Optics 2: REFRACTION & LENSES. REFRACTION Refraction: is the bending of waves because of the change of speed of a wave when it passes from one medium

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Optics 2: Optics 2: REFRACTION & REFRACTION &

LENSES LENSES

REFRACTION

Refraction: is the bending of waves because of the change of speed of a wave when it passes from one medium to another.

The greater the difference in the speed of the waves, the greater the bending of the waves.


Normal: the line perpendicular to the surface.

Incident ray: is the ray of light that strikes the surface.

Reflected ray: is the ray of light that bounces off the surface.

Refracted ray: is the ray of light that enters the material.

Point of Incidence: is the point at which the light strikes the surface.

Angle of Incidence: the angle between the incident ray and the normal to the surface.

Angle of Reflection: the angle between the reflected ray and the normal to the surface.

Angle of Refraction: the angle between the refracted ray and the normal to the surface.

When a ray of light travels from a less dense medium to a denser medium; the refracted ray moves towards the normal to the surface.

water

Incident ray

Refracted ray

air

When a ray of light travels from a denser medium to a less dense medium; the refracted ray moves away from the normal to the surface.

Refracted ray

Incident ray

air

water


The amount of refraction depends upon:

1. The material through which the light travels.

2. The wavelength of light. The shorter the wavelength, the greater the refraction.

Violet light has a smaller wavelength than the other colors in the visible spectrum. Therefore, it is refracted the most.

THE LAW OF REFRACTIONTHE LAW OF REFRACTION

medium inlight of speedv

vacuum inlight of speedc

refraction of index

nv

cn

The greater the value of n, the greater the refraction.

Medium Refractive Index

Vacuum 1.00

Air 1.0003

Water 1.33

Ethanol 1.36

Crown glass 1.52

Quartz 1.54

Flint Glass 1.62

Diamond 2.42

Example #1Example #1

The index of refraction of The index of refraction of water is 1.33. Calculate the water is 1.33. Calculate the speed of light in waterspeed of light in water..

smsm

n

c

sm

nv

cn

/..

/3v

/3c

1.33

88

8

10262331

10

10


Find the speed of light in a) Find the speed of light in a) ethanol b) quartz c) flint ethanol b) quartz c) flint glass.glass.

smsm

n

c

smsm

n

c

smsm

n

c

smv

cn

/..

/3v---GlassFlint

/..

/3v---Quartz

/..

/3v---Ethanol

/3c

88

88

88

8

10861611

10

10951541

10

1022361

10

10


The speed of light in plastic The speed of light in plastic is 2 x 10is 2 x 1088 m/s. What is the m/s. What is the refractive index of the refractive index of the plastic?plastic?

5110

10

10

10

8

8

8

8

./2

/3

/2

/3c

?

sm

sm

v

cn

smv

sm

n

SNELL’S LAWSNELL’S LAW

normal the and ray refracted the between angle the

2 medium of index refractive

normal the and rayincident the between angle the

1 medium of index refractive

sinsin

2

2

1

1

2211

θ

n

θ

n

θnθn

Example #4Example #4A light ray of wavelength 589 nm traveling A light ray of wavelength 589 nm traveling through air strikes a smooth, flat slab of through air strikes a smooth, flat slab of crown glass (refractive index 1.52) at an crown glass (refractive index 1.52) at an angle of 30angle of 3000 to the normal. Find the angle to the normal. Find the angle of refraction.of refraction.

30

Incident ray

Refracted ray

Air=1.00

Glass=1.522θ

?

.1

3

.1

glass

glass

air

air

θ

n

θ

n

52

0

000

00

1

0

219521

30

521

30

52130001

..

sinsin

.

sinsin

sin.sin.

sinsin

glass

glass

glass

glassglassairair

θ

θ

θ

θnθn


Light in air is incident upon a Light in air is incident upon a piece of crown glass at an piece of crown glass at an angle of 45angle of 4500. What is the . What is the angle of refraction?angle of refraction?

?

.1

.1

2

2

0

1

1

52

45

00

θ

n

θ

n

00

1

2

0

2

2

2211

727521

45

521

45

52145001

..

sinsin

.

sinsin

sin.sin.

sinsin

θ

θ

θ

θnθn


A block of unknown material is A block of unknown material is submerged in water (refractive submerged in water (refractive index is 1.33). Light in the water is index is 1.33). Light in the water is incident on the block at an angle of incident on the block at an angle of 313100. The angle of refraction in the . The angle of refraction in the block is 27block is 2700. What is the index of . What is the index of refraction of the unknown refraction of the unknown material?material?

31

Incident ray

Refracted ray

Water=1.33

unknown

27

0

2

2

0

1

1

27

31

33

θ

n

θ

n

?

