chapter 26. the refraction of light: lenses and optical instruments

Chapter 26. The Refraction of Light: Lenses and Optical Instruments

26.1. The Index of Refraction26.2. Snell's Law and the Refraction of Light26.5. The Dispersion of Light: Prisms and Rainbows26.3. Total Internal Reflection26.4. Polarization and the Reflection and Refraction of Light26.6. Lenses26.7. The Formation of Images by Lenses26.8. The Thin-Lens Equation and the Magnification Equation26.10. The Human Eye 

26.1 The Index of Refraction

sm1000.3 8cLight travels through a vacuum at a speed

Light travels through materials at a speed less than its speedin a vacuum.

DEFINITION OF THE INDEX OF REFRACTION

The index of refraction of a material is the ratio of the speed of light in a vacuum to the speed of light in the material:

v

cn

material in thelight of Speed

in vacuumlight of Speed

26.1 The Index of Refraction

Table 26.2 I ndices of Refraction n of Crown Glass at Various Wavelengths

Approximate Color Wavelength in Vacuum (nm) Index of Refraction, n Red 660 1.520 Orange 610 1.522 Yellow 580 1.523 Green 550 1.526 Blue 470 1.531 Violet 410 1.538

Index of Refraction

The index of refraction n in the different materials is different for the same wave length of lights.

  The index of refraction n in the same

materials is different for different wave length of lights.

26.2 Snell’s Law and the Refraction of Light

SNELL’S LAW OF REFRACTION

When light travels from a material withone index of refraction to a material witha different index of refraction, the angleof incidence is related to the angle ofrefraction by

2211 sinsin nn

SNELL’S LAW

If n1>n2, then 1<2  

If n1<n2, then 1>2

26.2 Snell’s Law and the Refraction of Light

Example 1 Determining the Angle of Refraction

A light ray strikes an air/water surface at anangle of 46 degrees with respect to thenormal. Find the angle of refraction whenthe direction of the ray is (a) from air towater and (b) from water to air.

26.2 Snell’s Law and the Refraction of Light

54.0

33.1

46sin00.1sinsin

2

112

n

n (a)

(b)

332

96.0

00.1

46sin33.1sinsin

2

112

n

n

742

Check Your Understanding 1 The drawing shows three layers of liquids, A, B, and C, each with a different index of refraction. Light begins in liquid A, passes into B, and eventually into C, as the ray of light in the drawing shows. The dashed lines denote the normals to the interfaces between the layers. Which liquid has the smallest index of refraction?

26.2 Snell’s Law and the Refraction of Light

APPARENT DEPTH

Example 2 Finding a Sunken Chest

The searchlight on a yacht is being used to illuminate a sunkenchest. At what angle of incidence should the light be aimed?

26.2 Snell’s Law and the Refraction of Light

69.0

00.1

31sin33.1sinsin

1

221

n

n

441

313.30.2tan 12

26.2 Snell’s Law and the Refraction of Light

1

2

n

ndd

Apparent depth,observer directlyabove object

26.2 Snell’s Law and the Refraction of Light

Conceptual Example 4 On the Inside Looking Out

A swimmer is under water and looking up at the surface. Someoneholds a coin in the air, directly above the swimmer’s eyes. To theswimmer, the coin appears to be at a certain height above the water. Is the apparent height of the coin greater, less than, or the same as its actual height?

26.2 Snell’s Law and the Refraction of Light

THE DISPLACEMENT OF LIGHT BY A SLAB OF MATERIAL

26.3 Total Internal Reflection

Total Internal Reflection 

All the incident light is reflected back into the medium from which it came, a phenomenon called total internal reflection.

26.3 Total Internal Reflection

When light passes from a medium of larger refractive index into oneof smaller refractive index, the refracted ray bends away from the normal.

Critical angle21

1

2 sin nnn

nc

Conditions of total internal reflection:•Light from a medium of larger refractive index into one of smaller refractive index.•Incident angle larger than critical angle

26.3 Total Internal Reflection

Example 5 Total Internal Reflection

A beam of light is propagating through diamond and strikes the diamond-airinterface at an angle of incidence of 28 degrees. (a) Will part of the beamenter the air or will there be total internal reflection? (b) Repeat part (a) assuming that the diamond is surrounded by water. n=2.42 for diamond, n=1.33 for water

26.3 Total Internal Reflection

4.2442.2

00.1sinsin 1

1

21

n

nc(a)

(b) 3.3342.2

33.1sinsin 1

1

21

n

nc

26.3 Total Internal Reflection

Conceptual Example 6 The Sparkle of a Diamond

The diamond is famous for its sparkle because the light coming fromit glitters as the diamond is moved about. Why does a diamond exhibit such brilliance? Why does it lose much of its brilliance whenplaced under water?

26.3 Total Internal Reflection

26.3 Total Internal Reflection

26.4 Polarization and the Reflection and Refraction of Light

1

2tann

nB Brewster’s law

For incident angles other than 0°, unpolarized light becomes partially polarized in reflecting from a nonmetallic surface.

 • There is one special angle of incidence,

called Brewster angle, at which the reflected light is completely polarized parallel to the surface, the refracted ray being only partially polarized.

9

A person sitting at the beach is wearing a pair of Polaroid sunglasses and notices little discomfort due to the glare from the water on a bright sunny day. When she lies on her side, however, she notices that the glare increases. Why?

26.5 The Dispersion of Light: Prisms and Rainbows

The net effect of a prism is to change the direction of a light ray.

Light rays corresponding to different colors bend by different amounts.

26.5 The Dispersion of Light: Prisms and Rainbows

26.5 The Dispersion of Light: Prisms and Rainbows

Conceptual Example 7 The Refraction of Light Depends on TwoRefractive Indices

It is possible for a prism to bend light upward,downward, or not at all. How can the situationsdepicted in the figure arise?

26.5 The Dispersion of Light: Prisms and Rainbows

26.6 Lenses

Lenses refract light in such a way that an image of the light source isformed.

With a converging lens, paraxial rays that are parallel to the principalaxis converge to the focal point.

26.6 Lenses

With a diverging lens, paraxial rays that are parallel to the principalaxis appear to originate from the focal point.

26.6 Lenses

26.7 The Formation of Images by Lenses

RAY DIAGRAMS

26.7 The Formation of Images by Lenses

IMAGE FORMATION BY A CONVERGING LENS

In this example, when the object is placed further thantwice the focal length from the lens, the real image is inverted and smaller than the object.

26.7 The Formation of Images by Lenses

When the object is placed between F and 2F, the real image is inverted and larger than the object.

26.7 The Formation of Images by Lenses

When the object is placed between F and the lens, the virtual image is upright and larger than the object.

26.7 The Formation of Images by Lenses

IMAGE FORMATION BY A DIVERGING LENS

A diverging lens always forms an upright, virtual, diminished image.

26.8 The Thin-Lens Equation and the Magnification Equation

fdd io

111

o

i

o

i

d

d

h

hm

26.8 The Thin-Lens Equation and the Magnification Equation

Summary of Sign Conventions for Lenses

lens. converging afor is f

lens. diverging afor is f

lens. theofleft the toisobject theif is od

lens. theofright the toisobject theif is od  

  di is + for an image (real) formed to the right of the lens.

di is – for an image (virtual) formed to the left of the lens.

m is + for an image that is upright with respect to the object.

m is – for an image that is inverted with respect to the object.

26.8 The Thin-Lens Equation and the Magnification Equation

Example 9 The Real Image Formed by a Camera Lens

A 1.70-m tall person is standing 2.50 m in front of a camera. Thecamera uses a converging lens whose focal length is 0.0500 m. (a)Find the image distance and determine whether the image isreal or virtual. (b) Find the magnification and height of the imageon the film.

1m 6.19m 50.2

1

m 0500.0

1111 oi dfd

(a)

m 0510.0id real image

(b) 0204.0m 50.2

m 0510.0

o

i

d

dm

m 0347.0m 50.20204.0 oi mhh

Example 9 The Virtual I mage Formed by a Diverging Lens An object is placed 7.10 cm to the left of a diverging lens whose focal length is f=–5.08 cm (a diverging lens has a negative focal length). (a) Find the image distance and determine whether the image is real or virtual. (b) Obtain the magnification.

26.9 Lenses in Combination

The image produced by one lens serves asthe object for the nextlens.

