Light and Optics - Comprehensive Notes

Unit 10: Light & Optics

Learning Targets (General)

  • Explain polarization.

  • Explain how EM waves are transmitted, reflected, and absorbed.

  • Explain the index of refraction.

  • Solve problems involving Snell’s Law.

  • Explain light colors.

  • Identify the different behavior of light using mirrors and thin lenses (optical ray diagrams and thin lenses).

  • Perform calculations related to reflections from plane surfaces and especially focus on thin lenses.

Learning Targets (Lesson 1)

  • Explain polarization.

  • Explain how EM waves are transmitted, reflected, and absorbed.

  • Explain the index of refraction.

  • Solve problems involving Snell’s Law.

Polarization

  • Polarization refers to the direction of the electric field in a light wave or any other electromagnetic wave.

  • It demonstrates the wave properties of light.

  • The photoelectric effect shows light as a particle; polarization shows light as a wave.

Unpolarized vs. Polarized Light

  • Unpolarized Light: A light wave vibrating in more than one plane.

  • Polarized Light: Light waves in which the vibrations occur in a single plane.

  • Polarization: The process of transforming unpolarized light into polarized light.

  • A common incandescent light bulb produces unpolarized light because each atom in a heated filament sends out a light wave that has random polarizations.

  • Light from the sun is also unpolarized.

Polarizers

  • A polarizer is a filter that transmits light waves with only one direction of polarization.

  • A light polarizer has a transmission axis, which is the direction of polarized light that it transmits.

  • A polarizer affects both the intensity and the polarization of a beam of light.

  • Polarizers are found in practical applications like camera filters and sunglasses.

Effects of a Polarizing Filter

  • When unpolarized light encounters a polarizer with a vertical transmission axis:

    • Light with vertical polarization passes through.

    • Light with horizontal polarization is blocked.

    • On average, half of the light passes through the polarizer.

Polarization by Reflection

  • Light is also polarized when it reflects from a smooth surface.

  • If reflected light is polarized horizontally, polarizing sunglasses with a vertical transmission axis block the glare.

  • Polarized sunglasses reduce glare by preventing reflected rays from reaching the eyes.

  • If two polarizing films are at right angles to each other, no light passes through, making it opaque.

Properties of Electromagnetic Waves

  • Electromagnetic waves have all the properties of waves:

    • Reflection: Obeys the Law of Reflection.

    • Transmission: And therefore, refraction.

    • Absorption: Converted into heat (e.g., asphalt on a hot summer day).

Reflection

  • Reflection is the bouncing of a wave off a boundary.

    • Incident Wave: The wave that strikes the boundary (incoming wave).

    • Reflected Wave: The wave leaving the boundary (outgoing wave).

  • Law of Reflection: Angle of incidence equals the angle of reflection, measured from a normal line to the boundary.

  • The normal line is perpendicular to the boundary between surfaces.

Ray Diagrams

  • Ray diagrams represent waves as a straight line and are used to represent electromagnetic waves.

Wave Fronts

  • Reflection can also be drawn as wave fronts.

Types of Reflection

  • Specular Reflection:

    • Incident parallel rays remain parallel after reflection.

    • Occurs off smooth surfaces like mirrors, glass, calm water, smooth ice, or polished metal.

  • Diffuse Reflection:

    • Incident parallel rays are scattered after reflection.

    • Occurs off rough surfaces like human skin, brick walls, concrete, paper, plastic cups, rough water, rough ice.

    • Most objects are detected with diffuse reflection.

Refraction

  • Refraction is the bending of light when it is transmitted from one medium to another due to a change in speed.

  • The speed of all waves changes depending on the medium.

  • The speed of light is fastest in a vacuum and slows down depending on the medium.

  • Refraction depends on the angle of incident and speeds of the wave in the different mediums.

  • All rays are measured from a normal line that is drawn from the boundary between the two mediums.

Index of Refraction

  • The change in speed can be quantified using the index of refraction.

  • It is the factor by which the speed of light is reduced.

