Focus questionsFocus questions

What is the wave nature of light?

How does light behave?What are the primary colors of

light? of pigments?How are images formed?

Light and SightLight and Sight

Light And SightLight And Sight

Properties of lightBehavior of light

Reflection Formation of images in mirrors

Refraction ColorFormation of images in lenses

The Human Eye

Light a form of energyLight a form of energy

Part 1 – Properties of Part 1 – Properties of LightLight

Light travels in straight lines:

Laser

Light travels VERY FAST – around 300,000 kilometres per second.

At this speed it can go around the world 8 times in one second.

Light travels much faster than sound. For example:

1) Thunder and lightning start at the same time, but we will see the lightning first.

2) When a starting pistol is fired we see the smoke first and then hear the bang.

We see things because they reflect light into our eyes:

Homework

Luminous and non-luminous objects

A luminous object is one that produces light.

A non-luminous object is one that reflects light.

Luminous objects Reflectors

Shadows

Shadows are places where light is “blocked”:

Rays of light

Properties of Light Properties of Light summarysummary

1) Light travels in straight lines2) Light travels much faster than sound3) We see things because they reflect

light into our eyes4) Shadows are formed when light is

blocked by an object

Behavior of Behavior of Light:Light:ReflectionReflection

Behavior of LightBehavior of LightReflection from a mirror:

Incident ray

Normal

Reflected ray

Angle of incidence

Angle of reflection

Mirror

The Law of ReflectionThe Law of Reflection

Angle of incidence = Angle of Angle of incidence = Angle of reflectionreflection

In other words, light gets reflected from a surface at ____ _____ angle it hits it.

The same !

!!

Clear vs. Diffuse ReflectionClear vs. Diffuse Reflection

Smooth, shiny surfaces have a clear reflection:

Rough, dull surfaces have a diffuse reflection.

Diffuse reflection is when light is scattered in different directions

Behavior of LightBehavior of LightImage formation in mirrors

The Law of ReflectionThe Law of ReflectionFor specular reflection the incident angle

i equals the reflected angle r

i r

The angles are measured relative to the normal, shown here as a dotted line.

Image formed by a Plane Image formed by a Plane MirrorMirrorA mirror is an object that reflects light. A

plane mirror is simply a flat mirror. Consider an object placed at point P in front

of a plane mirror. An image will be formed at point P´ behind the mirror.

For a plane mirror:

do = -di and ho = hi

hi

do = distance from object to mirror

di = distance from image to mirror

ho = height of object

hi = height of image

Image is behind mirror: di < 0

ImagesImages

An image is formed at the point where the rays of light leaving a single point on an object either actually intersect or where they appear to originate from.

If the light rays actually do intersect, then the image is a real image. If the light only appears to be coming from a point, but is not physically there, then the image is a virtual image.

We define the magnification, m, of an image to be:

o

i

o

i

d

d

h

hm

heightobject

height image

If m is negative, the image is inverted (upside down).

Plane MirrorsPlane Mirrors

A plane mirror image has the following properties:The image distance equals the object distance ( in

magnitude )The image is unmagnified

The image is virtual: negative image distance di < 0

m>0, The image is not inverteddo di

o

i

o

i

d

d

h

hm

heightobject

height image

Curved or Spherical Curved or Spherical mirrorsmirrors

Curved MirrorsCurved MirrorsA curved mirror is a

mirror whose surface shape is spherical with radius of curvature R. There are two types of spherical mirrors: concave and convex.

We will always orient the mirrors so that the reflecting surface is on the left. The object will be on the left.

Focal Focal PointPoint

When parallel rays (e.g. rays from a distance source) are incident upon a spherical mirror, the reflected rays intersect at the focal point F, a distance R/2 from the mirror.

For a concave mirror, the focal point is in front of the mirror (real).

For a convex mirror, the focal point is behind the mirror (virtual).

The incident rays diverge from the convex mirror, but they trace back to a virtual focal point F.

Focal LengthFocal LengthThe focal length f is the

distance from the surface of the mirror to the focal point.

CF = FA = radius = FM

The focal length FM is half the radius of curvature of a spherical mirror.

Sign Convention: the focal length is negative if the focal point is behind the mirror.

For a concave mirror, f = ½R

For a convex mirror, f = ½R (R is always positive)

Ray Ray TracingTracing

It is sufficient to use two of four principal rays to determine where an image will be located.

