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6.4 Total internal reflection  (Page 4/8)

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The picture shows binoculars with prisms inside. The light through one of the object lenses enters through the first prism and suffers total internal reflection and then falls on the second prism and gets total internally reflected and emerges out through one of the eyepiece lenses.
These binoculars employ corner reflectors with total internal reflection to get light to the observer’s eyes.

The sparkle of diamonds

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 24 . 4º size 12{"24" "." 4°} {} , and so when light enters a diamond, it has trouble getting back out. (See [link] .) Although light freely enters the diamond, it can exit only if it makes an angle less than 24 . 4º size 12{"24" "." 4°} {} . Facets on diamonds are specifically intended to make this unlikely, so that the light can exit only in certain places. Good diamonds are very clear, so that the light makes many internal reflections and is concentrated at the few places it can exit—hence the sparkle. (Zircon is a natural gemstone that has an exceptionally large index of refraction, but not as large as diamond, so it is not as highly prized. Cubic zirconia is manufactured and has an even higher index of refraction ( ≈ 2.17 size 12{»2 "." "17"} {} ), but still less than that of diamond.) The colors you see emerging from a sparkling diamond are not due to the diamond’s color, which is usually nearly colorless. Those colors result from dispersion, the topic of Dispersion: The Rainbow and Prisms . 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, while around 50% of the world’s clear diamonds come from central and southern Africa.

A light ray falls onto one of the faces of a diamond, gets refracted, falls on another face and gets totally internally reflected, and this reflected ray further undergoes multiple reflections when it falls on other faces.
Light cannot easily escape a diamond, because its critical angle with air is so small. Most reflections are total, and the facets are placed so that light can exit only in particular ways—thus concentrating the light and making the diamond sparkle.

Phet explorations: bending light

Explore bending of light between two media with different indices of refraction. See how changing from air to water to glass changes the bending angle. Play with prisms of different shapes and make rainbows.

Bending Light

Section summary

  • The incident angle that produces an angle of refraction of 90º size 12{"90"°} {} is called critical angle.
  • Total internal reflection is a phenomenon that occurs at the boundary between two mediums, such that if the incident angle in the first medium is greater than the critical angle, then all the light is reflected back into that medium.
  • Fiber optics involves the transmission of light down fibers of plastic or glass, applying the principle of total internal reflection.
  • Endoscopes are used to explore the body through various orifices or minor incisions, based on the transmission of light through optical fibers.
  • Cladding prevents light from being transmitted between fibers in a bundle.
  • Diamonds sparkle due to total internal reflection coupled with a large index of refraction.

Conceptual questions

A ring with a colorless gemstone is dropped into water. The gemstone becomes invisible when submerged. Can it be a diamond? Explain.

A high-quality diamond may be quite clear and colorless, transmitting all visible wavelengths with little absorption. Explain how it can sparkle with flashes of brilliant color when illuminated by white light.

Is it possible that total internal reflection plays a role in rainbows? Explain in terms of indices of refraction and angles, perhaps referring to [link] . Some of us have seen the formation of a double rainbow. Is it physically possible to observe a triple rainbow?

A double rainbow with spectacular bands of seven colors.
Double rainbows are not a very common observance. (credit: InvictusOU812, Flickr)

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.

Problems&Exercises

Verify that the critical angle for light going from water to air is 48.6º size 12{"48" "." 6°} {} , 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 24 . 4º size 12{"24" "." 4°} {} . Verify this. (b) What is the critical angle for light going from zircon to air?

An optical fiber uses flint glass clad with crown glass. What is the critical angle?

66 . 3º size 12{"66" "." 3°} {}

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 45 . 0º size 12{"45" "." 0°} {} , what must be the minimum index of refraction of the material from which the reflector is made?

> 1 . 414 size 12{>1 "." "414"} {}

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 68 . 4º size 12{"68" "." 4°} {} when submerged in water? What is the substance, based on [link] ? (b) What would the critical angle be for this substance in air?

A ray of light, emitted beneath the surface of an unknown liquid with air above it, undergoes total internal reflection as shown in [link] . What is the index of refraction for the liquid and its likely identification?

A light ray travels from an object placed in a denser medium n1 at 15.0 centimeter from the boundary and on hitting the boundary gets totally internally reflected with theta c as critical angle. The horizontal distance between the object and the point of incidence is 13.4 centimeters.
A light ray inside a liquid strikes the surface at the critical angle and undergoes total internal reflection.

1.50, benzene

A light ray entering an optical fiber surrounded by air is first refracted and then reflected as shown in [link] . Show that if the fiber is made from crown glass, any incident ray will be totally internally reflected.

The figure shows light traveling from n1 to n2 is incident on a rectangular transparent object at an angle of incidence theta 1. The angle of refraction is theta 2. On refraction, the ray falls onto the long side and gets totally internally reflected with theta 3 as the angle of incidence.
A light ray enters the end of a fiber, the surface of which is perpendicular to its sides. Examine the conditions under which it may be totally internally reflected.

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
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Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
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A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
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Source:  OpenStax, Physics subject knowledge enhancement course (ske). OpenStax CNX. Jan 09, 2015 Download for free at http://legacy.cnx.org/content/col11505/1.10
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