  • Formula: n = \frac{c}{v}

    • n = index of refraction

    • c = 3 \times 10^8 \frac{m}{s} (speed of light in a vacuum)

    • v = speed of the wave in the medium

  • For example, the index of refraction for water is 1.33, meaning light travels 1.33 times slower in water than in a vacuum.

  • The greater the change in the index of refraction between mediums, the greater the change in the direction of the wave.

Common Indices of Refraction

  • vacuum: 1.00000

  • air at 20°C: 1.00029

  • water at 20°C: 1.33

  • The highest speed is in a vacuum (n=1.0000000).

  • As n gets larger, the speed of light in a material gets slower (e.g., n = 3 is slower than n = 2).

  • Air is only slightly slower than in a vacuum (typically, n = 1.00 for air).

Example Calculation

  • What is the index of refraction for glass if light travels at 2.0 \times 10^8 \frac{m}{s}?

  • Formula: n = \frac{c}{v}

  • c = 3 \times 10^8 \frac{m}{s} (always)

  • n = \frac{3 \times 10^8}{2.0 \times 10^8} = 1.5

Direction of Bending

  • When a ray moves from a faster medium (less optically dense) to a slower medium (more optically dense), it will bend toward the normal.

    • Angle of Refraction < Angle of Incidence

  • When a ray moves from a slower medium (more optically dense) to a faster medium (less optically dense), it will bend away from the normal.

    • Angle of Refraction > Angle of Incidence

  • Less Dense → More Dense

    • Wavelength Decreases

    • Speed Decreases

    • Bends TOWARDS the normal

  • More Dense → Less Dense

    • Wavelength Increases

    • Speed Increases

    • Bends AWAY from the normal

Ranking Media Density

  • Use the diagram to rank the different media from least dense to most dense:
    N4 < N1 = N2 < N3

Snell’s Law

  • Snell’s Law is a mathematical description of how light bends when passing between mediums; a mathematical description of refraction.

No Bending Conditions

  • A ray will not bend if:

    1. There is no change in speed (same index of refraction).

    2. The angle of incidence is along the normal (0°).

Example Problem

  • Light travels from air into water with an index of refraction of 1.33.

    1. In which direction does the light bend?

    2. If the angle of incidence is 45°, what is the angle of refraction inside the water?

    3. Sketch the path of light as it changes media.

Solution:

  1. Air (n = 1) is less dense than water (n = 1.33), so the angle of the refracted ray will be less than the angle of the incident ray. It will bend toward the normal.

  2. n1\sin(\theta1) = n2\sin(\theta2)

    • (1.00)\sin(45) = (1.33)\sin(\theta)

    • 0.707 = 1.33\sin(\theta)

    • \sin(\theta) = \frac{0.707}{1.33} = 0.53

    • \theta = \sin^{-1}(0.53) = 32°

Refraction Example - Prism

  • A horizontal ray of light encounters a prism; after passing through the prism, the ray is deflected downward.

Atmospheric Refraction

  • When you see the sun just about to set, the sun is already below the horizon because the atmosphere acts like a giant prism and refracts sunlight.

  • Without an atmosphere, we would not be able to see the sun after it has passed below the horizon.

Learning Targets (Lesson 2)

  • Explain total internal reflection

  • Explain dispersion

  • Explain diffraction

  • Explain how light diffracts using a single or a double slit.

Total Internal Reflection

  • If the angle of incidence is increased, the angle of refraction increases as well.

  • At a critical angle, the refracted beam no longer enters the air but instead is parallel to the water-air boundary.

  • For angles greater than this critical angle, all of the light is reflected back into the water.

  • This can only happen when light is trying to enter a material with a lower index of refraction.

Dispersion

  • Dispersion is the spreading of white light into its component colors by refraction through a prism.

  • The index of refraction for a given material depends on the color of the light being refracted.

  • Materials generally have a higher index of refraction for light toward the blue end of the visible spectrum.

  • Blue light bends more when refracted than red light does.

