Unit 9
Light & Optics
1
A quick review of the properties of light.
• Light is a form of electromagnetic radiation
• Light travels as transverse waves having wavelength and frequency. fλ=c
• The velocity of EMR is 3.00 x 108 m/s
• The greater the frequency the higher the EMR energy.
• Color is our perception of EMR between 400­700 nanometers.
• Light travels in straight lines we call rays.
• Similar to sound, light can reflect and refract.
2
Light rays travel in a straight line. A light beam is a stream of light energy radiating from a source.
Label the diagrams of types of beams.
nverging
parallel
converging
diverging
Drag this to the target to reveal the answers.
3
Reflection of Light Rays
The law of reflection states that the angle of reflection must equal the angle of incidence to the normal line.
Law of Reflection
θi
32
θi = θ r
θr
o
32o
4
5
Why does the pen appear bent when it is put into the glass?
Click here
for the
answer
6
3
1. Which substance is denser? Water or air?
air
BB air
AA water
water
7
Imagine a car driving towards the sea at an angle. When the first front wheel hits the water, the resistance makes that wheel turn slower than the other wheel. As a result, the car rotates until the second wheel is also in the water. Then both wheels turn at the same time. The car stops rotating.
8
When the car comes out of the water, the righthand wheel turns faster than the left, so the car rotates again. When both wheels are out of the water, the car stops rotating and moves forward. This is exactly what happens when a light ray hits a denser medium.
9
So, light rays can either reflect or refract when striking a surface.
θi
θr
air
glass
10
Reflections produce virtual images.
x
w
The image looks like it is
behind the mirror. This is a
virtual image.
mirror
virtual images
x
w
1. A virtual image doesn't exist
2. A virtual image is right side up
3. For mirrors, the image is reversed
11
A Real Image
A Real Image
1. A real image really exist
2. A real image is upside down
3. A real image is reversed
12
Label the diagram of refraction.
Click here
for the
answer
13
The following pages are answers to the tasks in the lesson activity.
14
Light changes direction as it moves through the water. It does this because water is denser than air, so it slows the light rays down. As a result, the light changes direction slightly, giving the impression the pen is bent. This is called refraction.
Click here
to go back
15
Label the diagram of refraction.
incident ray
angle of incidence
angle of refraction
refracted ray
glass
normal
air
Click here
to go back
16
Ray Tracings
Ray tracings allow us to analyze a system involving mirrors and lenses to determine the location and properties of the resulting image produced.
It starts with placing the system onto a coordinate plane, identifying the position of the object and the focal point of the system. With that information, the position and properties of the resultant image can be determined.
Symbols used in ray tracings.
f = the focal length
do = the object distance from the lens or mirror
ho = the object height from the focal line
di = the image distance from the lens or mirror
hi = the image height from the focal line
m = the magnification of the image
17
Ray Tracing Calculations
The focal length, object distance, and image distance can be related by use of the "lens maker's formula."
1
____
f
1
____
do
=
di
+
1
____
di
f do
________
do ­ f
=
To Calculate Magnification
hi
m = ____
ho
­di
____
=
do
18
Virtual Image (from Wikipedia)
In optics, a virtual image is an image in which the outgoing rays from a point on the object always intersect at a point. A simple example is a flat mirror where the image of oneself is perceived at twice the distance from oneself to the mirror. That is, if one is half a meter in front of the mirror, one's image will appear to be at a distance of 1 meter away (or half a meter inside or behind the mirror).
To contrast, a real image is an image in which the outgoing rays from a point on the object pass through a single point. It is easiest to observe real images when projected on an opaque screen. A screen is not necessary for the image to form.
• When we look through a diverging lens (at least one concave surface) or look into a convex mirror, what we see is a virtual image. However, if we observe a focused image on a screen inside or behind a converging lens (at least one convex side) or in front of a concave mirror what we see on the screen is a real image because the image really is at the screen's location. If we position ourselves so that the screen is directly between ourselves and the optical device (mirror, lens, etc.), we can remove the screen and still observe the image. A converging lens and concave mirror are also capable of producing virtual images if the object is within the focal length. • For example, a plane or convex mirror forms a virtual image positioned behind the mirror. Although rays of light seem to come from behind the mirror, light from the source spreads and exists only in front of the mirror. In drawings of optical systems, virtual rays are conventionally represented by dotted lines. Optical rays represent paths on which light actually travels. A virtual ray (the dotted lines) represent perceived paths as seen by an observer looking into the optical device. The light rays do not travel on these dotted paths. A point on the image is located where the virtual rays intersect. 19
Real Image (from Wikipedia)
In optics, a real image is a representation of an object (source) in which the perceived location is actually a point of convergence of the rays of light that make up the image. If a screen is placed in the plane of a real image the image will generally become visible on the screen. Examples of real images include the image seen on a cinema screen (the source being the projector), the image produced on a detector in the rear of a camera, and the image produced on a human retina (the latter two pass light through an internal convex lens).
In ray diagrams (such as the images on the right), real rays of light are always represented by full, solid lines; perceived or extrapolated rays of light are represented by dashed lines. A real image occurs where rays converge, whereas a virtual image occurs where rays only appear to converge.
Real images can be produced by concave mirrors and converging lenses.
When we look into a convex mirror or see through a concave lens, what we see is not a real image. This image, which appears to be on other side of the lens or mirror plane, is known as a virtual image.
