Skip to content Skip to navigation Skip to collection information

OpenStax-CNX

You are here: Home » Content » Siyavula textbooks: Grade 10 Physical Science » Total internal reflection

Navigation

Table of Contents

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • Bookshare

    This collection is included inLens: Bookshare's Lens
    By: Bookshare - A Benetech Initiative

    Comments:

    "Accessible versions of this collection are available at Bookshare. DAISY and BRF provided."

    Click the "Bookshare" link to see all content affiliated with them.

  • FETPhysics display tagshide tags

    This module is included inLens: Siyavula: Physics (Gr. 10-12)
    By: Siyavula

    Review Status: In Review

    Click the "FETPhysics" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

  • Siyavula: Physical Science display tagshide tags

    This collection is included inLens: Siyavula textbooks: Physical Science
    By: Free High School Science Texts Project

    Click the "Siyavula: Physical Science" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Total internal reflection

Module by: Free High School Science Texts Project. E-mail the author

Total Internal Reflection and Fibre Optics

Total Internal Reflection

Investigation : Total Internal Reflection

Work in groups of four. Each group will need a raybox (or torch) with slit, triangular glass prism and protractor. If you do not have a raybox, use a torch and stick two pieces of tape over the lens so that only a thin beam of light is visible.

Aim:

To investigate total internal reflection.

Method:

  1. Place the raybox next to the glass block so that the light shines right through without any refraction. See "Position 1" in diagram.
    Figure 1
    Figure 1 (PG10C6_041.png)
  2. Move the raybox such that the light is refracted by the glass. See "Position 2".
    Figure 2
    Figure 2 (PG10C6_042.png)
  3. Move the raybox further and observe what happens.
    Figure 3
    Figure 3 (PG10C6_043.png)
  4. Move the raybox until the refracted ray seems to disappear. See "Position 4". The angle of the incident light is called the critical angle.
    Figure 4
    Figure 4 (PG10C6_044.png)
  5. Move the raybox further and observe what happens. See "Position 5". The light shines back into the glass block. This is called total internal reflection.
    Figure 5
    Figure 5 (PG10C6_045.png)

When we increase the angle of incidence, we reach a point where the angle of refraction is 90 and the refracted ray runs along the surface of the medium. This angle of incidence is called the critical angle.

Definition 1: Critical Angle

The critical angle is the angle of incidence where the angle of reflection is 90. The light must shine from a dense to a less dense medium.

If the angle of incidence is bigger than this critical angle, the refracted ray will not emerge from the medium, but will be reflected back into the medium. This is called total internal reflection.

Total internal reflection takes place when

  • light shines from an optically denser medium to an optically less dense medium.
  • the angle of incidence is greater than the critical angle.
Definition 2: Total Internal Reflection

Total internal reflection takes place when light is reflected back into the medium because the angle of incidence is greater than the critical angle.

Figure 6: Diagrams to show the critical angle and total internal reflection.
Figure 6 (PG10C6_046.png)

Each medium has its own unique critical angle. For example, the critical angle for glass is 42, and that of water is 48,8. We can calculate the critical angle for any medium.

Calculating the Critical Angle

Now we shall learn how to derive the value of the critical angle for two given media. The process is fairly simple and involves just the use of Snell's Law that we have already studied. To recap, Snell's Law states:

n 1 sin θ 1 = n 2 sin θ 2 n 1 sin θ 1 = n 2 sin θ 2
(1)

where n1n1 is the refractive index of material 1, n2n2 is the refractive index of material 2, θ1θ1 is the angle of incidence and θ2θ2 is the angle of refraction. For total internal reflection we know that the angle of incidence is the critical angle. So,

θ 1 = θ c . θ 1 = θ c .
(2)

However, we also know that the angle of refraction at the critical angle is 90. So we have:

θ 2 = 90 . θ 2 = 90 .
(3)

We can then write Snell's Law as:

n 1 sin θ c = n 2 sin 90 n 1 sin θ c = n 2 sin 90
(4)

Solving for θcθc gives:

n 1 sin θ c = n 2 sin 90 sin θ c = n 2 n 1 ( 1 ) θ c = sin - 1 ( n 2 n 1 ) n 1 sin θ c = n 2 sin 90 sin θ c = n 2 n 1 ( 1 ) θ c = sin - 1 ( n 2 n 1 )
(5)
Tip:
Take care that for total internal reflection the incident ray is always in the denser medium.

