TOTAL INTERNAL REFLECTIONand the

CRITICAL ANGLE

TOTAL INTERNAL REFLECTION

The inside surface of water or a glass block can act like a mirror.

Total Internal Reflection

Occurs when light reflects off of the inside wall of a denser medium (higher index of refraction)

Total Internal Reflection

Recall:• When light passes

from a dense material into a less dense medium, light reflects away from the normal

Total Internal Reflection

As the angle of incidence increases, the angle of refraction increases

Critical Angle

• At a certain angle, the refracted ray follows a path exactly along the surface of the dense medium

• When the angle of refraction is at 90o the incident angle is called the “critical angle”

Critical Angle

• Critical angle is the angle at which the refracted ray is at 90o

Critical Angle determines Total Internal Reflection

• If the incident ray is increased beyond the critical angle, the light is no longer refracted

• Instead, it is reflected back inside the medium• This is called “total internal reflection”• When incident angle is greater than the critical

angle (i>C), there is no refracted rays, all emergent rays are internally reflected

TOTAL INTERNAL REFLECTION

A light ray hits the inside face of a semicircular block.

Total Internal Reflection• A light ray hits the inside face of a

semicircular block as follows.• What will happen as the angle of incidence

increases?airglass

incident ray reflected ray

refracted ray

Total Internal Reflection

airglass

incident ray reflected ray

refracted ray

Total Internal Reflection

airglass

incident ray reflected ray

refracted ray

Total Internal Reflection

airglass

incident ray reflected ray

refracted ray

Total Internal Reflection

airglass

incident ray reflected ray

Total Internal Reflection

What happened?

airglass

incident ray reflected ray

refracted ray

airglass

incident ray reflected ray

Total Internal ReflectionAt a small angle of incidence:• Incident ray splits into refracted & reflected• Angle of refraction < 90o

• Angle of reflection = angle of incidence

airglass

incident ray reflected ray

refracted ray

Total Internal ReflectionAs the angle of incidence increases, the angle of refraction increases until…

airglass

incident ray reflected ray

refracted ray

Total Internal Reflection• Angle of refraction is at 90o, parallel to the

surface of the medium• At this point the angle of incidence = critical

angle (C)• Angle of incidence = C when angle of

refraction = 90o

airglass

incident ray reflected ray

refracted ray

Total Internal Reflection• As the angle of incidence increase beyond the

critical angle (>C), there is no more refracted ray• All emergent rays are totally reflected inside the

medium = Total Internal Reflection (TIR)

airglass

incident ray reflected ray

Conditions for TIR & Critical Angle• Light is traveling slower in the first medium than in the

second medium (v1 < v2) • Thus light is moving from medium of higher refractive

index to one of lower refractive index (n1 > n2)• Critical angle (C) is defined when the angle of refraction

is 90o to the normal (2 = 90o)• TIR occurs when angle of incidence is larger than the

critical angle (1 > C)

airglass

incident ray reflected ray

Calculating Critical Angle• Snell’s Law: n1 sin1 = n2 sin2

• Critical angle C = 1 thus solve for 1

At the critical angle, the refracted ray is a 90o = 2

• n1 sin1 = n2 sin90o (sin90o = 1)• n1 sin1 = n2 1 • n1 sin1 = n2

Rearrange equation to get: • sin1 = n2 / n1 1 = sin-1 (n2 / n1)

If medium 2 = air, then n2 = 1 1 = sin-1 (1 / n1)• C = sin-1 (1 / n1)

airglass

C = 1 r

refracted ray

reflected rayincident ray

R = 2

TOTAL INTERNAL REFLECTION• critical angles of different materials

Medium Refractive index

Critical angle

1.50–1.70 30–42GlassWaterPerspexDiamond

1.33 491.5 422.42 24

TIR in DiamondsSparkling is due to:1. Cut of diamond faces2. High index of refraction which means a very

small critical angle (n = 2.42, C = 24.4°)Incident rays can undergo multiple TIR inside a diamond before exiting the top of the diamond.

TIR in Fiber Optics

• Technology that uses light to transmit information along glass cables

• Fibre optics cable is made up of a bundle of glass fibres

• Sample materials: high-purity glass, Lucite

TIR in Fiber Optics

• Fiber optics cable has a small critical angle, thus a high refractive index

• Light entering will always have an angle of incidence greater than the critical angle

TIR in Fiber OpticsLight does not escape as it travels along the

fiber optics cable because it undergoes total internal reflection

http://ecademy.agnesscott.edu/~asullivan/Pictures/TIR.jpg

TIR in Fiber Optics

TIR in Fiber OpticsAdvantages of Fiber Optics• Signals are not affected by

electrical storms.• Cable is smaller and lighter

than copper cable.• More signals can be carried

over longer distances.

• An endoscope is a flexible fibre optic cable through which internal cavities can be viewed.

• Routinely used in the diagnosis of cancer and ulcers.

Fiber Optics in Endoscopes

http://marylandcolonoscopy.com/wp-content/uploads/2010/05/CDR0000433287.jpg

Gastroscopy

• Endoscopy examination of a stomach

• Endoscope inserted through the patient's mouth and fed down through throat

• Image obtained by endoscope is projected onto a screen

• A surgical instrument for obtaining a biopsy has been fed through the endoscope cable and controlled by the doctor

http://www.sciencephoto.com/media/272329/enlarge

Digestive Endoscopy

•http://www.sciencephoto.com/media/126772/enlarge

Diagnosing Cancer

Doctors using a fibroscope to investigate suspected lung cancer in a patient's bronchi (airways). A fibroscope is a flexible fibre optic cable with a camera on the end, similar to an endoscope.

Photographed in Belgium. http://www.sciencephoto.com/media/137299/enlarge

TIR in Prisms • Plane mirror = glass + silvered surface• multiple reflection inside the glass• multiple images formed• nuisance in optical instruments

glass shee

tsilvered surface

I1 I2 I3Object

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Prisms• If light rays strike the inside

face at an angle > 42, glass prism behaves like a perfect mirror.

• Prisms are more useful than mirrors because it reflects almost 100% of light internally. Mirrors lose some light through absorption.

• Emergent can be 90o or 180o relative to incident ray.

Prisms in Periscopes• Instrument for observation from a concealed

position• Uses two triangular prisms (or mirrors) to change

direction of light by 90o • Used in war and in submarines

In War

• Land Periscope used by a German Staff Officer during 1914

• Lens was sixteen feet above the ground, protecting the officer from enemy observation.

http://www.historyofwar.org/Pictures/pictures_periscope_land.html

http://www.history.navy.mil/photos/images/i02000/i02649.jpg

Submarines

• American submarine commander inspects the horizon through the periscope (1942)

http://mg-34.com/index.php/photo-19391945/1574-the-commander-of-the-submarines-periscope-looks

http://web.mst.edu/~rogersda/military_service/periscopes.jpg

Submarines carry all kinds of extendable devices in their sail which allow them to sense above the ocean's surface. This shows a deployed periscope (on left) and other electronic surveillance and communications probes.

Prisms in Binoculars• Uses 2 prisms to change direction of light

by 180o

filmmirror

Prisms in Single-lens Camera

• A five-sided ‘pentaprism’ reflects light from the mirror into the eye.

Prisms and Retro-reflectors

• Device that returns incident light back in exactly the same direction from which it came

• Applications in bike reflectors, reflective strip on clothing, road signs

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Practice Problems

A ray of light traveling in the direction EO in air enters a rectangular block at an angle of incidence = 30. The resulting angle of refraction = 18.

a. Find the refractive index n of the block.

30

18

E

O

Practice ProblemsGiven: 1 = 30, 2 = 18, n1 (air) = 1

Required: n2 (block)

Analysis: n1 sin1 = n2 sin2

Solution: 1 x sin 30 = n2 sin 18 n2 = sin 30 / sin 18 = 1.62

Phrase: The index of refraction of the block is 1.62

30

18

E

O

Practice Problemsb. Find the critical angle C for the block.

30

18

E

O

Recall: If medium 2 = air, then

C = 1 = sin-1 (1 / n1)

Practice Problemsb. Find the critical angle C for the block.

Given: 2 = 90, n2 (air) = 1, n1 (block) = 1.62

Required: 1

Analysis: n1 sin1 = n2 sin2

Solution: 1.62 x sin 1 = 1 x sin 90 sin 1 = 1 / 1.621 = sin-1 (1 / 1.62) = 38.1

Phrase: The critical angle of the block is 38.1

30

18

E

O

Recall: If medium 2 = air, then

C = 1 = sin-1 (1 / n1)

30

A B

CD

Practice Problemsc. If the ray is incident on surface BC, from

which surface and at what angle will the ray leave the block?

30

A B

CD

Practice Problemsc. If the ray is incident on surface BC, from which surface and at

what angle will the ray leave the block?

Given: 1 = 60n1 (air) = 1n2 (block) = 1.62

Required: 2

Analysis: n1 sin1 = n2 sin2

Solution: 1 x sin 60 = 1.62 x sin 2

sin 2 = 1 x sin 60 / 1.622 = sin-1 (1 x sin 60 / 1.62) = 32.3

Practice Problemsc. If the ray is incident on surface BC, from which surface and

at what angle will the ray leave the block?

Recall:Angle of incidence = 60o

Angle of refraction = 32.3o

Critical angle = 38.1o

30

A B

CD

32.357.732.3

60

Draw refracted ray2.

Measure angle of ray2 hitting block. Angle is greater than critical angle of 38.1o thus ray3 will reflect. Draw ray3 following Law of Reflection.

Measure angle of ray3. Since it is the same angle as ray2, it will refract out at the same angle. Thus ray4 refracts at 60o from surface AD.

Practice ProblemsWhich of the following angles is the critical angle of glass?

A B

DC

Practice ProblemsWhich of the following angles is the critical angle of glass?

A B

DC

• A horizontal light ray hits a prism as shown.

• What happens to the light ray?

Practice Problems

45

A B C

• A horizontal light ray hits a prism as shown.

• What happens to the light ray?

Practice Problems

45

A B C