Total internal reflection refers to the complete reflection of a ray of light within a given medium from the surrounding surface. Here, the ray of light continues to be reflected within the medium (glass, water etc.) without being refracted off. In order to get a good understanding of what total internal reflection really is, it is important to understand refraction.
Different media have different densities. For instance, the densities of water, air and crown glass are 1g/cm3, 1.225kg/m3 and 2.59g/cm3 respectively. As a result, they also have different index of refraction (water-1.333, air-1.0003, crown glass-1.52).
Because of the different properties between different media, light travelling from one media to another not only changes speed (travelling differently in different media) but is also refracted (bent).
The image below will help understand refraction better.
n1 – water
n2 – air
ᶱ1 – angle of incident ray (Incident ray is the ray that strikes the surface)
ᶱ2- angle of refracted ray (refracted ray is the ray that is transmitted to the second medium)
As the ray of light moves from water (incident ray) to air (refracted ray) it is possible to see in the image above that the ray of light is bent at an angle. The dotted light in the image forms a 90 degrees angle with the surface between the two media.
As a result of the differences in density and thus the refractive index between the two media, the angle of incidence and the angle of refraction are always different. In this case, the angle of incidence is smaller (due to higher density of water) while the angle of refraction tends to be larger.
* In the diagram, the dotted line forms a 90 degree angle with the surface between the two media. The angles of incident and refraction and the angles formed between the rays and the dotted line (also referred to as the normal)
Having understood how refraction occurs, it is now possible to understand total internal reflection.
By increasing the incident angle (ᶱ1) in the image above, the refracted angle is also increased further. As the incident angle continues to increase, there reaches a point where the refracted angle forms a 90 degrees angle with the dotted line (where the refracted ray is parallel with the surface between the two media). This is referred to as the critical angle. At this point, the refracted ray is not transmitted in to the second medium (in this case air) but rather forms between the surface of the water and the air.
If the incident angle is increased further at this point, then the refracted angle moves from the surface and back to the first media (water) given that it is now reflected. Here, it is no longer the refracted ray, but a reflected ray of light. As a result, total internal reflection occurs.
Here, it is important to know the difference between the refracted ray and a reflected ray. Whereas a refracted ray of light is transmitted from one medium to another (from a dense medium to a less dense medium) a reflected ray of light is not transmitted to the second medium. Rather, it is reflected back into the same medium.
* Critical angle - this is the angle of incidence beyond which the ray of light passing through the denser medium to the surface of the less dense medium and is no longer refracted, but totally reflected.
* For water and air, the critical angle is 48.6 degrees (angle of incidence or ᶱ1) beyond this angle (say 50) then total internal reflection occurs.
The critical angle (θc) is easily obtained using Snell's law which states that:
n1 sinθi = n2 sin θt
n1 - refractive index of media 1
sin θi - sin of angle of incidence
n2 - refractive index of media 2
sin θt - sin of refracted angle (90degrees at critical angle)
Here, the goal is to find the value of θi when θt if at 90 degrees (sinθt = 1). By obtaining the angle of incidence, it becomes possible to get the critical angle.
To get the critical angle therefore:
θc = θi = inverse of sin of n2/n1
The refraction index of air is 1.00 while that of acrylic glass is about 1.50. If a ray of light is travelling from the glass into air, then getting the critical angle would involve the following calculation:
θc = θi = inverse sin of 1.00/1.50
Following calculation, the critical angle obtained from this is 41.8 degrees. Here, it is worth noting that this is simply the critical angle at which the refracted ray forms a 90 degree angle with the surface between the two medium. By increasing this critical angle from 41.8 to above (say 42, 43 or 45 etc) then total internal reflection occurs.
Total internal reflection is very useful. As a result, it has a number of applications that include:
Use in right angled isosceles prism - These prisms can turn light through 90 and 180 degrees based on internal reflection. right angled isosceles prism are mostly used in various optical instruments.
Diamonds - Essentially, faces of a diamond are cut in a manner that allows the light entering to fall at a given angle, which in turn results in multiple, total internal reflections at various angles while at the same time remaining within the diamond. This is what results in the spackles.
Fiber Optics - An optic fiber is as thick as human hair. they are composed of fine quality glass or quartz fiber and coated with a thin layer of material with lower refractive index. This has a number of uses, which include fiber optic diagnostic tools, fiber optic cables used in telecommunications as well as in endoscopes where fiber optics are used by physicians to view inside the body.