Rainbows

  • Dispersion is responsible for rainbows but you need the rain droplets to disperse the sunlight into its component colors.

  • When sunlight enters a drop, it is separated into its red and violet components by dispersion.

  • The light then reflects from the back of the drop and undergoes additional dispersion as it leaves the drop.

Double Rainbows

  • Double rainbows can occur when you have two internal reflections within each droplet.

  • The sequence of colors in a secondary rainbow is reversed from that in the primary rainbow.

Diffraction

  • Diffraction is the bending of a wave as it passes through a slit or around the edge of a barrier.

Diffraction through Slits and Barriers

  • Light can be diffracted as it passes through a slit or by a reflective surface with ridges on it.

  • This is why a CD reflects colored light when white light is incident upon it; the different frequencies are bent different amounts.

Diffraction through Two Slits

  • The diffraction through two slits causes interference in the light, which causes dark and light bands.

  • Bright bands are created by constructive interference, and dark bands are created by destructive interference.

  • The diffracted waves, one from each slit, overlap causing interference patterns.

Single Beam Diffraction

  • When a single beam of one color is diffracted:

    • Green light is bent less than red light.

    • Dark and light bands can be clearly seen.

  • When multiple sources and frequencies are diffracted through multiple splits, amazing patterns can form.

Diffraction and Spectral Composition

  • Different wavelengths of light will be diffracted by different amounts, splitting white light into its compositional spectra.

  • The compositional spectra can be used to analyze light sources such as light from distant stars and used to identify materials as they are heated and give off EM waves.

Radio and Microwave Diffraction

  • Radio and microwave waves can be diffracted over hills and around buildings so that you can still get a signal without being in direct line of sight of a tower.

Blue Sky and Red Sunsets

  • Blue sky is caused by light scattering from air molecules.

  • Molecules in the atmosphere scatter light rays.

  • Shorter wavelengths (blue, violet) are scattered more easily.

  • At noon, there is less atmosphere, so there is less scattering, thus a blue sky and yellow sun.

  • Sunset and sunrise appear red because you are looking at the sun through a long expanse of the atmosphere.

Thin Films

*Interference results from a double reflection in thin films like bubbles and oil slicks.

Learning Targets (Lesson 3)

  • Explain light colors

  • Explain why objects “have” color

  • Determine what you should see by the type of incoming light that is absorbed by an object

Primary Colors of Light

  • Traditional colors: Yellow, Red, Green, Blue

  • Actual Priner Light Colors: Magenta, White, Cyan

Eyes and Photoreceptors

  • Eyes have photoreceptors (cells):

    • Cones - sensitive to color

    • Rods - sensitive to intensity

  • You can see objects when the light from an object enters your eyes and strikes these cells

  • Visible light range: 400 nm - 700 nm

  • Human eyes have three types of light-sensitive cells:

    • Cones most sensitive to red

    • Cones most sensitive to green

    • Cones most sensitive to blue

Visible Light and Seeing Color

  • Because the human eye has cells that can detect red, green, and blue light, these colors are known as light primary colors.

  • All colors we see in nature are produced in our eyes by different amounts of the primary colors.

  • Where all three overlap, you get white. Since red, green, and blue add together to produce white light, we call these colors additive primary colors.

  • This is different than if we were to mix pigments like paints, markers, crayons, or colored pencils.

  • Pigments are created from the primary colors of pigment (also called the secondary colors of light).

  • Pigments are chemicals that absorb selective wavelengths - they prevent certain wavelengths of light from being transmitted or reflected. These are magenta, yellow, and cyan.

  • Pigment primary colors are considered subtractive primary colors.

Additive and Subtractive Colors

  • Additive Primary Colors:

    • Red, Green, Blue

    • Two or more are added together to create other colors, or even white light

  • Subtractive Primary Colors:

    • Magenta, Cyan, Yellow

    • When two or more are combined, they are actually subtracting light. When all are combined, they produce black; that is, all light is absorbed in this case.