The parallel ray (P ray) reflects through the focal point. The focal ray (F ray) reflects parallel to the axis, and the center-of-curvature ray (C ray) reflects back along its incoming path. The Mid ray (M ray) reflects with equal angles at the axis of symmetry of the mirror.

Ray Tracing – ExamplesRay Tracing – Examples

Virtual imageReal image

The Mirror EquationThe Mirror EquationThe ray tracing technique

shows qualitatively where the image will be located. The distance from the mirror to the image, di, can be found from the mirror equation:

fdd io

111

do = distance from object to mirror

di = distance from image to mirror

f = focal length

m = magnification

Sign Conventions:

do is positive if the object is in front of the mirror (real object)

do is negative if the object is in back of the mirror (virtual object)

di is positive if the image is in front of the mirror (real image)

di is negative if the image is behind the mirror (virtual image)

f is positive for concave mirrors

f is negative for convex mirrors

m is positive for upright images

m is negative for inverted images

o

id

dm

Using mirrorsUsing mirrorsTwo examples:

1) A periscope

2) A car headlight

How do you explain these?How do you explain these?

RefractionRefraction

Incident ray

Refracted ray

Emergent ray

RefractionRefraction

RefractionRefraction

The Refraction of LightThe Refraction of LightThe speed of light is different in different materials. We define the index of refraction, n, of a material to be the ratio of the speed of light in vacuum to the speed of light in the material:

n = c/vWhen light travels from one medium to another its velocity and wavelength change, but its frequency remains constant.

Snell’s LawSnell’s LawIn general, when light enters a new material its

direction will change. The angle of refraction is related to the angle of incidence 1 by Snell’s Law:

where v is the velocity of light in the medium.

Snell’s Law can also be written as

n1sin1 = n2sin2

constantv

sin sin

2

2

1

1

v

The angles 1 and 2 are measured relative to the line normal to the surface between the two materials.

ColourColour

White light is not a single colour; it is made up of a mixture of the seven colours of the rainbow.

We can demonstrate this by splitting white light with a prism:

This is how rainbows are formed: sunlight is “split up” by raindrops.

The colours of the rainbow:The colours of the rainbow:

RedOrangeYellowGreenBlue

IndigoViolet

Why are objects colored?Why are objects colored?

Adding coloursAdding coloursWhite light can be split up to make separate

colours. These colours can be added together again.

The primary colours of light are red, blue and green:Adding blue and

red makes magenta (purple)

Adding blue and green makes cyan

(light blue)

Adding all three makes white again

Adding red and green makes yellow

Seeing colourSeeing colourThe colour an object appears depends on the

colours of light it reflects.

For example, a red book only reflects red light:

White

light

Only red light is

reflected

A white hat would reflect all seven colours:

A pair of purple trousers would reflect purple light (and red and blue, as purple is made up of red and

blue):

Purple light

White

light

Using coloured lightUsing coloured light

If we look at a coloured object in coloured light we see something different. For example, consider a this pair of shirt and shorts:

White

light

Shorts look blue

Shirt looks red

In different colours of light they would look different:

Red

lightShirt looks red

Shorts look black

Blue

light

Shirt looks black

Shorts look blue

Some further examples:

Object Colour of lightColour object seems to be

Red socks

Red Red

Blue Black

Green Black

Blue teddy

Red Black

Blue

Green

Green camel

Red

Blue

Green

Magenta book

Red

Blue

Green

Using filtersUsing filtersFilters can be used to “block” out different colours of

light:

Red Filte

r

Magenta

Filter

Investigating filtersInvestigating filters

Colour of filter Colours that could be “seen”

Red

Green

Blue

Cyan

Magenta

Yellow

Red

Magenta

White

Yellow

Blue Green

Cyan

LenseLensessLight is reflected from

a mirror. Light is refracted through a lens.

Focal PointFocal PointThe focal point of a lens is the point

where parallel rays incident upon the lens converge.

converging lens

diverging lens

How does a lens form an How does a lens form an image?image?

Ray Tracing for LensesRay Tracing for Lenses

The P ray propagates parallel to the principal axis until it encounters the lens, where it is refracted to pass through the focal point on the far side of the lens. The F ray passes through the focal point on the near side of the lens, then leaves the lens parallel to the principal axis. The M ray passes through the middle of the lens with no deflection (in thin lens limit).

Just as for mirrors we use three “easy” rays to find the image from a lens. The lens is assumed to be thin.

The Lens The Lens Equationhttp://www.physics.uoguelph.ca/applets/Intro_physics/kisalev/java/clens/index.html 

Data and AnalysisData and Analysis How does the image distance q of a

convex lens change as the object distance p is decreased?

