Reflection and RefractionReflection and Refraction

PhysicsPhysics

Mr. PadillaMr. Padilla

ReflectionReflection

Whenever a wave reaches a boundary Whenever a wave reaches a boundary between media, some or all of the wave between media, some or all of the wave bounces back into the first medium.bounces back into the first medium.

The more rigid the second medium, the The more rigid the second medium, the more of the wave is reflected and the less more of the wave is reflected and the less that is transmitted.that is transmitted.

Metal vs. Glass - metal more rigid to Metal vs. Glass - metal more rigid to light, more reflection.light, more reflection.

Law of ReflectionLaw of Reflection

Rays of any wave that travel in, bounce Rays of any wave that travel in, bounce back according to the law of reflection.back according to the law of reflection.

The angle of incidence is equal to the The angle of incidence is equal to the angle of reflection.angle of reflection.– θθ = = θθ’’

Both the angle of incidence and the angle Both the angle of incidence and the angle of reflection are measured from the of reflection are measured from the normal.normal.

ReflectionReflection Reflection from a mirror:Reflection from a mirror:

Incident ray

Normal

Reflected ray

Angle of incidence

Angle of reflection

Mirror

DiffusionDiffusion

When rays hit a rough surface, they do not When rays hit a rough surface, they do not bounce straight off. They are reflected in bounce straight off. They are reflected in many different directionsmany different directions

This is called a diffuse reflection.This is called a diffuse reflection. Does this still follow the law of reflection?Does this still follow the law of reflection? Yes – The surface is at many different Yes – The surface is at many different

angles, but each ray is still bound by the angles, but each ray is still bound by the law of reflection.law of reflection.

Clear vs. Diffuse ReflectionClear vs. Diffuse Reflection

Smooth, shiny surfaces Smooth, shiny surfaces have a have a clearclear reflection: reflection:

Rough, dull surfaces have a diffuse reflection.

Diffuse reflection is when light is scattered in different directions

MirrorsMirrors Mirrors are set into Mirrors are set into

three different types - three different types - plane (flat), convex plane (flat), convex (diverging), concave (diverging), concave (converging).(converging).

When rays reflected When rays reflected from a mirror appear to from a mirror appear to originate from behind originate from behind the mirror, you see a the mirror, you see a virtual image.virtual image.

It is virtual because the It is virtual because the light does not actually light does not actually start there.start there.

Ex: The image you Ex: The image you see in a bathroom see in a bathroom mirror appears to be mirror appears to be behind the mirror. Is behind the mirror. Is it really?it really?

No - It is a virtual No - It is a virtual image.image.

Virtual ImageVirtual Image

Terminology• Object distanceObject distance – the distance from the mirror to the – the distance from the mirror to the

object. The value is always a positive number.object. The value is always a positive number.• Image distanceImage distance – the distance from the mirror to the – the distance from the mirror to the

image. An image can be real (inverted and able to be image. An image can be real (inverted and able to be projected on a screen), or virtual (right-side-up and not projected on a screen), or virtual (right-side-up and not able to be projected on a screen).able to be projected on a screen).

• Focal pointFocal point – the point where parallel rays meet (or appear – the point where parallel rays meet (or appear to meet) after reflecting from a mirror.to meet) after reflecting from a mirror.

• Focal lengthFocal length – the distance from the focal point to the – the distance from the focal point to the mirror.mirror.

– Always (+) for converging mirrorAlways (+) for converging mirror

– Always (-) for diverging mirrorAlways (-) for diverging mirror

Mirror Equation

11 = = 11 + + 11focal length object dist. image dist.focal length object dist. image dist.

11 = = 11 + + 11 ff p p qq

Many situations involving mirrors can also Many situations involving mirrors can also be solved using ray diagrams.be solved using ray diagrams.

Ray DiagramRay Diagram

In order to see where a reflection is seen, In order to see where a reflection is seen, you need to draw a ray diagram.you need to draw a ray diagram.

This is a diagram that traces the rays This is a diagram that traces the rays from the source to the observer’s eye.from the source to the observer’s eye.

Let’s do some examples.Let’s do some examples.

Rules for Drawing Reference Rules for Drawing Reference RaysRays

RayRay Line drawn from objectLine drawn from object Line drawn from Line drawn from

to mirrorto mirror mirror to image mirror to image

after reflectionafter reflection

11Parallel to principle axisParallel to principle axis thru focal pt. Fthru focal pt. F

22Thru focal pt. FThru focal pt. F parallel to princ. axisparallel to princ. axis

33Thru center of curvature CThru center of curvature C back along itself thru Cback along itself thru C

Concave Mirror #1• If an object is located more than one focal If an object is located more than one focal

length from a converging mirror as shown length from a converging mirror as shown below, the image it forms is real, inverted, and below, the image it forms is real, inverted, and in front of the mirror. in front of the mirror.

