Optics

Mark Lesmeister

Dawson High School Physics

REFLECTION AND MIRRORSPART I

Unless otherwise noted, images from Serway and Faughn, Holt Physics, © Holt, Rinehart and Winston, 2002

Light Rays

• Electromagnetic waves can be approximated as rays.

• Rays are lines drawn perpendicular to the wavefronts.

• A light ray travels in a straight line.

Animation courtesy Dan Russell, Kettering University

When will light reflect?• When light travels through a

substance, it travels in a straight line.

• When light strikes a different substance, three things can happen:– If the new material is

transparent to light, the light will be transmitted. It may change paths.

– If the new material is not transparent to light, part of the light will be absorbed, and the rest will be reflected.

Describing Light Paths• We describe the path light

takes when it encounters a barrier using certain angles.

• The angle between the incoming light ray and the normal to the surface is called the angle of incidence.

• The angle between the reflected light ray and the normal to the surface is called the angle of reflection.

θ

θ’

θi

θr

Types of reflection

• Diffuse reflection- light reflected from a rough surface, so that a beam of light is reflected in many directions.

• Specular reflection- light reflected from a smooth surface, so that a beam of light is reflected in only one direction. Specular reflection forms an image.

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Discovery Lab: Mirrors and the Law of Reflection

• The hand mirrors in this lab are brand new, and were purchased with personal funds.

• The mirrors in the optics kits are fragile.

• The levels in this lab use lasers which can damage eyesight.

• Safety Notes: Never point laser lights at any person.

Discovery Lab Part 1: The Image in a Mirror

• Work in pairs at your desks.• For this experiment, hold the large flat hand mirrors as flat

as possible.• Look at your image in the mirror. Look at the image of

something else in room in the mirror. Discuss with your partner how the image relates to the object you are viewing. For example: Is the image upright or inverted? Is it larger or smaller than the object? Is it reversed (left to right)? How far away from the surface of the mirror does it appear to be compared to the object?

Discovery Lab Part 2: The Law of Reflection

• Work in pairs at your desks.• Place the flat mirror from the optics kit on a piece of

white paper.• Point the laser so that it reflects off the flat mirror.• Try various angles of incidence, and derive a relation

between angle of incidence and angle of reflection.

Law of reflection• The angle of incidence equals angle of

reflection.• = q q’

Ray diagrams• The location of an image can be

predicted using a ray diagram.• In such a diagram, do is the

distance from the object to the mirror, and di is the distance from the image to the mirror.

• If di is “behind the mirror”, it is negative.

• Your textbook uses p and q.

do di

Flat mirrors• Flat mirrors form a virtual

image.– When light rays from an

object reflect off a flat mirror, the rays appear to intersect at a point behind the mirror.

– Light rays that only appear to intersect form a virtual image.

– Such an image cannot be projected on a physical surface.

– The image distance is negative. ©2008 by W.H. Freeman and Company

Flat mirrors

• When light reflects off a flat mirror, – |Object distance| = |image distance| (do = -di)– The image is the same size as the object.

do di

Homework

• Using a ray diagram, show that a mirror which is not at least half as long as you are tall cannot show you your entire image at once.

REFRACTION PART II

Various images from Serway and Faughn, Holt Physics, © Holt, Rinehart and Winston, 2002

Refraction• Waves like light can sometimes bend as

they travel from one medium to another.• This is called refraction.

Index of refraction

mediumin speed

in vacuum speed refraction ofindex

v

cn

• Refraction can be explained as the result of a change in wave speed.

• The ratio of the speed of light in a vacuum to the speed of light in a medium is the index of refraction.

Snell’s Law

• When light passes into a slower medium, it is bent toward the normal.

• ni (sinqi)= nr (sinqr)

qr

qi

Applying Snell’s Law

• Find the angle of refraction of a light ray entering a diamond from the following materials at an angle of 30 degrees:– Water– Cubic zirconia

qr

qi

Applying Snell’s Law

• A light ray (589 nm) travelling through air strikes an unknown substance at 60.00o and forms an angle of 41.42o with the normal inside the material. What material is it?