Figure 7
Khan academy video on refraction - 1

Exercise 1: Critical Angle 1

Given that the refractive indices of air and water are 1 and 1,33, respectively, find the critical angle.

Solution
  1. Step 1. Determine how to approach the problem :

    We know that the critical angle is given by:

    θ c = sin - 1 ( n 2 n 1 ) θ c = sin - 1 ( n 2 n 1 )
    (6)
  2. Step 2. Solve the problem :
    θ c = sin - 1 ( n 2 n 1 ) = sin - 1 ( 1 1 , 33 ) = 48 , 8 θ c = sin - 1 ( n 2 n 1 ) = sin - 1 ( 1 1 , 33 ) = 48 , 8
    (7)
  3. Step 3. Write the final answer :

    The critical angle for light travelling from water to air is 48,848,8.

Exercise 2: Critical Angle 2

Complete the following ray diagrams to show the path of light in each situation.

Figure 8
Figure 8 (PG10C6_047.png)

Figure 9
Figure 9 (PG10C6_048.png)

Figure 10
Figure 10 (PG10C6_049.png)

Figure 11
Figure 11 (PG10C6_050.png)

Solution
  1. Step 1. Identify what is given and what is asked :

    The critical angle for water is 48,848,8.

    We are asked to complete the diagrams.

    For incident angles smaller than 48,848,8 refraction will occur.

    For incident angles greater than 48,848,8 total internal reflection will occur.

    For incident angles equal to 48,848,8 refraction will occur at 9090.

    The light must travel from a high optical density to a lower one.

  2. Step 2. Complete the diagrams :

    Figure 12
    Figure 12 (PG10C6_051.png)

    Refraction occurs (ray is bent away from the normal)

    Figure 13
    Figure 13 (PG10C6_052.png)

    Total internal reflection occurs

    Figure 14
    Figure 14 (PG10C6_053.png)

    θ c = 48 , 8 θ c = 48 , 8

    Figure 15
    Figure 15 (PG10C6_054.png)

    Refraction towards the normal (air is less dense than water)

Fibre Optics

Total internal reflection is a powerful tool since it can be used to confine light. One of the most common applications of total internal reflection is in fibre optics. An optical fibre is a thin, transparent fibre, usually made of glass or plastic, for transmitting light. Optical fibres are usually thinner than a human hair! The construction of a single optical fibre is shown in Figure 16.

The basic functional structure of an optical fibre consists of an outer protective cladding and an inner core through which light pulses travel. The overall diameter of the fibre is about 125 μμm (125×10-6m125×10-6m) and that of the core is just about 50 μμm (10×10-6m10×10-6m). The mode of operation of the optical fibres, as mentioned above, depends on the phenomenon of total internal reflection. The difference in refractive index of the cladding and the core allows total internal reflection in the same way as happens at an air-water surface. If light is incident on a cable end with an angle of incidence greater than the critical angle then the light will remain trapped inside the glass strand. In this way, light travels very quickly down the length of the cable.

Figure 16: Structure of a single optical fibre.
Figure 16 (PG10C6_055.png)

Fibre Optics in Telecommunications

Optical fibres are most common in telecommunications, because information can be transported over long distances, with minimal loss of data. The minimised loss of data gives optical fibres an advantage over conventional cables.

Data is transmitted from one end of the fibre to another in the form of laser pulses. A single strand is capable of handling over 3000 simultaneous transmissions which is a huge improvement over the conventional co-axial cables. Multiple signal transmission is achieved by sending individual light pulses at slightly different angles. For example if one of the pulses makes a 72,23 angle of incidence then a separate pulse can be sent at an angle of 72,26! The transmitted data is received almost instantaneously at the other end of the cable since the information coded onto the laser travels at the speed of light! During transmission over long distances repeater stations are used to amplify the signal which has weakened somewhat by the time it reaches the station. The amplified signals are then relayed towards their destination and may encounter several other repeater stations on the way.

Fibre Optics in Medicine

Optic fibres are used in medicine in endoscopes.

Note: Interesting Fact :

Endoscopy means to look inside and refers to looking inside the human body for diagnosing medical conditions.

