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  • Explain the phenomenon of total internal reflection.
  • Describe the workings and uses of fiber optics.
  • Analyze the reason for the sparkle of diamonds.

A good-quality mirror may reflect more than 90% of the light that falls on it, absorbing the rest. But it would be useful to have a mirror that reflects all of the light that falls on it. Interestingly, we can produce total reflection using an aspect of refraction .

Consider what happens when a ray of light strikes the surface between two materials, such as is shown in [link] (a). Part of the light crosses the boundary and is refracted; the rest is reflected. If, as shown in the figure, the index of refraction for the second medium is less than for the first, the ray bends away from the perpendicular. (Since n 1 > n 2 size 12{n rSub { size 8{1} }>n rSub { size 8{2} } } {} , the angle of refraction is greater than the angle of incidence—that is, θ 1 > θ 2 size 12{θ rSub { size 8{1} }>θ rSub { size 8{2} } } {} .) Now imagine what happens as the incident angle is increased. This causes θ 2 size 12{θ rSub { size 8{2} } } {} to increase also. The largest the angle of refraction θ 2 size 12{θ rSub { size 8{2} } } {} can be is 90º size 12{"90"°} {} , as shown in [link] (b).The critical angle     θ c size 12{θ rSub { size 8{c} } } {} for a combination of materials is defined to be the incident angle θ 1 size 12{θ rSub { size 8{1} } } {} that produces an angle of refraction of 90º . That is, θ c is the incident angle for which θ 2 = 90º . If the incident angle θ 1 is greater than the critical angle, as shown in [link] (c), then all of the light is reflected back into medium 1, a condition called total internal reflection .

Critical angle

The incident angle θ 1 size 12{θ rSub { size 8{1} } } {} that produces an angle of refraction of 90º size 12{"90"°} {} is called the critical angle, θ c size 12{θ rSub { size 8{1} } } {} .

In the first figure, an incident ray at an angle theta 1 with a perpendicular line drawn at the point of incidence travels from n1 to n2. The incident ray suffers both refraction and reflection. The angle of refraction is theta 2. In the second figure, as theta 1 is increased, the angle of refraction theta 2 becomes 90 degrees and the angle of reflection corresponding to 90 degrees is theta c. In the third figure, theta c greater than theta i, total internal reflection takes place and instead of refraction, reflection takes place and the light ray travels back into medium n1.
(a) A ray of light crosses a boundary where the speed of light increases and the index of refraction decreases. That is, n 2 < n 1 size 12{n rSub { size 8{2} }<n rSub { size 8{1} } } {} . The ray bends away from the perpendicular. (b) The critical angle θ c size 12{θ rSub { size 8{c} } } {} is the one for which the angle of refraction is . (c) Total internal reflection occurs when the incident angle is greater than the critical angle.

Snell’s law states the relationship between angles and indices of refraction. It is given by

n 1 sin θ 1 = n 2 sin θ 2 . size 12{n rSub { size 8{1} } "sin"θ rSub { size 8{1} } =n rSub { size 8{2} } "sin"θ rSub { size 8{2} } } {}

When the incident angle equals the critical angle ( θ 1 = θ c size 12{θ rSub { size 8{1} } =`θ rSub { size 8{c} } } {} ), the angle of refraction is 90º size 12{"90"°} {} ( θ 2 = 90º size 12{θ rSub { size 8{2} } =`"90" rSup { size 8{0} } } {} ). Noting that sin 90º =1 size 12{"sin"" 90"°"=1"} {} , Snell’s law in this case becomes

n 1 sin θ 1 = n 2 . size 12{n rSub { size 8{1} } "sin"θ rSub { size 8{1} } =n rSub { size 8{2} } } {}

The critical angle θ c size 12{q rSub { size 8{c} } } {} for a given combination of materials is thus

θ c = sin 1 n 2 / n 1 for size 12{θ rSub { size 8{c} } ="sin" rSup { size 8{ - 1} } left ( {n rSub { size 8{2} } } slash {n rSub { size 8{1} } } right )} {} n 1 > n 2 . size 12{n rSub { size 8{1} }>n rSub { size 8{2} } } {}

Total internal reflection occurs for any incident angle greater than the critical angle θ c size 12{q rSub { size 8{c} } } {} , and it can only occur when the second medium has an index of refraction less than the first. Note the above equation is written for a light ray that travels in medium 1 and reflects from medium 2, as shown in the figure.

How big is the critical angle here?

What is the critical angle for light traveling in a polystyrene (a type of plastic) pipe surrounded by air?

Strategy

The index of refraction for polystyrene is found to be 1.49 in [link] , and the index of refraction of air can be taken to be 1.00, as before. Thus, the condition that the second medium (air) has an index of refraction less than the first (plastic) is satisfied, and the equation θ c = sin 1 n 2 / n 1 size 12{θ rSub { size 8{c} } ="sin" rSup { size 8{ - 1} } left ( {n rSub { size 8{2} } } slash {n rSub { size 8{1} } } right )} {} can be used to find the critical angle θ c size 12{θ rSub { size 8{c} } } {} . Here, then, n 2 = 1 . 00 size 12{n rSub { size 8{2} } =1 "." "00"} {} and n 1 = 1 . 49 size 12{n rSub { size 8{1} } =1 "." "49"} {} .

