Investigator y Pr o ject
Ak s h a t A Am e e s h th
1 2 B B S u m m er F F i e l d s S Sch ool N e w D Delhi
TEACHER SIGNATURE
Total internal reflection is an optical phenomenon that happens when a ray of light strikes a medium boundary at an angle larger than a particular critical angle with respect to the normal to the surface. If the refractive index is lower on the other side of the boundary and the incident angle is greater than the critical angle, no light can pass through and all of the light is reflected. The critical angle is the angle of incidence above which the total internal reflectance occurs. When a light beam crosses a boundary between materials with different kinds of refractive indices, the light beam will be partially refracted at the boundary surface, and partially reflected. However, if the angle of incidence is greater (i.e. the ray is closer to being parallel to the boundary) than the critical angle – the angle of incidence at which light is refracted such that it travels along the boundary – then the light will stop crossing the boundary altogether and instead be totally reflected back internally. This can only occur where light travels from a medium with a higher [n1=higher refractive index] to one with a lower refractive index [n2=lower refractive index]. For example, it will occur when passing from glass to air, but not when passing from air to glass.
Total internal reflection can be demonstrated using a semicircular block of glass or plastic. A "ray box" shines a narrow beam of light (a "ray") onto the glass. The semi-circular shape ensures that a ray pointing towards the centre of the flat face will hit the curved surface at a right angle; this will prevent refraction at the air/glass boundary of the curved surface. At the glass/air boundary of the flat surface, what happens will depend on the angle? Where is θC the critical angle measurement which is caused by the sun or a light source (measured normal to the surface): • If θ < θC , the ray will split. Some of the ray will reflect off the boundary, and some will refract as it passes through. This is not total internal reflection. • If θ > θC , the entire ray reflects from the boundary. None passes through. This is called total internal reflection.
This physical property makes optical fibres useful and prismatic binoculars possible. It is also what gives diamonds their distinctive sparkle, as diamond has an unusually high refractive index.
The critical angle is the angle of incidence above which total internal reflection occurs. The angle of incidence is measured with respect to the normal at the refractive boundary (see diagram illustrating Snell's law). Consider a light ray passing from glass into air. The light emanating from the interface is bent towards the glass. When the incident angle is increased sufficiently, the transmitted angle (in air) reaches 90 degrees. It is at this point no light is transmitted into air. The critical angle is given by Snell's law.
=
Rearranging Snell's Law, we get incidence
=
To find the critical angle, we find the value for when and thus .The resulting value of is equal to the critical angle . Now, we can solve for , and we get the equation for the critical angle:
= °
=
− = = () If the incident ray is precisely at the critical angle, the refracted ray is tangent to the boundary at the point of incidence. If for example, visible light were travelling through acrylic glass (with an index of refraction of 1.50) into air (with an index of refraction of 1.00), the calculation would give the critical angle for light from acrylic into air, which is
. − = ( ) = . .
A lesser-known aspect of total internal reflection is that the reflected light has an angle dependent phase shift between the reflected and incident light. Mathematically this means that the Fresnel reflection coefficient becomes a complex rather than a real number. This phase shift is polarization dependent and grows as the incidence angle deviates further from the critical angle toward grazing incidence. The polarization dependent phase shift is long known and was used by Fresnel to design the Fresnel rhomb which allows transforming circular polarization to linear polarization and vice versa for a wide range of wavelengths (colours), in contrast to the quarter wave plate. The polarization dependent phase shift is also the reason why TE and TM guided modes have different dispersion relations.
From glass to air the critical angle is about 42o but it varies from one medium to another. The material that gives the smallest critical angle is diamond. That is why they sparkle so much! Rays of light can easily be made to 'bounce around inside them' by careful cutting of the stone and the refraction at the surfaces splits the light into a spectrum of colours! Relatively speaking, the critical angle 24.4o for the diamondair boundary is extremely small. This property of the diamond-air boundary plays an important role in the brilliance of a diamond gemstone. Having a small critical angle, light has the tendency to become "trapped" inside of a diamond once it enters. Most rays approach the diamond at angles of incidence greater than the critical angle (as it is so small) so a light ray will typically undergo TIR several times before finally refracting out of the diamond. This gives diamond a tendency to sparkle. The effect can be enhanced by the cutting of a diamond gemstone with a 'strategically' planned shape.