• You can actually project this image onto a piece You can actually project this image onto a piece of paper.of paper.

• Both Both pp and and qq have positive values. have positive values.

Concave Spherical Mirror with Concave Spherical Mirror with Image Greater the Focal LengthImage Greater the Focal Length

Concave Mirror #2

• If an object is at the focal point, no image is If an object is at the focal point, no image is formed because the reflected rays are formed because the reflected rays are parallel.parallel.

Concave Spherical Mirror with Concave Spherical Mirror with Image Equal to the Focal LengthImage Equal to the Focal Length

Concave Mirror #3• If an object is located less than one focal length If an object is located less than one focal length

from a converging mirror, the image it forms is from a converging mirror, the image it forms is virtual, upright, enlarged, and behind the virtual, upright, enlarged, and behind the mirror.mirror.

• You must look into the mirror to see the image.You must look into the mirror to see the image.• pp is (+) and is (+) and qq is (-) is (-)

Concave Spherical Mirror with Concave Spherical Mirror with Image Less than One Focal LengthImage Less than One Focal Length

Magnification relates image and Magnification relates image and object sizesobject sizes

Curved mirrors form images that are not the Curved mirrors form images that are not the same size as the object.same size as the object.

Magnification – the measure of how large Magnification – the measure of how large or small the image is with respect to the or small the image is with respect to the original object’s size.original object’s size.

Magnification = Magnification = image heightimage height = = --qq

object height object height pp

Sample Problem 14BSample Problem 14B

A concave spherical mirror has a focal A concave spherical mirror has a focal length of 10.0 cm. Locate the image of a length of 10.0 cm. Locate the image of a pencil that is placed upright 30.0 cm from pencil that is placed upright 30.0 cm from the mirror. Find the magnification of the the mirror. Find the magnification of the image. Draw a ray diagram to confirm your image. Draw a ray diagram to confirm your answer.answer.

Convex Mirror

• The image formed by a diverging mirror is The image formed by a diverging mirror is always virtual, upright, smaller, and behind the always virtual, upright, smaller, and behind the mirror.mirror.

• The image can be seen only by looking into the The image can be seen only by looking into the mirror.mirror.

• pp is (+) while is (+) while qq is (-) is (-)

Convex Spherical MirrorConvex Spherical Mirror

Sample Problem 14CSample Problem 14C

An upright pencil is placed in front of a An upright pencil is placed in front of a convex spherical mirror with a focal length convex spherical mirror with a focal length of 8.00 cm. An erect image 2.50 cm tall is of 8.00 cm. An erect image 2.50 cm tall is formed 4.44 cm behind the mirror. Find the formed 4.44 cm behind the mirror. Find the position of the object, the magnification of position of the object, the magnification of the image, and the height of the pencil.the image, and the height of the pencil.

SummarySummary

3 Rays to draw3 Rays to draw– In parallel to the In parallel to the

principal axis, out thru principal axis, out thru focal pointfocal point

– In thru the focal point, In thru the focal point, out parallel to the out parallel to the principal axisprincipal axis

– In thru the center of In thru the center of curvature, out thru the curvature, out thru the center of curvaturecenter of curvature

Mirror equationMirror equation

Magnification Eqn.Magnification Eqn.

qpf

111

p

q

h

hM

'

RefractionRefraction

Waves bend when Waves bend when they pass from one they pass from one medium to another.medium to another.

This is because one This is because one part of the wave is part of the wave is made to travel slower made to travel slower or faster than the or faster than the other.other.

Which way does it Which way does it bend?bend?

When waves are When waves are slowed down they slowed down they bend toward the bend toward the normal.normal.

When they are sped up When they are sped up they bend away from they bend away from the normal. the normal.

Draw a ray diagram to Draw a ray diagram to show this.show this.

Sound WavesSound Waves

Sound Waves often bend when they pass Sound Waves often bend when they pass through areas of unequal temperature.through areas of unequal temperature.

Sound travels faster through warmer air so Sound travels faster through warmer air so it tends to bend away from the warm air. it tends to bend away from the warm air.

Light can be bent for the same reason.Light can be bent for the same reason.

Snell’s LawSnell’s Law

The index of refraction is different for The index of refraction is different for different materialsdifferent materials

n = c/vn = c/v Snell’s Law can help us determine how Snell’s Law can help us determine how

much a wave, or ray, is bent.much a wave, or ray, is bent. Every material has an index of refraction (n)Every material has an index of refraction (n) nnii sin sin ii = n = nrr sin sin rr

Draw an illustration to show this. Draw an illustration to show this.

