# 25.4 Total internal reflection  (Page 4/8)

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## 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 $\text{24}\text{.}4º$ , 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 $\text{24}\text{.}4º$ . 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 ( $\approx 2.17$ ), 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.

## 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.

## Section summary

• The incident angle that produces an angle of refraction of $\text{90º}$ 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?

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 $\text{48.6º}$ , 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 $\text{24}\text{.}4º$ . 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?

$\text{66}\text{.}3º$

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 $\text{45}\text{.}0º$ , what must be the minimum index of refraction of the material from which the reflector is made?

$>1\text{.}\text{414}$

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 $\text{68}\text{.}4º$ 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?

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.

Calculate the work done by an 85.0-kg man who pushes a crate 4.00 m up along a ramp that makes an angle of 20.0º20.0º with the horizontal. (See [link] .) He exerts a force of 500 N on the crate parallel to the ramp and moves at a constant speed. Be certain to include the work he does on the crate an
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BELLO
the information provided is not enough
aliyu
Hmmmm maybe the question is logical
yusuf
where are the parameters for calculation
HENRY
there is enough information to calculate an AVERAGE acceleration
Kwok
mistake, there is enough information to calculate an average velocity
Kwok
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Abel
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Abel
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what are the types of radioactivity
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what is static friction
It is the opposite of kinetic friction
Mark
static fiction is friction between two surfaces in contact an none of sliding over on another, while Kinetic friction is friction between sliding surfaces in contact.
MINDERIUM
I don't get it,if it's static then there will be no friction.
author
It means that static friction is that friction that most be overcome before a body can move
kingsley
static friction is a force that keeps an object from moving, and it's the opposite of kinetic friction.
author
It is a force a body must overcome in order for the body to move.
Eboh
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Eboh
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force is something which is responsible for the object to change its position
MINDERIUM
more technically it is the product of mass of an object and Acceleration produced in it
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wave is disturbance in any medium
iqra
energy is distributed in any medium through particles of medium.
iqra
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we have to first figure out .... wats a particle accelerator first
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The resistive force of surface.
iqra
Who can tutor me on simple harmonic motion
on both a string and peldulum?
Anya
spring*
Anya
Yea
yusuf
Do you have a chit-chat contact
yusuf
I dont have social media but i do have an email?
Anya
Which is
yusuf
Where are you chatting from
yusuf
I don't understand the basics of this group
Jimmy
teach him SHM init
Anya
Simple harmonic motion
yusuf
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the write question should be " How many Topics are in O- Level Physics, or other branches of physics.
effiom
how many topic are in physics
Praise
Praise what level are you
yusuf
If u are doing a levels in your first year you do AS topics therefore you do 5 big topic i.e particles radiation, waves and optics, mechanics,materials, electricity. After that you do A level topics like Specific Harmonic motion circular motion astrophysics depends really
Anya
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yusuf
Heat nd Co for a level
yusuf
yh I need someone to explain something im tryna solve . I'll send the question if u down for it
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Tamdy
hallow
Boniface
Boniface
the range of objects and phenomena studied in physics is
Boniface