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In daily life it is easy to demonstrate total internal reflection for example by looking upwards when underwater - you will be able to see a cone of your surroundings (areas where angle of incidence is lower than critical) and reflection of other underwater object everywhere else (where angle of incidence is higher than critical). In other (much simplified) words: when underwater the water surface will in some cases work as a mirror (due to total internal reflection).
Dispersion of Light
The index of refraction of medium is dependent on the frequency of incoming light ray. Therefore if light with with wide frequency spectrum (such as daylight) enters for example glass prism, the component frequency bands (for visible colors) will diffract under slightly different angles. The result is light divided into colorful "strip" for each of basic colors. The very same effect is behind rainbow which is natural occurrence of dispersion.
Diffraction of light in prism courtesy Wikipedia: 
Practical Use of Dispersion
Dispersion is used in spectrometers - devices which are used in many fields of science to analyze the chemical composition of objects. It is based on the fact that different chemical elements emit and absorb different wavelenghts of light, and this spectra can be seen using spectrometers.
In other fields, the dispersion can be a nuisance: in camera lenses it leads to chromatic aberration and in optical cables chromatic dispersion limits the maximum bandwidth of the fiber (though this effect is not as strong as modal dispersion which is caused by longer paths of reflected rays as opposed to those that travel straight through along the core).
Further Reading/Watching