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Total internal reflection, coupled with a large index of refraction, explains why diamonds sparkle more than other materials. The critical angle for a diamond-to-air surface is only , so when light enters a diamond, it has trouble getting back out ( [link] ). Although light freely enters the diamond, it can exit only if it makes an angle less than . Facets on diamonds are specifically intended to make this unlikely. Good diamonds are very clear, so that the light makes many internal reflections and is concentrated before exiting—hence the bright sparkle. (Zircon is a natural gemstone that has an exceptionally large index of refraction, but it is not as large as diamond, so it is not as highly prized. Cubic zirconia is manufactured and has an even higher index of refraction , but it is still less than that of diamond.) The colors you see emerging from a clear diamond are not due to the diamond’s color, which is usually nearly colorless. The colors result from dispersion, which we discuss in Dispersion . Colored diamonds get their color from structural defects of the crystal lattice and the inclusion of minute quantities of graphite and other materials. The Argyle Mine in Western Australia produces around 90% of the world’s pink, red, champagne, and cognac diamonds, whereas around 50% of the world’s clear diamonds come from central and southern Africa.
Explore refraction and reflection of light between two media with different indices of refraction. Try to make the refracted ray disappear with total internal reflection. Use the protractor tool to measure the critical angle and compare with the prediction from [link] .
A ring with a colorless gemstone is dropped into water. The gemstone becomes invisible when submerged. Can it be a diamond? Explain.
The gemstone becomes invisible when its index of refraction is the same, or at least similar to, the water surrounding it. Because diamond has a particularly high index of refraction, it can still sparkle as a result of total internal reflection, not invisible.
The most common type of mirage is an illusion that light from faraway objects is reflected by a pool of water that is not really there. Mirages are generally observed in deserts, when there is a hot layer of air near the ground. Given that the refractive index of air is lower for air at higher temperatures, explain how mirages can be formed.
How can you use total internal reflection to estimate the index of refraction of a medium?
One can measure the critical angle by looking for the onset of total internal reflection as the angle of incidence is varied. [link] can then be applied to compute the index of refraction.
Verify that the critical angle for light going from water to air is , as discussed at the end of [link] , regarding the critical angle for light traveling in a polystyrene (a type of plastic) pipe surrounded by air.
(a) At the end of [link] , it was stated that the critical angle for light going from diamond to air is Verify this. (b) What is the critical angle for light going from zircon to air?
a. ; b.
An optical fiber uses flint glass clad with crown glass. What is the critical angle?
At what minimum angle will you get total internal reflection of light traveling in water and reflected from ice?
Suppose you are using total internal reflection to make an efficient corner reflector. If there is air outside and the incident angle is , what must be the minimum index of refraction of the material from which the reflector is made?
You can determine the index of refraction of a substance by determining its critical angle. (a) What is the index of refraction of a substance that has a critical angle of when submerged in water? What is the substance, based on [link] ? (b) What would the critical angle be for this substance in air?
a. 1.43, fluorite; b.
A ray of light, emitted beneath the surface of an unknown liquid with air above it, undergoes total internal reflection as shown below. What is the index of refraction for the liquid and its likely identification?
Light rays fall normally on the vertical surface of the glass prism shown below. (a) What is the largest value for such that the ray is totally reflected at the slanted face? (b) Repeat the calculation of part (a) if the prism is immersed in water.
a. ; b.
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