Total Internal Reflection Physics Investigatory Project PDF Class 12

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INTRODUCTION

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.

OPTICAL DESCRIPTION

Total internal reflection can be demonstrated using a semi-circular 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 the critical angle measurement which is caused by the sun or a light source (measured normal to the surface):

If Θ<Θ_C , 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>Θ_C , 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.

CRITICAL ANGLE

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.

Phase Shift upon Total Internal Reflection

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.

Total Internal Reflection in Diamond

From glass to air the critical angle is about 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 for the diamond-air 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.

Application of Total Internal Reflection

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 using Soda Bottle

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.

MATERIAL REQUIRED

Empty soda pop bottle (2 Litre)
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 centre 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.

PRECAUTION

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 coloured light.