• Ice (n = 1.309)

MIRRORS AND LENSESPART III

Curved Mirrors• Curved mirrors are often

classified as concave or convex.

• Curved mirrors whose surface has the shape of the surface of a sphere are called spherical mirrors.– Spherical mirrors have a

center of curvature, indicated by “C” in our diagrams.

– Light rays passing through the center of curvature are perpendicular to the mirror.

C

C

Curved Mirrors

• Concave mirrors may form real or virtual images.– A real image is formed

when the light rays from a single point on the object actually intersect at a single point later on.

– A real image can be projected. A virtual image cannot.

• Convex mirrors always form virtual images.

C

C

Lenses

• Lenses are transparent objects that refract light rays, causing them to converge or diverge to make an image.

• Lenses can have one side convex and the other concave. So lenses are classified as converging or diverging.

Mirrors and Lenses Discovery Lab

• Follow the directions on the handout.

Focal Point

• Rays of light that enter a mirror or lens parallel to the principal axis will reflect or refract along lines that intersect at a common point.– This point is called the focal point.– The focal length f is the distance from the mirror or lens to

the focal point.– For a spherical mirror, the focal length is one half of the

radius of curvature. In other words, the focal point is halfway to the center of curvature.

C F

Focal Point

• Rays of light that enter a mirror or lens parallel to the principal axis will reflect or refract along lines that intersect a common point.– This point is called the focal point.– The focal length f is the distance from the mirror or lens to

the focal point.– Since light can enter a lens from either side, lenses have a

focal point on either side.

C F

Locating an Image from a Curved Mirror with a Ray Diagram

• An image will be located at the point that the rays of light from a single point appear to be coming from.

• We can trace at least three of the rays of light that leave a single point on our object:– Rays parallel to the principal axis reflect along a

line containing the focal point, and vice versa.– Rays that go in through the center of curvature

reflect out the same way.

CC F

Mirror Ray Diagram 1

CC F

Mirror Ray Diagram 2

CC F

Mirror Ray Diagram 3

C

F

Mirror Ray Diagram 4

C

Locating an Image from a Lens with a Ray Diagram

• As with mirrors, we can trace at least three of the rays of light that leave a single point on our object:– Rays parallel to the

principal axis refract along a line containing the focal point, and vice versa.

– Rays that go in through the center of the lens pass straight through.

Lens Ray Diagram 1

FF

Lens Ray Diagram 2

FF

Mirror equation

length focal

1

distance image

1

distanceobject

1

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fdd io

• The mirror equation is

– The focal length is the distance of the focal point from the mirror.

– Distances behind the mirror are considered negative.

Magnification

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o

i

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• The object and image distances will also tell us the size of the reflected images.

• If the magnification is negative, the image is inverted.

Concave Mirrors

• Concave mirrors are often used to magnify objects.– Example- Makeup mirrors.

• Because concave mirrors can produce real images, which can be projected, they are also used in optical devices like telescopes.

Concave Mirror Practice

• A certain concave mirror has a 10 cm focal length. Describe the image location, type, orientation and magnification if the object is located at 30 cm, 15 cm, and 5 cm.

Convex Spherical Mirrors

• These mirrors are often used to image large areas in a small space.

• The mirror equation holds for these mirrors.– The focal point and center

of curvature are behind the mirror, so f and R are negative.

– Convex mirrors always produce image that are virtual, upright and smaller.

©2008 by W.H. Freeman and Company

Convex Spherical Mirrors

• The radius of curvature of a convex mirror is 12 cm. Where is the focal point?

• Find the image locations for this mirror if the object locations are p= 1 cm, 2 cm, 3 cm, 6 cm, 12 cm, 30 cm, 50 cm

Converging Lens

• Can produce real or virtual images.

• Focal point is on opposite side of lens as incoming light rays.

Diverging lenses• Focal point is on same side

of lens as incoming light rays.

• Image will appear inside focal point.

• Diverging lenses produce images that are virtual, upright and smaller.