Total internal reflection is the operating principle of optical fibres, which are used in endoscopes and telecommunications. Total internal reflection is the operating principle of automotive rain sensors, which control automatic windscreen/windshield wipers. Another application of total internal reflection is the spatial filtering of light. Prismatic binoculars use the principle of total internal reflections to get a very clear image. Gonioscopy employs total internal reflection to view the anatomical angle formed between the eye's cornea and iris. Optical fingerprinting devices use frustrated total internal reflection in order to record an image of a person's fingerprint without the use of ink. A Total internal reflection fluorescence microscope uses the evanescent wave produced by TIR to excite fluorophores close to a surface. This is useful for the study of surface properties of biological samples.
Total internal reflection can be observed while swimming, when one opens one's eyes just under the water's surface. If the water is calm, its surface appears mirror-like. One can demonstrate total internal reflection by filling a sink or bath with water, taking a glass tumbler, and placing it upsidedown over the plug hole (with the tumbler completely filled with water). While water remains both in the upturned tumbler and in the sink surrounding it, the plug hole and plug are visible since the angle of refraction between glass and water is not greater than the critical angle. If the drain is opened and the tumbler is kept in position over the hole, the water in the tumbler drains out leaving the glass filled with air, and this then acts as the plug. Viewing this from above, the tumbler now appears mirrored because light reflects off the air/glass interface. This is different phenomenon from reflection and refraction. Reflection occurs when light goes back in same medium. Refraction occurs when light travels from different mediums. Here both are not happening. This is due to both and a mixture of both. Another common example of total internal reflection is a critically cut diamond. This is what gives it maximum spark.
Explanation In this case, n air = 1.00 n water = 1.33. Therefore:
In this demo light will continually reflect through the stream of water creating total internal reflection (TIR). The stream of water will 'carry' the light though, to the end of the stream.
Total Internal Reflection is the principle behind fiber optics.
Materials
empty soda pop bottle (2 liter) tape hand drill drill bits water green laser bucket old books, etc for stands
Procedure
First set up the soda bottle by drilling a hole near the bottom of the bottle. Begin with a drill bit that has a diameter which is slightly larger than the diameter of the laser that will be used. We used a 1/4 inch drill bit, however sizes as small as 7/32 inch worked as well. First tape the hole and then fill the bottle with water. The cap will prevent leaking because it creates a vacuum in the bottle. Stand the soda bottle on top of a stack of books so the hole is facing the bucket. The laser should be placed in a binder clip so it stays on, and then set on a stack of books and papers. The laser should be lined up so that the laser light goes through the soda bottle, and into the center of the hole. See for details. Carefully remove the tape and then unscrew the top of the soda bottle. The light should reflect within the stream of water so that you could see at least a few points of
reflection. The light should be visible through the entire stream. If the reflections of the light aren’t clear, it may be necessary to expand the hole by drilling through the existing hole with a larger drill bit. This process may need to be repeated several times.
Notes
This is a messy experiment. Be ready to adjust the bucket which catches the stream of water. Also be aware that the stream's curvature will change as the water level decreases. It will bend closer to the bottle, and the bucket may need to be adjusted again. When the water level is a little above the hole there will be no total internal reflection although the stream will continue. Place the cap back on, or put the bottle inside of the bucket. Make sure to have lots of paper towels! Towels or rags could be useful too. However, this mess is water, and therefore easy to clean up. Some resources suggest putting a drop of food coloring in the bottom of the bucket to match the laser light, giving the appearance that the water has permanently 'trapped' the colored light.
Following Books and websites were a source for my project.
Wikipedia
NCERT Physics Textbook for class 12
Feynman Lectures on Physics
Google
