Optics, a fancy word for light

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Law of Reflection

• This states the angle of incidence equals the angle of reflection. What that means is if I bounce of a light ray at 25⁰ relative to the surface, it would leave at 25⁰ relavative to the surface.

• This law is written as θr = θi

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Refraction of Light Rays

Normal Line

Boundary

air

water

Incident light ray

Reflected light ray

Refracted Light ray

i

Angle of incidence Angle of

reflection

r

Angle of Refraction

R

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Reflection of Light Waves

Law of Reflection

Angle of Incidence = Angle of Reflection

i

r

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Problems with Reflection

• A light hits a mirror at 52⁰ to the normal. The mirror then rotates 35⁰ around the point where the beam strikes the mirror so that t he angle of incidence of the light ray decreases (smaller). The axis of rotation is perpendicular to the plane of the incident and reflected rays. What is the angle of rotation on the reflected ray?

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• How to solve these kinds of problems:– Draw a picture of what is going on.– Add your light rays into the diagram.– Write out our knowns and unknowns. – Solve for unknowns using appropriate

laws/idea’s

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• Diagram: see board

• Known: initial angle is 52⁰, change in mirror rotation, 35⁰

• Unknown: Change in reflection after rotation

• Because we’re reducing the angle of incidence we rotate the mirror counter clockwise.

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• Θi, final= Θi, intial- ∆Θmirror

• 52⁰ – 35⁰ = 17⁰, which means our new angle is 17 ⁰ from the new normal (due to rotation)

• Look at new diagram on board• Using the law of reflection• Θr, final= Θr, intial

• 17⁰ counterclockwise from new normal (in = out)• ∆Θr= 52⁰ + 35⁰ - 17⁰ = 70⁰ clockwise from the original

angle. • See final diagram of what this means as I’m sure

some of you are slightly confused as the math doesn’t add up

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• Try some of these type son page 460.

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Plane Mirrors• Plane mirrors: A flat smooth surface from which light

is reflected in a specular reflection. • Object: The source of light or illuminated image we’re

looking at in the mirror. • Diverging rays: rays(light, sight, etc) spreading out as

we look at an image.• Virtual image: The image seen by looking at the mirror

with diverging rays, always on the opposite side of the mirror. See picture on 461. Use your cell phone to prove my point.

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Continued • Some other stuff related to that business

from before:– As we get closer to the mirror the closer the

image appears to be, the farther away we get the farther away it appears to be.

– Anyone want to tell me when you can get tricked by this and its dangerous?

– Like here

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Height and Position• Again I apologize as I can’t find these images, so lets

look at 462 together.• What do you notice?

• di = -do

• In a plane mirror the distance from the image is the same as original. The negative means that image is virtual.

• hi = ho This means the heights of both original and image are the same

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Image Orientation

• If you have an iphone 4 or newer pull it out and snap a self picture.

• If not…what happens to your image when you look in a mirror?

• Things go opposite, ie right is left and left if right, so the image is reversed.

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Curved Mirrors: This just got serious

• A concaved mirror, is exactly as it sounds, a mirror that has a cave in it.

• In it we have:– A principal axis: a straight line perpendicular to the

middle of the mirror.– Centre(C) and radius(r) of the curvature (seen on

next slide)– Focal point(F) and focal length(ƒ) (again on next

slide.14

Yes from your text via camera phone

• You’ll notice here that the focal length (point) and is half the radius so : ƒ = r/2

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So what does all this mean?

• It means when you point the middle (or principal axis) of a concave mirror towards on object, say like the sun, all the rays get reflected onto a single point (focal point).

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Finding the image

• First lets watch this little video, instead of my typing mad notes.

• Real image: An inverted (because of concave) optical image that is either bigger/smaller because on location?

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MOAR!

• Here’s an applet that might help

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Imagine Image

• So here’s the break down:– If the original is outside C (twice the focal point,

or more then the radius) you get an inverted smaller image.

– If the original is inside C (less then the raduis) you get an inverted image that’s large.