.1

52127

31331

2731331

2

2

2211

.sin

sin.

sinsin.

sinsin

n

n

θnθn

Critical AngleCritical Anglethe incident angle that causes the incident ray to the incident angle that causes the incident ray to

refract along the boundary between the two refract along the boundary between the two surfaces.surfaces.

RR = 90 = 90°° Refracted ray

Incident ray

air

water



When the angle of incidence is less When the angle of incidence is less than the critical angle; normal than the critical angle; normal

refraction takes place.refraction takes place.

Ri

ci

θθ

θθ

Rθ

Refracted ray

Incident ray

air

water

iθ

When the angle of incidence is When the angle of incidence is equal to the critical angle; the equal to the critical angle; the

refracted ray is on the boundary.refracted ray is on the boundary.

090

R

ci

θ

θθRefracted ray

Incident ray

air

water

090

iθ

When the angle of incidence is greater than When the angle of incidence is greater than the critical angle; the critical angle; total internal reflectiontotal internal reflection

occurs. There is no refracted ray.occurs. There is no refracted ray.

)Reflection ofLaw (

Ray Refracted No

ri

ci

θθ

θθ

Incident ray

air

water

iθReflected ray

rθ

TOTAL INTERNAL REFLECTION TOTAL INTERNAL REFLECTION CONDITIONSCONDITIONS

Light is going from a denser Light is going from a denser medium to a less dense medium.medium to a less dense medium.

Light is incident at an angle Light is incident at an angle greater than the critical angle.greater than the critical angle.

TOTAL INTERNAL REFLECTION TOTAL INTERNAL REFLECTION OUTCOMESOUTCOMES

There is no refracted ray.There is no refracted ray.There is only a reflected ray that There is only a reflected ray that stays in the denser medium.stays in the denser medium.Total internal reflection and Total internal reflection and proper faceting causes diamonds proper faceting causes diamonds and crystal glass to sparkle and crystal glass to sparkle brilliantly.brilliantly.

EFFECTS OF REFRACTIONEFFECTS OF REFRACTIONMiragesMirages

Lingering daylight after the sun is Lingering daylight after the sun is below the horizon.below the horizon.

An object in water, appears to be An object in water, appears to be closer than it really is.closer than it really is.

Spoon appears bent when placed in a Spoon appears bent when placed in a glass of water.glass of water.

LENSESLENSESLenses are curved transparent Lenses are curved transparent objects. They form images through objects. They form images through refraction of light. They are usually refraction of light. They are usually made from plastic or glass.made from plastic or glass.

Two main types of lenses:Two main types of lenses:

1.1. Convex Convex

2. Concave2. Concave



Convex LensConvex Lens

Convex LensConvex Lens

C F C F

Focus or Focal Point:Focus or Focal Point: is the point on the principal is the point on the principal axis where the parallel rays all come together axis where the parallel rays all come together after passing through the lens.after passing through the lens.

The distance between the focus and the center The distance between the focus and the center of the lens is called the of the lens is called the focal length.focal length.

C C

RULES FOR DRAWING CONVEX LENS RULES FOR DRAWING CONVEX LENS RAY DIAGRAMSRAY DIAGRAMS

Any ray parallel to the optical axis will be Any ray parallel to the optical axis will be refracted through F.refracted through F.

C F C F


Any ray passing through F will be refracted Any ray passing through F will be refracted parallel to the principal axis.parallel to the principal axis.

C F C F


Any ray passing through O continues Any ray passing through O continues straight throughstraight through

C F C F

When object is between F and OWhen object is between F and O

Image is VirtualImage is Virtual

EnlargedEnlarged

And UprightAnd Upright

Used in a magnifying glassUsed in a magnifying glass

C F C F

When object is at FWhen object is at F

No image is formedNo image is formed

Used in a telescope.Used in a telescope.

C F C F

When object is between F and CWhen object is between F and C

Image is enlarged, real, and invertedImage is enlarged, real, and inverted

Used in optical instruments.Used in optical instruments.

C F C F

When object is at CWhen object is at C

Image is same size, real, and invertedImage is same size, real, and inverted


C F C F

When object is beyond CWhen object is beyond C

Image is reduced, real, and invertedImage is reduced, real, and inverted


C F C F

Concave LensConcave Lens

Concave LensConcave Lens

C F C F

RULES FOR DRAWING CONCAVE LENS RULES FOR DRAWING CONCAVE LENS RAY DIAGRAMSRAY DIAGRAMS

Any ray parallel to the optical axis appears Any ray parallel to the optical axis appears to be refracted through F.to be refracted through F.