Different Refractive IndexMaterial Refractive Index

Air 1.0003

Water 1.33

Glycerin 1.47

Immersion Oil 1.515

Glass 1.52

Flint 1.66

Zircon 1.92

Diamond 2.42

Lead Sulfide 3.91

We will use n = 1.00 for air when solving problems.

Sample Problem 15A

A light wave of wavelength 589 nm (produced by a sodium lamp) traveling through air strikes a smooth, flat slab of crown glass at an angle of 30.0o to the normal. Find the angle of refraction, rr..

LightLight

Light bends when it travels through Light bends when it travels through different material.different material.

A glass block will look shallower than it A glass block will look shallower than it actually is.actually is.

Water in a pond will appear shallower as Water in a pond will appear shallower as well…both will be ¾ their true depth.well…both will be ¾ their true depth.

What about a mirage? How is it formed?What about a mirage? How is it formed?

PrismPrism

Not all light bends the same amount.Not all light bends the same amount. Light of higher frequencies bend more than Light of higher frequencies bend more than

light of lower frequencies. light of lower frequencies. It is this difference that causes a prism to It is this difference that causes a prism to

disperse light into a rainbow.disperse light into a rainbow.

Total Internal ReflectionTotal Internal Reflection

At a certain angle light will no longer be At a certain angle light will no longer be transmitted out of a material.transmitted out of a material.

This is called the critical angle.This is called the critical angle. In water light hitting from an angle of less In water light hitting from an angle of less

than 48 degrees cannot enter the air.than 48 degrees cannot enter the air. This beam is experiencing total internal This beam is experiencing total internal

reflection.reflection.

Total Internal Reflection cont.Total Internal Reflection cont.

This is used in the cut of diamonds to make This is used in the cut of diamonds to make them shine more. them shine more.

This is also very useful in optical fibers, This is also very useful in optical fibers, sometimes called light pipes.sometimes called light pipes.– These fibers are good for getting light into These fibers are good for getting light into

inaccessible placesinaccessible places– Most importantly, they can also be used to Most importantly, they can also be used to

transfer information (fiber optics)transfer information (fiber optics)

LensesLenses

What is a Lens?What is a Lens?

A lens is a piece of glass that has just the right A lens is a piece of glass that has just the right shape to bend parallel rays of light so that they shape to bend parallel rays of light so that they cross and form an image. cross and form an image.

The light bending (refraction) is due to the The light bending (refraction) is due to the difference in the speed of light in glass and air.difference in the speed of light in glass and air.

Lenses are found in eye glasses, magnifying Lenses are found in eye glasses, magnifying glasses, telescopes, microscopes, binoculars, your glasses, telescopes, microscopes, binoculars, your eyes, etc…eyes, etc…

TypesTypes

There are two main types of lensesThere are two main types of lenses– ConvergingConverging – Lens is thicker in the middle and – Lens is thicker in the middle and

causes rays of light to converge. Sometimes causes rays of light to converge. Sometimes called a convex or double convex lens.called a convex or double convex lens.

– Diverging Diverging – Lens is thinner in the middle and – Lens is thinner in the middle and causes rays of light to diverge or spread apart. causes rays of light to diverge or spread apart. AKA double concave lens.AKA double concave lens.

Converging LensesConverging Lenses

These points of These points of importance are true for all importance are true for all lenseslenses

Principal axis – line Principal axis – line joining the center of joining the center of curvature of each of its curvature of each of its surfaces.surfaces.

Focal point – Point at Focal point – Point at which a beam of parallel which a beam of parallel light, parallel light to the light, parallel light to the principal axis, converges.principal axis, converges.

Focal plane – Incident Focal plane – Incident parallel beams that are parallel beams that are not parallel to the not parallel to the principal axis focus at principal axis focus at points above or below the points above or below the focal point. focal point.

Focal length – distance Focal length – distance between the center of a between the center of a lens and its focal point.lens and its focal point.

A lens has 2 focal points, A lens has 2 focal points, center of curvatures, and center of curvatures, and two focal planes.two focal planes.

Picture… (pg 571)Picture… (pg 571)

Image formationImage formation

Virtual Image: the rays that reach your eye Virtual Image: the rays that reach your eye behave as if they came from the image behave as if they came from the image location.location.

Real Image: When the object is far enough Real Image: When the object is far enough away to be beyond the focal point of a away to be beyond the focal point of a converging lens, light from the object does converging lens, light from the object does converge and can be focused on the screen.converge and can be focused on the screen.