A real image is exemplified by a science toy/demonstration called "Mirage" which consists of two facing parabolic mirrors. One faces up, the other faces down one with a hole at its center. A real image of an object at the apex of the lower mirror appears just above the hole in the upper mirror.
20
Ray Tracing Steps for a Diverging Mirror
Ray #1 ­ Draw a line parallel from the object to the surface of the mirror. Then draw a dotted line to the focal point. Ray #2 ­ Draw a solid line from the object to the center of the mirror at the focal line. Then draw a solid line reflecting away from the mirror. Continue this line behind the mirror using a dotted line.
The intersection of the two dotted lines marks the location of the virtual image.
21
ho =
do =
f=
Diverging Mirrors
22
ho =
do =
f=
Diverging Mirrors
23
ho =
do =
f=
Diverging Mirrors
24
Now let's calculate the same values using
the lens maker's and magnification
formula.
di
ho = 5
do = 8
f = -10
m = ­d
______
i do
hi
m = ______
ho
di
=
f do
________
do ­ f
= (­10)(8) = ­4.444
8 ­ (­10)
= ­ 4.44
______
8
= 0.56
hi = ho m = (5)(0.56) = 2.777
hi =
di =
m =
25
Ray Tracing Steps for a Converging Mirror
Object is Outside the Focal Point
Ray #1 ­ Draw a solid parallel line from the object to the mirror then through the focal point.
Ray #2 ­ Draw a solid line from the object to the center of the mirror then continue with the reflection.
The intersect of these two rays will be the inverted real image.
Object is at the Focal Point
Ray #1 ­ Draw a solid parallel line from the object to the mirror then through the focal point.
Ray #2 ­ Draw a solid line from the object to the center of the mirror then continue with the reflection.
Since the two rays will not intersect, there is no image real or virtual.
Object is Inside the Focal Point
Ray #1 ­ Draw a solid parallel line from the object to the mirror then through the focal point.
Ray #2 ­ Draw a solid line from the focal point through the object to the mirror. Then draw a dotted parallel line extending behind the mirror. The intersection of these two rays will be behind the indicating an upright virtual image.
26
ho =
do =
f=
Converging Mirrors
27
ho =
do =
f=
Converging Mirrors
28
ho =
do =
f=
Converging Mirrors
29
Ray Tracing for Diverging Lenses
Ray #1 ­ Draw a parallel line from the object to the center of the lens. The draw a diagonal line extending to the focal point on the same side as the object.
Ray #2 ­ Draw a line from the object through the center of the lens.
The intersection of these two lines will produce a virtual image near the original object.
30
ho =
do =
f=
Diverging Lenses
31
Ray Tracing for Converging Lenses
Ray #1 ­ Draw a parallel line from the object to the center of the lens. The draw a diagonal line extending to the focal point on the opposite side of the lens.
Ray #2 ­ Draw a line from the object through the center of the lens.
The intersection of these two lines will produce a real image.
32
ho =
do =
f=
Converging Lenses
33
di
=
f do
________
do ­ f
m = ­di 34
ho =
do =
f=
Converging Lenses
35
ho =
do =
f=
Diverging Lenses
36
37
Optical Experiment #1
A) Index of Refraction
Snell's Law
The index of refraction is equal to the ratio of the sine of the angle of incidence and the sine of the angle of refraction.
η = sin i
sin r
38
Optical Experiment #1
B) Focal Length of Converging Lenses
39
Optical Experiment #1
C) Diffraction Pattern
L = distance of diffraction grating to paper.
d = distance marked on the DG plate
x = distance between the dots on the paper
n = the number of spaces between the dots
40
Internal Reflections & Fiber Optics
http://www.usfacetersguild.org/articles/bob_keller/refractive_index/
http://www.tutorvista.com/topic/refractive­index­list
Total internal reflections can be demonstrated using a semi­circular glass block. A "ray box" shines a narrow beam of light onto the glass. The semi­circular shape ensures that a ray pointing towards the centre of the flat face will hit the curved surface at a right angle; this will prevent refraction at the air/glass boundary of the curved surface. At the glass/air boundary of the flat surface, what happens will depend on the angle. Where θc is the critical angle (measured normal to the surface):
• If θ < θc, the ray will split. Some of the ray will reflect off the boundary, and some will refract as it passes through. • If θ > θc, the entire ray reflects from the boundary. None passes through. This is called total internal reflection. This physical property makes optical fibers useful and prismatic binoculars possible. It is also what gives diamonds their distinctive sparkle, as diamond has an extremely high refractive index.
41
Substance State Refractive Index Air Gas 1.000293 Ice Solid 1.31 Water Liquid 1.33 Ethyl Alcohol Liquid 1.36 Fluorite Solid 1.43 Quartz Solid 1.54 Salt Solid 1.54 Tourmaline Solid 1.62 Garnet Solid 1.73­1.89 Cubic Zirconia Solid 2.14 ­ 2.20 Diamond Solid 2.41 42
Internal Reflections & Fiber Optics
Critical angle
The critical angle is the angle of incidence above which total internal reflection occurs. The angle of incidence is measured with respect to the normal at the refractive boundary. The critical angle θc is given by:
η = 1
______
sin θCR
43
The Human Eye & Vision Correction
44
45
Which lens would help correct this problem?
46
Which lens would help correct this problem?
47
What is a stigmatism?
48