C F C F

RULES FOR DRAWING CONCAVE LENS RULES FOR DRAWING CONCAVE LENS RAY DIAGRAMSRAY DIAGRAMS

Any ray passing through O continues Any ray passing through O continues straight throughstraight through

C F C F

Object is placed between F and the LensObject is placed between F and the Lens

C F C F

Image is reduced, virtual, and uprightImage is reduced, virtual, and upright

Used in telescopes and cameras.Used in telescopes and cameras.

Object is placed at FObject is placed at F

C F C F



Object is placed between F and CObject is placed between F and C

C F C F



Object is placed at CObject is placed at C

C F C F



Object is placed beyond CObject is placed beyond C

C F C F



Lens EquationLens Equation

f is negative if lens is concavef is negative if lens is concave

ddii is negative if image is virtual, if image is is negative if image is virtual, if image is

formed on the same side as the objectformed on the same side as the object

ddii is positive if image is real, if the image is is positive if image is real, if the image is

formed on the opposite side as the objectformed on the opposite side as the object

hhii is negative if image is inverted is negative if image is inverted

M < 1 the image is smaller than the objectM < 1 the image is smaller than the object

M > 1 the image is larger than the objectM > 1 the image is larger than the object


An object is 32 cm to the left of a An object is 32 cm to the left of a convex lens of 8 cm focal length. convex lens of 8 cm focal length. Use the equation to locate the Use the equation to locate the image.image.

?

i

o

d

cmd

cmf

32

8

cmd

d

d

d

d

ddf

i

i

i

i

i

io

7103

32

32

31

32

141

32

1

8

11

1

32

1

8

1

111

.


A 20 cm high object is placed 10 A 20 cm high object is placed 10 cm in front of a concave lens with cm in front of a concave lens with a focal length of 10 cm. Find the a focal length of 10 cm. Find the image distance, magnification, image distance, magnification, and height. Describe the image. and height. Describe the image. Draw a ray diagram.Draw a ray diagram.

?

?

?

m

h

d

cmh

cmd

cmf

i

i

o

o

20

10

10

virtualcmd

d

d

d

ddf

i

i

i

i

io

.....5

10

21

10

1

10

11

1

10

1

10

1

111

smaller

cm

cm

d

dm

o

i

......2

110

5

upright......cmhcm

h

h

hm

i

i

o

i

10202

1

virtualcmd i .....5

smallerm ...... 2

1

C F C F

uprightcmhi .....10


An object is placed to the left of a An object is placed to the left of a 25 mm focal length convex lens, 25 mm focal length convex lens, so that its image is the same size so that its image is the same size as the object. What is the image as the object. What is the image and object location?and object location?

1

25

m

d

d

cmf

i

o

?

?

mmd

d

dd

ddf

o

o

oo

io

50

25

12

11

25

1

111

oi

o

i

dd

d

d

1


An object is placed 30 cm in front of a An object is placed 30 cm in front of a converging lens with a focal length of 10 cm. converging lens with a focal length of 10 cm. Find the image distance, magnification, and Find the image distance, magnification, and describe the image.describe the image.

?

?

m

d

cmd

cmf

i

o 30

10

realcmd

d

d

d

d

ddf

i

i

i

i

i

io

....15

30

21

30

131

30

1

10

11

1

30

1

10

1

111

invertednegativeh

h

hm

smaller

m

i

o

i

.......

.

......

50

5030

15

LASERLASER

Is a device that produces Is a device that produces an intense, nearly an intense, nearly parallel beam of parallel beam of coherent light. They are coherent light. They are very high energy light very high energy light sources.sources.


EYE DEFECTSEYE DEFECTSFarsightednessFarsightedness: person cannot focus : person cannot focus near by objects. Far away objects appear near by objects. Far away objects appear clear while closer objects appear blurred. clear while closer objects appear blurred. The person has an abnormality called The person has an abnormality called hyperopia.hyperopia.

The image is focused behind the retina.The image is focused behind the retina.

CORRECTION OF FARSIGHTEDNESSCORRECTION OF FARSIGHTEDNESS

EYE DEFECTSEYE DEFECTSNearsightednessNearsightedness: person cannot focus : person cannot focus far away objects. Near by objects appear far away objects. Near by objects appear clear while objects further away appear clear while objects further away appear blurred. The person has an abnormality blurred. The person has an abnormality called called myopia.myopia.

The image is focused in front of the The image is focused in front of the retina.retina.

CORRECTION OF NEARSIGHTEDNESSCORRECTION OF NEARSIGHTEDNESS

Documents

Optics 2: REFRACTION & LENSES. REFRACTION Refraction: is the bending of waves because of the change of speed of a wave when it passes from one medium