Color Addition Rules

  • R + G = Y

  • R + B = M

  • G + B = C

  • Unequal intensities will result in different other colors that we might have seen

Color Subtraction Rules

  • W - B = (R + G + B) - B = R + G = Y

  • C - B = (G + B) - B = G

  • The color of an object does not reside in the object itself. Rather, the color is in the light that shines upon the object and that ultimately becomes reflected or transmitted to our eyes.

Why Do Objects Have Color?

  • White light enters.

  • The red surface absorbs the green and blue light.

  • Red ray of light is reflected.

Color Reflection Examples

  • A - The object looks white because it reflects all of the primary colors of light

  • B - It would look cyan because it reflects both green and blue light

  • C - The object would look magenta because it reflects red and blue light

  • D - It would look yellow because it reflects red and green light

  • E, F, & G - The object only reflects one color of light so it would look that color. Ex. In G, it only reflects blue light so it would look blue. Red and green are absorbed by the pigment.

  • H - All colors of light are absorbed so the object will look black

Learning Targets (Lesson 4)

  • I can identify the different behavior of light using mirrors and thin lenses (optical ray diagrams and thin lenses)

  • I can perform calculations related to reflections from plane surfaces and especially focus on thin lenses

Mirrors and Lenses

  • Virtual Image - Image made by diverging light rays. (The light rays move apart and do not touch)

    • image looks like it is behind the mirror.

    • image cannot be projected onto a screen.

  • Real Image - Image create by converging light rays. (The light rays move together and intersect at a measurable point)

    • image is on the same side of the mirror as the object.

    • image can be projected onto a screen.

  • If light rays remain parallel after hitting a mirror or lens, then no image will be produced.

Reflective Surfaces (Mirrors)

  • Flat (Plane) Mirror - A reflective surface with no curve

  • Concave Mirror - A reflective surface that curves inward toward the viewer (think cave)

  • Convex Mirror - A reflective surface that curves outward away from the viewer

Flat Mirror

  • Virtual Images

  • Image is reversed (think selfies)

  • Images are the same distance and size behind the mirror as the object is in front of the mirror

  • Image is upright

  • Image is found with virtual rays because the light rays diverge

Shortest Mirror Problem

  • To save money you would like to buy the shortest mirror that will allow you to see your entire body. Should the mirror’s height be half of your height, two-thirds of your height, or equal to your height?

  • First, in order for you to see your feet, the mirror must extend from your eyes downward to a point halfway between your eyes and feet, as shown. Similarly, the mirror must extend upward from your eyes half the distance to the top of your head. Altogether, then, the mirror must have a height equal to half of your total height.

Heads-Up Display

  • Heads-up display movie theater for hearing impaired.

Concave Mirror and Center of Curvature

  • The center of curvature (C) is always twice the length of the distance from the focal point (F) to vertex (A). Sometimes C is labeled as 2F. The F is always ½ radius.

Concave Mirror Characteristics

  • Can create real or virtual images depending on the location in front of the mirror

  • Causes light rays to converge.

  • Where the rays intersect, an image is formed.

  • The image in THIS diagram is inverted, reduced, and real.

Focal Point

  • Focal distance: The focal point is where rays parallel to the principal axis will cross.

Convex Mirror

  • The center of curvature (C) is always twice the length of the distance from the focal point (F) to vertex (A). Sometimes C is labeled as 2F. The F is always ½ radius.

  • The reflected rays are always diverging. The focus is on the opposite side from where the object will be.

Concave vs Convex Mirrors

  • Concave Mirrors: Light Rays Converge

  • Convex Mirrors: Light Rays Diverge

How to Draw Ray Diagrams

  • Drawing Ray Diagrams is as easy as 1, 2, 3!

    1. Parallel rays go through focus

    2. Rays through focus go parallel

    3. Rays through the center do not bend

  • Image occurs where all lines meet.