Ray DiagramsRay Diagrams

Ray diagramsRay diagrams: shows the : shows the principal rays that can be principal rays that can be used to determine the size used to determine the size and location of the and location of the image.image.

To locate the position of To locate the position of the image, you only need the image, you only need to have rays from a point to have rays from a point on an object. Any point on an object. Any point except for the point on except for the point on the principal axis will the principal axis will work, but it is easier to work, but it is easier to choose the head of the choose the head of the arrow.arrow.

3 Rays3 Rays 1. In parallel, out through 1. In parallel, out through

other focal pointother focal point 2. Straight through the 2. Straight through the

center of the lens, that center of the lens, that does not change direction.does not change direction.

3. In through the focal 3. In through the focal point, out parallel on the point, out parallel on the other side of the lens.other side of the lens.

EquationsEquations

We get to use the We get to use the same equations as for same equations as for mirrorsmirrors

And And

Sweet!!Sweet!!

p + object in front of lens p + object in front of lens (-) object behind lens(-) object behind lens

q + image in back of lens q + image in back of lens (-) image in front of (-) image in front of lens lens

f + converging lens (-) f + converging lens (-) diverging lensdiverging lens

qpf

111

h

h

p

qM

'

Diverging lenses produce only a virtual image

Sample Problem 15B

An object is placed 30.0 cm in front of converging lens and then 12.5 cm in front of a diverging lens. Both lenses have a focal length of 10.0 cm. For both cases, find the image distance and the magnification. Describe the images.

The CameraThe Camera

A film camera consists of a lens and sensitive film A film camera consists of a lens and sensitive film mounted in a light tight box. mounted in a light tight box.

Cameras make use of a compound lens to Cameras make use of a compound lens to minimize distortions called aberrationsminimize distortions called aberrations

The amount of light that gets to the film is The amount of light that gets to the film is regulated by a shutter and a diaphragm.regulated by a shutter and a diaphragm.

The TelescopeThe Telescope

A simple telescope uses a A simple telescope uses a lens to form real image of lens to form real image of a distant object.a distant object.

Eyepiece – the second Eyepiece – the second lens that is positioned so lens that is positioned so the image produced by the the image produced by the first lens is within one first lens is within one focal length of the focal length of the eyepiece.eyepiece.

When looking through a When looking through a telescope you are looking telescope you are looking at an image of an image.at an image of an image.

A third lens or a pair of A third lens or a pair of reflecting prisms is used reflecting prisms is used in the terrestrial telescope in the terrestrial telescope which produces an image which produces an image that is right side up.that is right side up.

Telescopes that use Telescopes that use lenses are refracting lenses are refracting telescopes. telescopes.

Large astronomical Large astronomical telescopes use mirrors telescopes use mirrors instead of lenses.instead of lenses.

Compound MicroscopeCompound Microscope

A compound microscope uses two converging A compound microscope uses two converging lenses of short focal length.lenses of short focal length.

Objective Lens- first lens. Produces a real image Objective Lens- first lens. Produces a real image of a close object.of a close object.

Eyepiece – 2Eyepiece – 2ndnd lens. Forms a virtual image of the lens. Forms a virtual image of the first imagefirst image

This instrument is called a compound microscope This instrument is called a compound microscope because it enlarges an already enlarged imagebecause it enlarges an already enlarged image

The EyeThe Eye

Iris – the colored part Iris – the colored part of the eye that of the eye that surrounds the opening surrounds the opening & controls the amount & controls the amount of light that enters the of light that enters the eyeeye

Pupil – Opening Pupil – Opening through which light through which light passespasses

Cornea – transparent Cornea – transparent covering where light covering where light entersenters

Retina – a layer of Retina – a layer of tissue at the back of tissue at the back of the eye, extremely the eye, extremely sensitive to light.sensitive to light.

Eye cont…Eye cont…

Fovea – The small region in the center of our field Fovea – The small region in the center of our field of view where we have the most distinct visionof view where we have the most distinct vision

Blind spot – small spot in the retina where the Blind spot – small spot in the retina where the nerves carrying all the info leave the eye in a nerves carrying all the info leave the eye in a narrow bundlenarrow bundle

Farsighted – lens focuses behind retinaFarsighted – lens focuses behind retina Nearsighted – lens focuses in front of retinaNearsighted – lens focuses in front of retina

Book WorkBook Work

Ch. 15 Review and AssessCh. 15 Review and Assess– p. 587 #10-14p. 587 #10-14

– p. 588 #24-26p. 588 #24-26