Solution

The critical angle is given by

θ c = sin 1 n 2 / n 1 . size 12{θ rSub { size 8{c} } ="sin" rSup { size 8{ - 1} } left ( {n rSub { size 8{2} } } slash {n rSub { size 8{1} } } right )} {}

Substituting the identified values gives

θ c = sin 1 1 . 00 / 1 . 49 = sin 1 0 . 671 42.2º. alignl { stack { size 12{θ rSub { size 8{c} } ="sin" rSup { size 8{ - 1} } left ( {1 "." "00"} slash {1 "." "49"} right )="sin" rSup { size 8{ - 1} } left (0 "." "671" right )} {} #="42" "." 2° "." {} } } {}

Discussion

This means that any ray of light inside the plastic that strikes the surface at an angle greater than 42.2º will be totally reflected. This will make the inside surface of the clear plastic a perfect mirror for such rays without any need for the silvering used on common mirrors. Different combinations of materials have different critical angles, but any combination with n 1 > n 2 size 12{n rSub { size 8{1} }>n rSub { size 8{2} } } {} can produce total internal reflection. The same calculation as made here shows that the critical angle for a ray going from water to air is 48 . size 12{"48" "." 6°} {} , while that from diamond to air is 24 . size 12{"24" "." 4°} {} , and that from flint glass to crown glass is 66 . size 12{"66" "." 3°} {} . There is no total reflection for rays going in the other direction—for example, from air to water—since the condition that the second medium must have a smaller index of refraction is not satisfied. A number of interesting applications of total internal reflection follow.