– If the original is inside the focal point (f or half the radius) you get a large, upright image.

– For diagrams of this see page 465. 19

And with the math…• So obviously because science rules and it

married math, I know right who does that, we can find our image using math.

• Mirror equation: 1 = 1 + 1 f di do

The reciprocal of the focal length is equal to the sum of the reciprocals of image and objects(original) position.

*This is only approximately correct as light in real life sprays out (diverges) and the mirrors themselves can have nicks and abrasions. 20

Magnification

• How much bigger or smaller did we get, yup there's a formula for that too.

• m = hi = -di

ho do

The magnification of an object by a spherical mirror is defined as the image height divided b the object height, is equal to the negative of the image position divided by the object position.

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Formula Sheet• You may wish to add the following to your

formula sheet as I manipulated them for you!!

• di= fdo/ do – f distance image from mirror

• do= fdi / di- f distance object from mirror (original)

• f = dido / do + di focal point based on image and original

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Concave Example

• A concave mirror has a radius of 20 cm. A 2cm tall object is placed 30 cm from the mirror. What is the image position and height?

• Draw a ray diagram of the info you know!

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• Known: – Object height = 2cm

– Object distance = 30cm

– Radius of mirror = 20cm

Known without knowing: Focal point: 10cm (radius / 2)

Unknown: Image distance Image height

Again, the image is the thing we’d see, NOT the actual item.

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Solution• Using the formula from a few slides ago, trying to find image

distance it’s…

• di= fdo/ do – f

• di= (10cm)(30cm)/(30-10) = 15cm, real image (in front of the mirror, so its real)

• Part 2 hi = -di hi= -di x ho

ho do do

• (-15)(2) / (30) = (-1cm)• Mean its 1cm tall (smaller) and inverted• Lets try 469 problems 12-16

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Convex Mirrors

• What do you get when you look at a convex mirror? (outside of a spoon). The same thing, right side up, but smaller and wider.

• The image we get is a virtual image, so the distance is negative.

• Forumla from before is the same for convex mirrors.

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Example• A convex mirror, used for secruity

purposes, in a bus station has a focal point of -0.50m. A creeper who is 1.7m tall is 6 meters from the mirror. Where would the creeper be, (IE like the virtual image) and how tall would he appear.

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• Known:– Height of the object:

1.7m

– Distance from mirror for object: 6m

– Focal point: -0.5m

• Unknown:• Image distance

• Image height

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Solution• di= fdo/ do – f = (-0.5)(6)/(6 – (-0.5))

• This is -0.46m, so virtual image behind the mirror

• Part 2 hi = -di hi= -di x ho

ho do do

• -(-.46)(1.7) / (6)= 0.13m, so smaller and upright

• Try 472 17-21

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Table 17-1

• Pretty good summary of what just happened.

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Snell’s Law

States the relationship between angle of incidence and the angle of refraction

n1sin(θ1)=n2sin(θ2)

Where n = index of refraction

This is a measure of the relative speed of light in a given medium.

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The larger the index of refraction (n) the slower the speed of light in that medium.

• Different mediums have different indexice32

Snell’s General Law of Refraction

Incident medium i

R

Refracted medium

ni x sin i = nr x sin R

This equation works for all different media! 33

Example

• A light beam in air hits a sheet of crown glass at an angle of 30 degrees. What is angle of refraction? Index of light is 1.00 and index of crown glass is 1.52.

• Hint draw a diagram

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Solution• Angle 1 = 30 degree, index 1= 1.00• Angle 2= ?, index 1.52

• n1sin(θ1)=n2sin(θ2) moving things around I get …

• θ2= sin-1(n1 x sin(θ2)) n2

• Putting all the info in I get a solution of 19.2⁰

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Snell’s General Law of Refraction

water 23o

RFlint glass

Example #1:

What is the angle of refraction?36

Snell’s General Law of Refraction

ni x sin i = nr x sin RSolution:

1.33 x sin 23o = 1.61 x sin R

1.33 x 0.3907 = 1.61x sin R

0.5197

1.61 = sin R

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Snell’s General Law of Refraction

Solution (con’t):

= sin R0.3228

Therefore:

18.8o = R (angle of refraction)

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Snell’s General Law of Refraction

Example #2

Medium?31.4o

55o

Quartz (crystal)

Determine the incident medium.

