# 13.4 Total internal reflection

 Page 1 / 3

## 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.
2. Move the raybox such that the light is refracted by the glass. See "Position 2".
3. Move the raybox further and observe what happens.
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.
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.

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

Critical Angle

The critical angle is the angle of incidence where the angle of reflection is 90 ${}^{\circ }$ . 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.
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.

Each medium has its own unique critical angle. For example, the critical angle for glass is 42 ${}^{\circ }$ , and that of water is 48,8 ${}^{\circ }$ . 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:

${n}_{1}sin{\theta }_{1}={n}_{2}sin{\theta }_{2}$

where ${n}_{1}$ is the refractive index of material 1, ${n}_{2}$ is the refractive index of material 2, ${\theta }_{1}$ is the angle of incidence and ${\theta }_{2}$ is the angle of refraction. For total internal reflection we know that the angle of incidence is the critical angle. So,

${\theta }_{1}={\theta }_{c}.$

However, we also know that the angle of refraction at the critical angle is 90 ${}^{\circ }$ . So we have:

${\theta }_{2}={90}^{\circ }.$

We can then write Snell's Law as:

${n}_{1}sin{\theta }_{c}={n}_{2}sin{90}^{\circ }$

Solving for ${\theta }_{c}$ gives:

$\begin{array}{ccc}\hfill {n}_{1}sin{\theta }_{c}& =& {n}_{2}sin{90}^{\circ }\hfill \\ \hfill sin{\theta }_{c}& =& \frac{{n}_{2}}{{n}_{1}}\left(1\right)\hfill \\ \hfill \therefore {\theta }_{c}& =& {sin}^{-1}\left(\frac{{n}_{2}}{{n}_{1}}\right)\hfill \end{array}$
Take care that for total internal reflection the incident ray is always in the denser medium.

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

1. We know that the critical angle is given by:

${\theta }_{c}={sin}^{-1}\left(\frac{{n}_{2}}{{n}_{1}}\right)$
2. $\begin{array}{ccc}\hfill {\theta }_{c}& =& {sin}^{-1}\left(\frac{{n}_{2}}{{n}_{1}}\right)\hfill \\ & =& {sin}^{-1}\left(\frac{1}{1,33}\right)\hfill \\ & =& 48,{8}^{\circ }\hfill \end{array}$
3. The critical angle for light travelling from water to air is $48,{8}^{\circ }$ .

Preparation and Applications of Nanomaterial for Drug Delivery
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
hi
Loga
Got questions? Join the online conversation and get instant answers! By OpenStax By Yasser Ibrahim By Stephen Voron By OpenStax By Joanna Smithback By OpenStax By P. Wynn Norman By Anh Dao By OpenStax By Frank Levy