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Questions & Answers

hi guys can you teach me how to solve a logarithm?
Villaflor Reply
how about a conceptual framework can you simplify for me? needed please
Villaflor
Hello what happens when electrone stops its rotation around its nucleus if it possible how
Afzal
I think they are constantly moving
Villaflor
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S.M
not possible to fix electron position in space,
S.M
Physics
Beatriz
yes of course Villa flor
David
equations of kinematics for constant acceleration
Sagcurse Reply
A bottle full of water weighs 45g when full of mercury,it weighs 360g.if the empty bottle weighs 20g.calculate the relative density of mercury and the density of mercury....pls I need help
Lila Reply
well You know the density of water is 1000kg/m^3.And formula for density is density=mass/volume Then we must calculate volume of bottle and mass of mercury: Volume of bottle is (45-20)/1000000=1/40000 mass of mercury is:(360-20)/1000 kg density of mercury:(340/1000):1/50000=(340•40000):1000=13600
Sobirjon
the latter is true
Sobirjon
100g of water is mixed with 60g of a liquid of relative density 1.2.assuming no changes in volume occurred,find the average relative density of the mixture...take density of water as 1g/cm3 and density of liquid 1.2g/cm3
Lila
plz hu can explain Heisenberg's uncertainty principle
Emmanuel Reply
who can help me with my problem about acceleration?
Vann Reply
ok
Nicholas
how to solve this... a car is heading north then smoothly made a westward turn during the travel the speed of the car remains constant at 1.5km/h what is the acceleration of the car? the total travel time of the car as it smoothly changed its direction is 15 minutes
Vann
i think the acceleration is 0 since the car does not change its speed unless there are other conditions
Ben
yes I have to agree, the key phrase is, "the speed of the car remains constant...," all other information is not needed to conclude that acceleration remains at 0 during the entire time
Luis
who can help me with a relative density question
Lila
1cm3 sample of tin lead alloy has mass 8.5g.the relative density of tin is 7.3 and that of lead is 11.3.calculate the percentage by weight of tin in the alloy. assuming that there is no change of volume when the metals formed the alloy
Lila
morning, what will happen to the volume of an ice block when heat is added from -200°c to 0°c... Will it volume increase or decrease?
adefenwa Reply
no
Emmanuel
hi what is physical education?
Kate
BPED..is my course.
Kate
No
Emmanuel
I think it is neither decreases nor increases ,it remains in the same volume because of its crystal structure
Sobirjon
100g of water is mixed with 60g of a liquid of relative density 1.2.assuming no changes in volume occurred,find the average relative density of the mixture. take density of water as 1g/cm3 and density of liquid as 1.2g/cm3
Lila
Sorry what does it means"no changes in volume occured"?
Sobirjon
volume can be the amount of space occupied by an object. But when an object does not change in shape it will still occupy the same space. Thats why the volume will still remain the same
Ben
Most soilds expand when heated but if it changes state at 0C it will have less volume. Ice floats because it is less dense ie a larger mass per unit volume.
Richard
how to calculate velocity
Okwethu Reply
v=d/t
Emeka
his about the speed?
Villaflor
how about speed
Villaflor
v=d/t
Nisha
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Jacob Reply
Mine is good. How about you?
Chase
Hi room of engineers
lawan Reply
yes,hi sir
Okwethu
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akinmeji
Hello
Mishael
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Jerry
hi
Sakhi
hi
H.C
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akinmeji
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Ajayi
good morning ppl
ABDUL
If someone has not studied Mathematics enough yet, should theu study it first then study Phusics or Study Basics of Physics whilst srudying Math as well?
Riaz Reply
whether u studied maths or not, it is advisable to start from d basics cuz it is essential to know dem
Nuru
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Badmus
wow, you got this w/o knowing math
Thomas
I guess that's it
Thomas
later people
Thomas
mathematics is everywhere
Anand
thanks but dat doesn't mean it is good without maths @Riaz....... Maths is essential in sciences particularly wen it comes to PHYSICS but PHYSICS must be started from the basic which may also help in ur mathematical ability
Nuru
A hydrometer of mass 0.15kg and uniform cross sectional area of 0.0025m2 displaced in water of density 1000kg/m3.what depth will the hydrometer sink
Lila
16.66 meters?
Darshik
16.71m2
aways
,i have a question of let me give answer
aways
the mass is stretched a distance of 8cm and held what is the potential energy? quick answer
aways
oscillation is a to and fro movement, it can also be referred to as vibration. e.g loaded string, loaded test tube or an hinged door
Olatunji Reply
what property makes the magnet to break?
Akshaya Reply
difference between charge and force
uwadiae Reply
charges: these are groups of ions which can be positive or negative. while force is said to be push or pull of an object. Generally, charge deals with ions while force deals with particles.
akinmeji
define oscillation
Munachukwu
what is up thrust
Lila Reply
upward force exerted by water on a body.
Matthew
A hydrometer of mass 0.15kg and of uniform cross sectional area 0.0025m2 displaced in water of density 1000kg/m3.what depth will the hydrometer sink
Lila
archimedes principle
Nicholas
mg=p(area x height)g
Nicholas
solve for height
Nicholas
what is matter
daniel Reply
Anything that has mass. And it occupies space. So it has volume.
wenhe
stages of matter.
daniel
States of matter are solid liquid gas and plasma
wenhe
what are Newtown's law
Lila
An object as rest will remain at rest or in motion will remain at motion. Force is mass times acceleration. And a force will have equal and opposite reaction.
wenhe
do we have any thing like plasma as a states of matter
daniel
no
Nicholas
Plasma is a state of matter. It's much later on. The sun for example is not a gas ball. Its plasma.
wenhe
why is plasma a state of matter
Lila
In lower grades you are taught that there are 3 states of matter. But later on, you'll learn that if you eat gas enough. It turns to plasma
wenhe
Heat*
wenhe
yes we have plasma as a state of matter
akinmeji
it is anything that occupie space and has mass
Anand
I never head of that before
daniel
Anything that occupies space and has mass is matter.
wenhe
what is the difference between vapor and gas
Lila
Plasma is best described as an ionized gas because it is made up of positively and negatively charged particles.
akinmeji
Vapour is gas.
wenhe
Aside plasma, we also have Bose- Einstein. this is also another state of matter
akinmeji
was bose Einstein discovered by Albert Einstein
Lila
We have like 6 states or more. But those are newly discovered.
wenhe
OK, thanks at list I have experience about that one now.
daniel
Einstein​ predicted it
wenhe
With another person
wenhe
what are the other states
Lila
Fermionic condensate
wenhe
OK what is Albert Einstein
daniel
And maybe more. I just rmb those. Tbh for school you only need to know 4.
wenhe
Albert Einstein​is the name of a scientist
wenhe
OK
daniel
what is the physical state of water and salt
Lila
can I ask off topic question?
Kristine
Both are matter. So can theoretically exist in all those states. But in room temperature, water is liquid and salt is solid.
wenhe
Yes
wenhe
Its about precalculus
Kristine
I'm not very good at maths. But if I can answer... Lol
wenhe
The reflector of a radiotelescope is in the shape of a parabola revolve its axis, if the diameter of the reflector is 400ft. above the vertex of the parabola, what should be the depth of reflector?
Kristine
Are there any other factors given?
wenhe
Or just that?
wenhe
matter is merely energy condensed to a slow vibration
Vashist
Cuz with those factors, I can't solve it.
wenhe
none
Kristine
Well. There must be another factor given or something. Like an equation of the parabola. Or else I can't solve it
wenhe
explain why water and salt are compounds
Lila
That's chem. But both water and salt are made of more than 1 element. So they are compounds.
wenhe
Compound meaning 2 or more things added together.
wenhe
salt chemically is combination of sodium n chloride whereas water is oxygen n hydrogen
Friday
deficiency of vitamin E cause ?
Friday
I don't know if this is the equation or formula your looking for; (x-h)²=4c(y-k) (x-h)²=-4c(y-k) (y-k)²=-4c(x-h) (y-k)²=4c(x-h)
Kristine
If the parabola opens downward, the equation will be (x-h)²=-4c(y-k). If the parabola opens upward, (x-h)²=4c(y-k). If the parabola opens to the left it will be -4c and if the parabola opens to the right it will be 4c
Kristine
Practice Key Terms 4

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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