The main part of an endoscope is the optical fibre. Light is shone down the optical fibre and a medical doctor can use the endoscope to look inside a patient. Endoscopes are used to examine the inside of a patient's stomach, by inserting the endoscope down the patient's throat.

Endoscopes allow minimally invasive surgery. This means that a person can be diagnosed and treated through a small incision. This has advantages over open surgery because endoscopy is quicker and cheaper and the patient recovers more quickly. The alternative is open surgery which is expensive, requires more time and is more traumatic for the patient.

Total Internal Reflection and Fibre Optics
  1. Describe total internal reflection, referring to the conditions that must be satisfied for total internal reflection to occur.
    Click here for the solution.
  2. Define what is meant by the critical angle when referring to total internal reflection. Include a ray diagram to explain the concept.
    Click here for the solution.
  3. Will light travelling from diamond to silicon ever undergo total internal reflection?
    Click here for the solution.
  4. Will light travelling from sapphire to diamond undergo total internal reflection?
    Click here for the solution.
  5. What is the critical angle for light traveling from air to acetone?
    Click here for the solution.
  6. Light traveling from diamond to water strikes the interface with an angle of incidence of 86. Calculate the critical angle to determine whether the light be totally internally reflected and so be trapped within the water.
    Click here for the solution.
  7. Which of the following interfaces will have the largest critical angle?
    1. a glass to water interface
    2. a diamond to water interface
    3. a diamond to glass interface
    Click here for the solution.
  8. If the fibre optic strand is made from glass, determine the critical angle of the light ray so that the ray stays within the fibre optic strand.
    Click here for the solution.
  9. A glass slab is inserted in a tank of water. If the refractive index of water is 1,33 and that of glass is 1,5, find the critical angle.
    Click here for the solution.
  10. A diamond ring is placed in a container full of glycerin. If the critical angle is found to be 37,4 and the refractive index of glycerin is given to be 1,47, find the refractive index of diamond.
    Click here for the solution.
  11. An optical fibre is made up of a core of refractive index 1,9, while the refractive index of the cladding is 1,5. Calculate the maximum angle which a light pulse can make with the wall of the core. NOTE: The question does not ask for the angle of incidence but for the angle made by the ray with the wall of the core, which will be equal to 90- angle of incidence.
    Click here for the solution.

Figure 17

Summary

  1. We can see objects when light from the objects enters our eyes.
  2. Light rays are thin imaginary lines of light and are indicated in drawings by means of arrows.
  3. Light travels in straight lines. Light can therefore not travel around corners. Shadows are formed because light shines in straight lines.
  4. Light rays reflect off surfaces. The incident ray shines in on the surface and the reflected ray is the one that bounces off the surface. The surface normal is the perpendicular line to the surface where the light strikes the surface.
  5. The angle of incidence is the angle between the incident ray and the surface, and the angle of reflection is the angle between the reflected ray and the surface.
  6. The Law of Reflection states the angle of incidence is equal to the angle of reflection and that the reflected ray lies in the plane of incidence.
  7. Specular reflection takes place when parallel rays fall on a surface and they leave the object as parallel rays. Diffuse reflection takes place when parallel rays are reflected in different directions.
  8. Refraction is the bending of light when it travels from one medium to another. Light travels at different speeds in different media.
  9. The refractive index of a medium is a measure of how easily light travels through the medium. It is a ratio of the speed of light in a vacuum to the speed of light in the medium. n=cvn=cv
  10. Snell's Law gives the relationship between the refractive indices, angles of incidence and reflection of two media. n1sinθ1=n2sinθ2n1sinθ1=n2sinθ2
  11. Light travelling from one medium to another of lighter optical density will be refracted towards the normal. Light travelling from one medium to another of lower optical density will be refracted away from the normal.
  12. Objects in a medium (e.g. under water) appear closer to the surface than they really are. This is due to the refraction of light, and the refractive index of the medium. n= real depth apparent depth n= real depth apparent depth
  13. Mirrors are highly reflective surfaces. Flat mirrors are called plane mirrors. Curved mirrors can be convex or concave. The properties of the images formed by mirrors are summarised in Table 3.2.
  14. A real image can be cast on a screen, is inverted and in front of the mirror. A virtual image cannot be cast on a screen, is upright and behind the mirror.
  15. The magnification of a mirror is how many times the image is bigger or smaller than the object. m= image height (hi) object height (h0)m= image height (hi) object height (h0)
  16. The critical angle of a medium is the angle of incidence when the angle of refraction is 9090 and the refracted ray runs along the interface between the two media.
  17. Total internal reflection takes place when light travels from one medium to another of lower optical density. If the angle of incidence is greater than the critical angle for the medium, the light will be reflected back into the medium. No refraction takes place.
  18. Total internal reflection is used in optical fibres in telecommunication and in medicine in endoscopes. Optical fibres transmit information much more quickly and accurately than traditional methods.