How does the height of the image change as the object distance is decreased?

Write the equation in determining the linear magnification m of a convex lens using p and q. Call this Eq (1)

 

Data and AnalysisData and Analysis Using Excel graph m vs q. What does the graph

show?. When m is zero, what is q?. This is the q intercept. Relate this observation with your answer to (c). Compare the value of the q intercept with the focal length of the mirror. What then is the physical meaning of the q-intercept?

Extend your graph until it intersects the vertical axis m. Compute the slope of your graph. Compare the value of the slope and the q-intercept. How are they related?. Express the relationship IN AN EQAUTION using the physical meaning of the q –intercept you found. Call this Eq (2).

Write the equation of the line graph. Call this Eq (3) 

Make a data table Make a data table

p q M = q/p

f

2 2 1 1

1.5 3 2

1.23 5.16 4.2

1.8 2.25 1.25

2.2 1.83 .83

2.4 1.71 .71

2.7 1..58 .59

2.8 1.55 .55

p – object distance

q – image distance

f – focal length

m - magnification

q q/p = m2 13 25.16 4.22.25 1.251.83 .831.71 .711.58 .591.55 .55

The Thin Lens EquationThe Thin Lens EquationThe ray tracing technique shows qualitatively where the image from a lens will be located. The distance from the lens to the image, can be found from the thin-lens equation: fdd io

111

Sign Conventions: do is positive for real objects (from which light

diverges) do is negative for virtual objects (toward which light

converges)di is positive for real images (on the opposite side of

the lens from the object)di is negative for virtual images (same side as object)f is positive for converging (convex) lensesf is negative for diverging (concave) lensesm is positive for upright imagesm is negative for inverted images

fdd io

111

The eye and the cameraThe eye and the camera

The eye modelThe eye model

The Human EyeThe Human EyeThe human eye is a dynamic optical device that adjusts

its focal length to keep the image location positioned at the retina:

Optics of the EyeOptics of the Eye1. The “normal” eye can be modeled as a simple lens

system with an effective focal length (& optical power) and a fixed image distance, i:

2. The job of the eye is to focus images on the retina. The image distance is therefore fixed at 1.8 cm (or 0.018 m).

3. When the eye cannot adequately focus an image on the retina, correction may be needed

4. The 4 common vision problems:a. Myopia (near sightedness, short far & near point)b. Hypermetropia (far sightedness, long far & near point)c. Astigmatism (warped lens optics, focal length not uniform on

all axes in the eye)d. Presbyopia (normal distance vision but inability to

accommodate for close objects)

1 1 1 = +

f p 0.018m

Distance Vision OpticsDistance Vision Optics1. When viewing distant objects, the lens power

of the eye (& focal length) of the eye is given by:

2. The lens power is 55.6 diopters & the focal length is:

f = 0.018 m1. When a person is near sighted (myopic),

he/she cannot see objects at infinity (“infinity” is the “far point” for a normal eye)– Myopic far point < Normal far point

-11 1 1 1 = + = = 55.6 m

f 0.018 m 0.018 m

Distance Vision OpticsDistance Vision Optics

Example: A person with -2.0 diopter distance correction.

a. This person has a lens power of 57.6 & needs this “minus” correction to lower the effective lens power to a “normal” 55.6:

b. The far point for this person is: p = 2 m {any object beyond this distance is not in focus}

1 1 1 = + = 57.6 diopters p = 2.0 m

f p 0.018 m

Near Vision OpticsNear Vision Optics1. When viewing close-in objects, the lens power of

the eye (& focal length) of the eye is given by:

2. The lens power is 59.6 diopters & the focal length is: f = 0.0168 m

3. A far sighted (hyperopic) person cannot see objects at close distances even though the eye is accomodating normally– Hyperopic near point > Normal near point (0.25 m)

-11 1 1 = + = 59.6 m

f 0.25 m 0.018 m

Near Vision OpticsNear Vision Optics

Example: A person with +2.0 diopter vision correction.

a. This person has a (near) lens power of 57.6 & needs this “plus” correction to raise the effective lens power to a “normal” close distance power of 59.6:

b. The near point for this person is: p = 0.49 m {any object closer is not in focus}

c. People w/presbyopia have normal distance lens power but are unable to adjust for closer objects, thus needing “reader” glasses

1 1 1 = + = 57.6 diopters p = 0.49 m

f p 0.018 m