Thin-lens equation

length focal

1

distance image

1

distanceobject

1

111

fdd io

p q

Using the lens equation

• The front of the lens is the side that light enters from.• do is positive if it is in front of the lens.• di is positive if it is in back of the lens, negative if it is

in front of the lens.• f is positive for converging lenses, negative for

diverging lenses.

Magnification and Lenses

• Use the same equation for magnification that we used for mirrors.

• o

i

d

dM

Practice

• When an object is placed 3 cm in front of a converging lens, a real image is formed 6 cm in back of the lens. Find the focal length.

Practice• Where would you place an object in order to produce

a virtual image 10 cm. from a converging lens with a focal length of 15 cm? From a diverging lens of the same focal length?– Hint: Remember that q is negative (virtual image) and that

f is positive for a converging lens but negative for a diverging lens.

OPTICAL PHENOMENAPART IV

Images from Serway and Faughn, Holt Physics, © Holt, Rinehart and Winston, 2002 unless otherwise credited.Above graphic from Pink Floyd, “Dark Side of The Moon”

Internal Reflection

• Recall the three things that can happen to a wave when it encounters a change in medium.

• Reflection of light off an internal boundary is called internal reflection.

• Observe internal reflection using your glass prism. Does it appear to follow the law of reflection?

Total Internal Reflection

• When light passes to a medium with a lower index of refraction, it bends away from the normal.

• If the angle of incidence is great enough, the angle of refraction will be so large, the light will not exit the medium.

• Instead, reflected.• This is known as total internal reflection.

Total Internal Reflection: Critical Angle

rrii nn sinsin

90 is when is rcritical

i

rc

rrci

n

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sin

90sinsin

©2008 by W.H. Freeman and Company

Total Internal Reflection Practice

• A beam of light hits the boundary between glycerine (n=1.473) and air at an angle of 45 degrees. Will the beam of light be internally reflected?

Glycerine

Atmospheric refraction

• A mirage is formed by the refraction of light through hot air just above the ground.

• This often results in an inverted image of above ground objects appearing on or below the ground.– Ex.- Blue sky appears as water on hot road.

©2008 by W.H. Freeman and Company

Dispersion• The index of refraction often depends on the frequency of

light being refracted.• Refracted light will often exhibit dispersion in which white

light is separated into component wavelengths.

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Dispersion and Rainbows

• Rainbows are caused by dispersion.

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Chromatic Aberration

• Dispersion is the cause of chromatic aberation, where different wavelengths of light are focused at different focal points by the lens.

Source: Wikipedia

Spherical Aberration

• Rays parallel to the principal axis should reflect through the focal point.

• Rays that are far away from the principal axis will not pass precisely through the focal point.

• This effect is called spherical aberration.

Parabolic mirrors• Parabolic mirrors are

concave mirrors whose surface is shape of a paraboloid.

• Parabolic mirrors eliminate spherical aberration.

• These mirrors are often used in reflecting devices.

• Telescopes• Flashlights• Solar ovens

OPTICAL DEVICESPART V

Images from Serway and Faughn, Holt Physics, © Holt, Rinehart and Winston, 2002unless otherwise stated.

Optical Devices: Fiber Optics

• Uses total internal reflection to carry a beam of light.

• Because the wavelength of light is so small, a lot of information can be transmitted using beams of light.

Eyes and Eyeglasses

• The cornea of the eye refracts light toward the light sensitive retina.

• The eye also has a crystalline lens that further refracts the light.

Nearsighted (Myopia)

Farsighted (Hyperopia)

Magnifying Glass

• Uses a single converging lens to view small objects.

Compound Microscope

• Uses more than one lens to view small objects.

Refracting Telescope

• Uses lenses to image distant objects.• Subject to chromatic aberration.

Reflecting Telescope• Uses parabolic mirrors to

image distant objects.• Not subject to chromatic

aberration.

Reflecting and Refracting Telescopes• Uses parabolic mirrors to

image distant objects.• Not subject to chromatic

aberration.

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