Exercises

  1. Give one word for each of the following descriptions:
    1. The image that is formed by a plane mirror.
    2. The perpendicular line that is drawn at right angles to a reflecting surface at the point of incidence.
    3. The bending of light as it travels from one medium to another.
    4. The ray of light that falls in on an object.
    5. A type of mirror that focuses all rays behind the mirror.
    Click here for the solution.
  2. State whether the following statements are TRUE or FALSE. If they are false, rewrite the statement correcting it.
    1. The refractive index of a medium is an indication of how fast light will travel through the medium.
    2. Total internal refraction takes place when the incident angle is larger than the critical angle.
    3. The magnification of an object can be calculated if the speed of light in a vacuum and the speed of light in the medium is known.
    4. The speed of light in a vacuum is about 3×1083×108 m.s-1-1.
    5. Specular reflection takes place when light is reflected off a rough surface.
    Click here for the solution.
  3. Choose words from Column B to match the concept/description in Column A. All the appropriate words should be identified. Words can be used more than once.
    Table 1
     Column AColumn B
    (a)Real imageUpright
    (b)Virtual imageCan be cast on a screen
    (c)Concave mirrorIn front
    (d)Convex mirrorBehind
    (e)Plane mirrorInverted
      Light travels to it
      Upside down
      Light does not reach it
      Erect
      Same size

    Click here for the solution.
  4. Complete the following ray diagrams to show the path of light.
    Figure 18
    Figure 18 (PG10C6_056.png)
    Figure 19
    Figure 19 (PG10C6_057.png)
    Figure 20
    Figure 20 (PG10C6_058.png)
    Figure 21
    Figure 21 (PG10C6_059.png)
    Figure 22
    Figure 22 (PG10C6_060.png)
    Figure 23
    Figure 23 (PG10C6_061.png)
    Click here for the solution.
  5. A ray of light strikes a surface at 35 to the surface normal. Draw a ray diagram showing the incident ray, reflected ray and surface normal. Calculate the angles of incidence and reflection and fill them in on your diagram.
    Click here for the solution.
  6. Light travels from glass (n = 1,5) to acetone (n = 1,36). The angle of incidence is 25.
    1. Describe the path of light as it moves into the acetone.
    2. Calculate the angle of refraction.
    3. What happens to the speed of the light as it moves from the glass to the acetone?
    4. What happens to the wavelength of the light as it moves into the acetone?
    5. What is the name of the phenomenon that occurs at the interface between the two media?

    Click here for the solution.
  7. A stone lies at the bottom of a swimming pool. The water is 120 cm deep. The refractive index of water is 1,33. How deep does the stone appear to be?
    Click here for the solution.
  8. Light strikes the interface between air and an unknown medium with an incident angle of 32. The angle of refraction is measured to be 48. Calculate the refractive index of the medium and identify the medium.
    Click here for the solution.
  9. Explain what total internal reflection is and how it is used in medicine and telecommunications. Why is this technology much better to use?
    Click here for the solution.
  10. A candle 10 cm high is placed 25 cm in front of a plane mirror. Draw a ray diagram to show how the image is formed. Include all labels and write down the properties of the image.
    Click here for the solution.
  11. A virtual image, 4 cm high, is formed 3 cm from a plane mirror. Draw a labelled ray diagram to show the position and height of the object. What is the magnification?
    Click here for the solution.
  12. An object, 3 cm high, is placed 4 cm from a concave mirror of focal length 2 cm. Draw a labelled ray diagram to find the position, height and properties of the image.
    Click here for the solution.

Collection Navigation

Content actions

Download:

Collection as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Module as:

PDF | More downloads ...

Add:

Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks