2-Total Internal Reflection - PPT slides

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TOTAL INTERNAL REFLECTION

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Total Internal Reflection

Occurs when light reflects off of the inside wall of a

denser medium (higher

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Recall:

▪ _{When light passes}

from a dense material into a less dense

medium, light reflects

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As the angle of incidence

increases, the angle of refraction

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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

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Critical Angle

▪ _{Critical angle} _{is the angle at which}

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Critical Angle determines

▪ 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

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Total Internal Reflection

▪ _{A light ray hits the inside face}

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▪ _{A light ray hits the inside face of a}

semicircular block as follows.

▪ _{What will happen as the angle of incidence}

increases?

air glass

incident ray reflected ray

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air glass

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Total Internal Reflection

air glass

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air glass

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air glass

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What

happened? air_glass

refracted ray

air glass

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Total Internal Reflection

▪ _{At a small angle of incidence:}

▪ _{Incident ray splits into refracted & reflected}

▪ _{Angle of refraction < 90}o

▪ _{Angle of reflection = angle of incidence}

air glass

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▪ _{As the angle of incidence increases, the}

angle of refraction increases until…

air glass

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Total Internal Reflection

▪ _{Angle of refraction is at 90}o_{, 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

air glass

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▪ _{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)

air glass

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▪ 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)

air glass

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▪ _{Snell’s Law:}_n₁ _sin₁ _{= n}₂ _sin₂

▪ _{Critical angle}_{C =}₁ _{thus solve for}₁

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

▪ n₁ sin₁ = n₂ sin90o ₍_sin₉₀o _{= 1}₎

▪ _n₁ _sin₁ _{= n}₂ ₁ ▪ n₁ sin₁ = n₂

Rearrange equation to get:

▪ sin₁ = n₂ / n₁

▪ ₁ _{= sin}-1 _(n

2 / n1)

▪ _{C = sin}-1 _(n

2 / n1)

If medium 2 = air, then n₂ = 1

▪ C = sin-1 ₍₁ _{/ n} 1)

air glass

C = ₁ r

refracted ray

reflected ray incident ray

R = ₂

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Critical angles of different materials

Medium Refractive Index Critical Angle

Glass 1.50-1.70 30o-42o

Water 1.33 49o

Perspex 1.5 42o

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TIR in Diamonds

Sparkling is due to:

1. Cut of diamond faces

2. High index of refraction which means a very small critical angle (n = 2.42, C = 24.4°)

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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}

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TIR in Fiber Optics

▪ _{Fiber optics cable has a small critical angle,} thus a high refractive index

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TIR in Fiber Optics

Light does not escape as it travels along the fiber optics cable because it undergoes total internal reflection

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TIR in Fiber Optics

Advantages of Fiber Optics

▪ _{Signals are not affected by}

electrical storms.

▪ _{Cable is smaller and lighter}

than copper cable.

▪ _{More signals can be carried}

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Fiber Optics in Endoscopes

▪ _{An endoscope is a}

flexible fibre optic cable through

which internal cavities can be viewed.

▪ _{Routinely used in}

the diagnosis of cancer and ulcers.

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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

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Digestive Endoscopy

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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.

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TIR in Prisms

▪ _{Plane mirror = glass + silvered surface}

▪ _{multiple reflection inside the glass}

▪ _{multiple images formed}

▪ _{nuisance in optical instruments}

glass

sheet silvered surface

I

₁

I

₂

I

₃

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45 45 45 45 45 45

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 ray can be 90} _or

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Prisms in Periscopes

▪ _{Instrument for observation from a concealed}

position

▪ _{Uses two triangular prisms (or mirrors) to}

change direction of light by 90

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In War

▪ _{Land Periscope}

used by a

German Staff Officer during 1914

▪ _{Lens was sixteen}

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Submarines

▪ _American

submarine commander inspects the horizon

through the periscope (1942)

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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

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Prisms in Binoculars

▪ _{Uses 2 prisms to change direction of light by}

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film mirror

Prisms in Single-lens Camera

▪ _{A five-}_{sided ‘pentaprism’ reflects light from}

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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

45

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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}

of the block.

30

18

E

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a. Find the refractive index of the block.

Given: ₁ = 30, ₂ = 18, n₁ (air) = 1

Required: n₂ (block)

Analysis: n₁ sin₁ = n₂ sin₂

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

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Practice Problems

▪ _{b. Find the critical angle C for the block.}

30

18

E

O

Recall: If medium 2 = air, then

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b. Find the critical angle C for the block.

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

Required: ₁

Analysis: n₁ sin₁ = n₂ sin₂

Solution:

1.62 x sin ₁ = 1 x sin 90 sin ₁ = 1 / 1.62

₁ = 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 / n 1)

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30

A

B

C

D

Practice Problems

▪ _{c. If the ray is incident on surface BC, from}

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30

A

B

C

D

Practice Problems

Given: ₁= 60 n₁ (air) = 1

n₂ (block) = 1.62

Required: ₂

Analysis:

n1 sin1 = n2 sin2

Solution:

1 x sin 60 = 1.62 x sin ₂ sin ₂= 1 x sin 60 / 1.62

₂= sin-1 ₍_{1 x sin}₆₀ _/ _{1.62) = 32.3}

▪ _{c. If the ray is incident}

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c. 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

C

D

32.3 57.7 32.3 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}_.

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Practice Problems

▪ _{Which of the following angles is the critical}

angle of glass?

A B

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Practice Problems

▪ _{Which of the following angles is the critical}

angle of glass?

A B

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▪ _{A horizontal light ray hits a}

prism as shown.

▪ _{What happens to the light}

ray?

Practice Problems

45

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▪ _{A horizontal light ray hits a}

prism as shown.

▪ _{What happens to the light}

ray?

Practice Problems

45