26.10 The Human Eye

ANATOMY

24

If we read for a long time, our eyes become “tired.” When this happens, it helps to stop reading and look at a distant object. From the point of view of the ciliary muscle, why does this refresh the eyes?

26.10 The Human Eye

OPTICS

The lens only contributes about 20-25% of the refraction, but its functionis important.

26.10 The Human Eye

NEARSIGNTEDNESS

The lens creates an image of the distance object at the far pointof the nearsighted eye.

26.10 The Human Eye

Example 12 Eyeglasses for the Nearsighted Person

A nearsighted person has a far point located only 521 cm from theeye. Assuming that eyeglasses are to be worn 2 cm in front of the eye, find the focal length needed for the diverging lens of the glassesso the person can see distant objects.

26.10 The Human Eye

cm 519

11111

io ddf

cm 519f

26.10 The Human Eye

FARSIGNTEDNESS

The lens creates an image of the close object at the near pointof the farsighted eye.

26.10 The Human Eye

THE REFRACTIVE POWER OF A LENS – THE DIOPTER

metersin

1diopters)(in power Refractive

f

Optometrists who prescribe correctional lenses and the opticianswho make the lenses do not specify the focal length. Insteadthey use the concept of refractive power.

26.11 Angular Magnification and the Magnifying Glass

The size of the image on the retina determines how largean object appears to be.

26.11 Angular Magnification and the Magnifying Glass

o

o

d

h sizeAngular radiansin

26.11 Angular Magnification and the Magnifying Glass

Example 14 A Penny and the Moon

Compare the angular size of a penny held at arms length with that ofthe moon.

rad 027.0cm 71

cm 9.1

o

o

d

hPenny

Moon rad 0090.0m 103.9

m 105.3

8

6

o

o

d

h

26.11 Angular Magnification and the Magnifying Glass

Angular magnification

M

Ndf

Mi

11

Angular magnificationof a magnifying glass

00

00

/

/

d

N

Nh

dhM

idfd

111

0

26.12 The Compound Microscope

To increase the angular magnification beyond that possible with a magnifyingglass, an additional converging lenscan be included to “premagnify” the object.

Angular magnification ofa compound microscope

eo

e

ff

NfLM

26.13 The Telescope

Angular magnification ofan astronomical telescope

e

o

f

fM

e

o

oi

ei

f

f

fh

fhM

/

/

26.14 Lens Aberrations

In a converging lens, sphericalaberration prevents light raysparallel to the principal axis fromconverging at a single point.

Spherical aberration can be reducedby using a variable-aperture diaphragm.

26.14 Lens Aberrations

Chromatic aberration arises when different colors are focused atdifferent points along the principal axis.

Conceptual Questions

2

Two slabs with parallel faces are made from different types of glass. A ray of light travels through air and enters each slab at the same angle of incidence, as the drawing shows. Which slab has the greater index of refraction? Why?

4

Two identical containers, one filled with water (n= 1.33) and the other filled with ethyl alcohol (n= 1.36), are viewed from directly above. Which container (if either) appears to have a greater depth of fluid? Why?

7

A man is fishing from a dock. (a) If he is using a bow and arrow, should he aim above the fish, at the fish, or below the fish, to strike it? (b) How would he aim if he were using a laser gun? Give your reasoning.

9

A person sitting at the beach is wearing a pair of Polaroid sunglasses and notices little discomfort due to the glare from the water on a bright sunny day. When she lies on her side, however, she notices that the glare increases. Why?

10

You are sitting by the shore of a lake on a sunny and windless day. Your Polaroid sunglasses are not equally effective at all times of the day in reducing the glare of the sunlight reflected from the lake. Account for this observation.

15

A beam of blue light is propagating in glass. When the light reaches the boundary between the glass and the surrounding air, the beam is totally reflected back into the glass. However, red light with the same angle of incidence is not totally reflected, and some of the light is refracted into the air. Why do these two colors behave differently?

20

Review Conceptual Example 7 as an aid in answering this question. A converging lens is made from glass whose index of refraction is n. The lens is surrounded by a fluid whose index of refraction is also n. Can this lens still form an image, either real or virtual, of an object? Why?