Reflectors - reflectors are typically fixed on various roads where they are used to indicate bending roads etc. They reflect light from headlights from cars guiding the driver along the path.
Total internal reflection also finds use in:
TIRF is a type of microscopy that allows for the imaging of various fluorescent molecules that are located near the glass/water or glass/specimen interface. This technique was developed in the early 80s and delivers very high axial resolution, which allows technicians and other users to be able to observe processes associated with the membrane.
To observe the fluorescent molecules, an evanescent wave is employed for the excitation of fluorophores rather than using direct illumination through light delivered from such sources as LEDs.
Here, the evanescent field occurs when the incident light is totally reflected at the interface between the two transparent media with varying refractive indices. With biological applications, the incident light is laser light while the interface is usually the glass of a cover slip and film of aqueous solution between the cover slip and adherent cells.
Here, as the energy of the evanescent field decreases exponentially with distance to the interface, it is only the fluorosophores in given proximities to the cover slip that are excited. This results in images with excellent signal-to-noise ratio since the fluorophores in the other parts of the cell are barely excited.
With outstanding high axial resolution of below 100nm obtained through this technique, it becomes possible to observe such membrane related processes like cell adhesion, binding of hormones, transport of molecules as well as various exocytic and endocytic processes like the release and uptake of neurotransmitters.
* Essentially, this technique was developed in order to restrict background fluorescence and thus increase signal-to-noise ration in the resulting image. Light is used to create an evanescent wave (field) at limited range within the sample and beyond an interface of two substrates with varying refractive index.
Prism-based and objective-based approaches are two of the main approaches used to achieve total internal reflection.
Here, a prism is attached to the surface of the cover slip. This then directs a focused beam of light towards the cover slip (medium interface). The prism allows for the angle of penetrating light to be adjusted to a critical angle. With the development of the objective-based approach, prism-based total internal reflection has become less popular.
* One of the main problems with the prism-based method is that the prism significantly limits access to the specimen. This makes it rather difficult to do certain things like changing media, add drugs or other substances or even carry out measurements.
Some of the other disadvantages of the prism-based system include:
With objective-based total internal reflection, light is directed to the specimen via the objective (the objective also collects the emitted fluorescence light). It is essential that the objective have a very high numerical aperture (NA) of over 1.45. (achieved by using immersion oil or other specialized liquid immersion media). This allows for an angle of incidence to be greater than the critical angle in order to form total internal reflection.
The objective-based total internal reflection has been shown to be more effective compared to the prism approach. This is due to the fact that the specimen is accessible while the incidence angle can be easily changed.
Here, the user can simply place the laser spot in different areas in the back focal place of the objective and choose the angle of incidence of the laser light thereby changing penetration depth of the wave.
The objective-based system also has an advantage over prism given that the laser system is directly coupled in to the microscope itself which helps reduce laser concerns.
internal reflection fluorescence microscopy is typically used for imaging
events occurring at the surface of the specimen (cell). However, it works well
with adherent cells given that this technique only illuminates the region near
the cover slip (part that has adhered to the cover slip) and cannot be used for
imaging non-adherent cells.
With some cells, it becomes necessary to coat the cover slip with such extracellular matrix molecules as polylysine to enhance cell adherence. It is also important to ensure that the refractive index of the cell is below the NA of the objective for analysis. If cells have a higher numerical aperture, as is the case with chromaffin cells, it becomes difficult to obtain TIRF images using the standard objectives.
This technique is particularly ideal for imaging of live cells. In the event that the cells are fixed, then they have to be mounted in a media with low refractive index (such as PBS).
Here, it might be important to avoid:
Total internal reflection fluorescence microscopy achieves what both widefield and confocal imaging techniques are unable to through its imaging capabilities.
As such, it has been used for:
Compared to other techniques like confocal microscopy, TIRF microscopy has an advantage in that technicians can be able to observe smaller sections of a specimen (100nm compared to 600 mn using confocal microscopy). Moreover, it has been shown to be the ideal technique for other applications that require restricted illumination and consequently reduced cell damage.
On the other hand, this
technique has been shown to be more economical during configuration given that
it does not really require complex scanning galvanometer systems. As such, it
can be easily applied to ordinary research grade laboratory microscopes.
Axelrod, Daniel (1 November 2001). "Total
Internal Reflection Fluorescence Microscopy in Cell Biology". Traffic. 2
Giancoli, D.C. (2000) Physics for Scientists and Engineers 3rd edition, Prentice Hall, New Jersey.
Richard Fitzpatrick (2007) Total Internal Reflection.