Total Internal Reflection (Cambridge O Level Physics)

Revision Note

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Author

Dan MG

Last updated

30 January 2024

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Total Internal Reflection

Sometimes, when light is moving from a denser medium towards a less dense one, instead of being refracted, all of the light is reflected
- This phenomenon is called total internal reflection
Total internal reflection (TIR) occurs when:

The angle of incidence is greater than the critical angle and the incident material is denser than the second material

Therefore, the two conditions for total internal reflection are:
- The angle of incidence > the critical angle
- The incident material is denser than the second material

Critical Angle and TIR

Total Internal Reflection, downloadable IGCSE & GCSE Physics revision notes

TIR occurs when the angle of incidence is greater than the angle of reflection

Total internal reflection is utilised in:
- Optical fibres e.g. endoscopes
- Prisms e.g. periscopes

Prisms

Prisms are used in a variety of optical instruments, including:
- Periscopes
- Binoculars
- Telescopes
- Cameras
They are also used in safety reflectors for bicycles and cars, as well as posts marking the side or edge of roads

A periscope is a device that can be used to see over tall objects
- It consists of two right-angled prisms

Periscope, downloadable IGCSE & GCSE Physics revision notes

Reflection of light through a periscope

The light totally internally reflects in both prisms

Internal Reflection in Prisms

tir-prisms-downloadable-igcse-and-gcse-physics-revision-notes

Single and double reflection through right-angled prisms

Examiner Tip

If asked to name the phenomena make sure you give the whole name – total internal reflection

Remember: total internal reflection occurs when light travels from a denser material to less dense material and ALL of the light is reflected.

If asked to give an example of a use of total internal reflection, first state the name of the object that causes the reflection (e.g. a right-angled prism) and then name the device in which it is used (e.g. a periscope)

Refractive Index & Critical Angle Equation

The critical angle, c, of a material is related to its refractive index, n
The relationship between the two quantities is given by the equation:

$\sin c = \frac{1}{n}$

This can also be rearranged to calculate the refractive index, n:

$n = \frac{1}{\sin c}$

This equation shows that:
- The larger the refractive index of a material, the smaller the critical angle
- Light rays inside a material with a high refractive index are more likely to be totally internally reflected

Worked example

Opals and diamonds are transparent stones used in jewellery. Jewellers shape the stones so that light is reflected inside.Compare the critical angles of opal and diamond and explain which stone would appear to sparkle more.

The refractive index of opal is about 1.5

The refractive index of diamond is about 2.4

Step 1: List the known quantities

Refractive index of opal, n_o = 1.5
Refractive index of diamond, n_d = 2.4

Step 2: Write out the equation relating critical angle and refractive index

$\sin c = \frac{1}{n}$

Step 3: Calculate the critical angle of opal (c_o)

sin(c_o) = 1 ÷ 1.5 = 0.6667

c_o = sin^–1 (0.6667) = 41.8 = 42°

Step 4: Calculate the critical angle of diamond (c_d)

sin(c_d) = 1 ÷ 2.4 = 0.4167

c_d = sin^–1 (0.4167) = 24.6 = 25°

Step 5: Compare the two values and write a conclusion

Total internal reflection occurs when the angle of incidence of light is larger than the critical angle (i > c)
In opal, total internal reflection will occur for angles of incidence between 42° and 90°
The critical angle of diamond is lower than the critical angle of opal (c_o> c_d)
This means light rays will be totally internally reflected in diamond over a larger range of angles (25° to 90°)
Therefore, more total internal reflection will occur in diamond hence it will appear to sparkle more than the opal

Examiner Tip

When calculating the value of the critical angle using the above equation:

First use the refractive index, n, to find sin(c)
Then use the inverse sin function (sin^–1) to find the value of c

Optical Fibres

Total internal reflection is used to reflect light along optical fibres, meaning they can be used for
- Communications
- Endoscopes
- Decorative lamps

Light travelling down an optical fibre is totally internally reflected each time it hits the edge of the fibre
This means information can be transmitted over long distances with minimal loss