Concave Mirrors Ray Diagrams

  • Object beyond C

    • Image located between F and C

    • Smaller

    • Real

    • Inverted

  • Object at C

    • Image located at C

    • Same size

    • Real

    • Inverted

  • Object between F and C

    • Image located beyond C

    • Enlarged

    • Real

    • Inverted

  • Object at F

    • Image does not exist (rays are parallel)

  • Object inside F (Between F and Mirror)

    • Image behind mirror

    • Enlarged

    • Virtual

    • Upright

Convex Mirror Characteristics

  • Image will always be virtual and upright

  • The farther the image is located from the mirror, the greater the reduction in size of the image

  • Objects appear farther away than they actually are

  • Note: Virtual rays (dashed lines) are extensions from the light rays (solid lines). They extend behind the mirror and locate the image. In this example, the image is upright, smaller, and virtual.

Lenses

  • Mirrors: Reflection

  • Lenses: Refraction

  • The shape of a lens causes further bending of light as a ray of light passes through the lens rather than reflecting off the surface.

Types of Lenses:

  • Convex Lens:

    • Converging Lenses

    • Convex meniscus

    • Plano-convex

    • Double convex

  • Concave Lens:

    • Diverging Lenses

    • Concave meniscus

    • Plano-concave

    • Double concave

Lens Characteristics:

  • Convex Lens:

    • A convex lens is also called a converging lens.

    • Convex lenses have two focal points, one on each side of the lens.

  • Concave Lens:

    • A concave lens is also called a diverging lens.

    • Concave lenses have virtual focal points.

Principal Rays:

Principal Rays show how lenses redirect light

  1. Midpoint Ray - The ray that goes through the middle of a lens.

  2. Parallel Ray - Is the ray parallel to the principal axis and is then bent so that it passes through the focal point.

  3. Focal-Point Ray - The ray from the focal point and then to the lens

Concave & Convex Lens Summary:

Type of lens properties including object location, Image orientation, image size, image type

  • CONCAVE LENS: arbitrary location/ upright, reduced, virtual

  • CONVEX LENS

    • beyond F / upside down, reduced, real

    • just beyond F / upside down, approaching inifinity/ real

    • just inside F / upright, approaching inifinity/ virtual

    • between lens and F /upright, enlarged, virtual

Concave len Summary:

  • Concave lenses will always produce the same image: upright, virtual, and smaller. The closer the object gets to the lens, the larger the image will become. Note the light rays always diverge.

Thin Lens and Mirror Equations

  • d_i is the distance of the image from the lens or mirror

  • d_0 is the distance of the object from the lens or mirror

  • f is the focal length from the lens or mirror

  • M is magnification ratio

  • h_O is the height of the object

  • h_i is the height of the image

Sign Conventions:

Math verifies the location of the images found in ray diagrams.

Sign conventions for the mirrors and lenses and what they mean

  • f:

    • concave mirror and convex lens +

    • convex mirror and concave lens-

  • d_i:

    • real image +

    • virtual image -

  • h_i:

    • upright +

    • inverted -

  • M:

    • upright image +

    • inverted image -

  • hi < hO (reduced)

  • hi > hO (enlarged)

  • image reduced
    =image same size
    *image enlarged

Example:

A 3 cm tall object is placed 10 cm from a convex lens that has a focal length of 7 cm. Use the equations to identify the image and draw a ray diagram to support your answer.
Real image (di = + 23.33 cm), Enlarged (hi > hO), Inverted (hi = - 7 cm).
Magnification shows that it is 2.33 times larger and upside down) (M < 0)

Concave Reflector:
Parallel beam of
light is produced
Bulb at Focus
Receiving Signals

  • Signals coming in reflecting off the bowl

  • Focusing up through the subreflector

  • Traveling down to be processing
    1
    3
    Observer
    uses of mirror for tree

  • light rays

Uses of Lenses

  • Lenses on glasses and contact lenses refocus light on the correct part of the eye

  • A magnifying glass is a convex lens used to magnify objects

  • Cameras, and telescopes

Refocting light entering eyes to point of focus for vison.