is total internal reflection?

 

 

A ray of light moving through Lucite is approaching a Lucite-air boundary. This ray of light will refract at the boundary. If the angle of incidence is increased, then the angle of refraction will be _____.


Snell's Law of Refraction:

The refraction of light towards or away from the normal follows a very predictable mathematical relationship known as Snell's law.
n1 • sin 1 = n2 • sin 2

where n1 and n2 are the indices of refraction of the two individual media and 1 and 2 are the angles of incidence and refraction within those media. Knowing any three of the four quantities in the equation, allows one to predict the fourth variable.


 


Refraction at a boundary is mathematically described by the Snell's law equation. The equation shows that the angle of refraction is dependent upon the angle of incidence. According to the equation, as the angle of incidence is increased, the angle of refraction is increased.


What effect will an increase in the angle of incidence have upon the subsequent angle of refraction?

 

 

A ray of light moving through Lucite is approaching a Lucite-air boundary. At the boundary a portion of the light will reflect and a portion will be transmitted into the air and refract. If the angle of incidence is increased, then the amount of light undergoing reflection will _____ and the amount of light undergoing refraction will _____.


Boundary Behavior: Transmission (Refraction) and Reflection:

Two things tend to happen when a light ray reaches the boundary between two transparent materials. A portion of the energy carried by the light is transmitted across the boundary and a portion is reflected off the boundary and remains in the original medium. The percentage of the light energy which is transmitted and the percentage which reflects depends mostly upon the angle of incidence. As the angle of incidence increases, the percentage of transmitted light decreases and the percentage of reflected light increases.

How does increasing the angle of incidence effect the amount of light (and brightness of it) which undergoes reflection (or refraction)?

 

 

A ray of light moving through Lucite is approaching a Lucite-air boundary. At the boundary a portion of the light will reflect and a portion will be transmitted into the air and refract. If the angle of incidence is increased, then the brightness of the reflected ray (B) will _____ and the brightness of the refracted ray (A) will _____.


Boundary Behavior: Transmission (Refraction) and Reflection:

Two things tend to happen when a light ray reaches the boundary between two transparent materials. A portion of the energy carried by the light is transmitted across the boundary and a portion is reflected off the boundary and remains in the original medium. The percentage of the light energy which is transmitted and the percentage which reflects depends mostly upon the angle of incidence. As the angle of incidence increases, the percentage of transmitted light decreases and the percentage of reflected light increases.


The brightness of a light ray is a sign of the amount of energy carried by the light ray. This fact can be combined with the statement in the Physics Rules section above to answer this question.


How does increasing the angle of incidence effect the amount of light (and brightness of it) which undergoes reflection (or refraction)?

 

 

Total internal reflection (TIR) does not always occur when light moving through one medium strikes a boundary with another medium. Two requirements must be met for TIR to occur. Which two statements below express these two requirements? Light must be _____.


Definition of Total Internal Reflection:

Total internal reflection (TIR) is the phenomenon which occurs when all the light which is approaching a boundary with a transparent medium undergoes reflection and remains within the original medium.


Requirements for Total Internal Reflection (TIR):

Two requirements must be met for total internal reflection to occur. First, light must be in the more dense medium heading toward the boundary with the least dense medium. Second, light must be approaching the boundary with an angle of incidence which is greater than the value of the so-called critical angle.

Many beginning students of physics become quite confused by the concept of a critical angle and its relationship to total internal reflection. It is a commonly held wrong belief that TIR occurs when the incident angle is equal to or even less than the critical angle. But don't be fooled! The incident angle must be greater than the critical angle for total internal reflection to occur.


What are the two requirements for total internal reflection to occur?

 

 

The critical angle refers to _____.


Definition of Critical Angle:

The critical angle is the largest angle of incidence for which refraction can occur for a particular boundary. When light is incident toward a boundary with a less dense medium at the critical angle, light refracts into the new medium with an angle of refraction of 90 degrees.

What is the critical angle?

 

 

The diagrams show incident rays approaching a boundary with a second medium. The relative index of refraction (n) of the two media is indicated. In which diagram(s) will total internal reflection occur (provided that the angle of incidence is sufficiently large)? List all that apply ... .


Requirements for Total Internal Reflection (TIR):

Two requirements must be met for total internal reflection to occur. First, light must be in the more dense medium heading toward the boundary with the least dense medium. Second, light must be approaching the boundary with an angle of incidence which is greater than the value of the so-called critical angle.


As mentioned in the Physics Rules section above, TIR can only take place provided that the incident ray is traveling within the more dense medium. The optical density of a medium is related to the index of refraction of the material (see Physics Rules section below). To be successful on this question, you will have to inspect each diagram carefully to determine if it satisfies the condition of light being in the more dense medium and heading towards the least dense medium.


Optical Density and the Index of Refraction:

Every material is identified by a unique index of refraction value. The index of refraction value is an experimentally determined value which provides a relative measure of the optical density of that material. The higher the index of refraction value, the more optically dense a material is.

How can one use index of refraction values for two media to determine if an incident ray could undergo total internal reflection?

How is the index of refraction value related to the density of a medium?

 

 

The diagrams show incident rays approaching a boundary with a second medium. The relative speed of light (v) in the two media is indicated. In which diagram(s) will total internal reflection occur (provided that the angle of incidence is sufficiently large)?


Requirements for Total Internal Reflection (TIR):

Two requirements must be met for total internal reflection to occur. First, light must be in the more dense medium heading toward the boundary with the least dense medium. Second, light must be approaching the boundary with an angle of incidence which is greater than the value of the so-called critical angle.


As mentioned in the Physics Rules section above, TIR can only take place provided that the incident ray is traveling within the more dense medium. The optical density of a medium is related to the speed at which light travels through that material (see Physics Rules section below). To be successful on this question, you will have to inspect each diagram carefully to determine if it satisfies the condition of light being in the more dense medium and heading towards the least dense medium.


Optical Density and the Speed of Light:

The speed at which light travels through a medium is dependent upon the optical density of that medium. Light travels fastest in media which are least optically dense.

How can one use index of refraction values for two media to determine if an incident ray could undergo total internal reflection?

How is the index of refraction value related to the density of a medium?

 

 

The diagrams show incident rays approaching a boundary with a second medium. The relative density (d) of the two media is indicated. In which diagram(s) will total internal reflection occur (provided that the angle of incidence is sufficiently large)?


Requirements for Total Internal Reflection (TIR):

Two requirements must be met for total internal reflection to occur. First, light must be in the more dense medium heading toward the boundary with the least dense medium. Second, light must be approaching the boundary with an angle of incidence which is greater than the value of the so-called critical angle.


As mentioned in the Physics Rules section above, TIR can only take place provided that the incident ray is traveling within the more dense medium. To be successful on this question, you will have to inspect each diagram carefully to determine if it satisfies the condition of light being in the more dense medium and heading towards the least dense medium.


How can one use index of refraction values for two media to determine if an incident ray could undergo total internal reflection?

How is the index of refraction value related to the density of a medium?