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Snell’s General Law of Refraction

ni x sin i = nr x sin RSolution:

ni x sin 31.4o = 1.54 x sin 55o

ni x 0.5201 = 1.26149

ni =0.5201

1.2615

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Snell’s General Law of Refraction

Solution (con’t):

= 2.42 ni

Therefore:

The incident medium is probably Diamond

Try on page 487

(index of refraction of the incidence medium)

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Snell’s Law

This means that the index of refraction can also be calculated by ratio of speeds:

n =CVm

Where:

C = 3.00 x 108 m/s (light in vacuum)Vm = speed of light in a medium

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Snell’s Law

Example 1:

Light travels at 1.87 x108 m/s a new plastic medium. What is the index of refraction for this new plastic?

Solution: n =CVm

n =3.00 x 108 m/s

1.87 x 108 m/s

n = 1.6043

Snell’s General Law of Refraction

Critical Angle and Total Internal Reflection

Remember the refraction of light lab, when you made the light ray go from water back into air, the refraction stopped at about 49o and you had the light ray bounce off the front of the semi-circular dish.

This is called total internal reflection.

The angle at which this occurs is called the critical angle.

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Snell’s General Law of Refraction

Total internal Reflection is very important in the design of binoculars and cameras.

Mirrors are only about 80 –90% efficient at returning light energy. This means that 10-20% of the light is lost as heat energy in heating up the mirror.

Total Internal Reflection is above 99% efficient in doing the same thing!

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Snell’s General Law of Refraction

Only occurs when the light ray travels from a higher index of refraction medium to a lower index of refraction medium.

For Example:

Water into Air or Diamond into glass46

Snell’s General Law of Refraction

Note:

At the Critical Angle the angle of refraction is always 90o!

This makes calculating the critical angle very easy!

ni x sin i = nr x sin R

But R = 90o at the critical Angle47

Snell’s General Law of Refraction

And Sin 90o = 1.00!!

This means that Snell’s Law becomes:

nc x sin ic = nr x 1.00

or

sin ic =nr

nc 48

Snell’s General Law of Refraction

What is the critical angle for a light ray going from water into air?

water air

sin ic =nr

nc 49

Snell’s General Law of Refraction

sin ic =1.0003

1.33

sin ic = 0.7521

ic = 49o

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Snell’s General Law of Refraction

This is a picture of a rainbow over the tennis courts at Immac one morning.

The rainbow is caused by a combination of refraction and total internal reflection inside water droplets suspended in the sky.

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Snell’s General Law of Refraction

1st refraction

light is spread out into individual colours

Total internal reflection

Send the light back out the front of the drop

2nd refraction

Further spreads the light colours out

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Snell’s General Law of Refraction

Mirages Caused by the bending of light rays as they move through different densities of air when it is heated unevenly

Mirage of water on a highway

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Snell’s General Law of Refraction

Mirages

They also make objects appear to be in the sky.

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Snell’s General Law of Refraction

The Test for this Chapter will be combined with the test for Ch. 18 Mirrors and lenses!!

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Lenses, for you glass people• Lens: A piece of transparent

material, like glass or plastic, used to focus light and make an image.

• Convex lens: Often called a converging lens because it brings outside light to a focus. The lens itself is thicker at the center then the outside.

• Concave lens: Thicker on the outside then in the middle. Often called a diverging lens.

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Application of this business

• Glasses so people can see:– Nearsightedness: when the image focal length

is too short, we use concave lens– Farsightedness: where the focal length is too

long, we use convex lenses are used.– Others: telescopes, binoculars, microscopes,

camera’s etc, call use lens to see/focus images

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The End!!!!

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