Whether seen as a source or reflected from an object, light is the only way we can see.

What is light? Light is one of the many types of energy that travels in

a transverse wave (or as a particle) at a frequency that resonates with our eyes, so we can “see” it.

Massless energy traveling at approx. 300,000 km/s.

Other forms of energy travel like this too and make up the Electromagnetic Spectrum.

Ray Model of lightOur brain understands the assumption that light travels

in straight lines.

Based on this assumption, we gain understanding of the physical world.

The ray model of light assumes light travels in straight line paths called rays.

Reflection When light strikes an object, the energy can be

absorbed, reflected, transmitted, or a combination of these depending on the material struck by the wave.

For very shiny objects like a silvered mirror, as much as 95% of incident light can be reflected.

When a narrow beam of light strikes an object, we define an angle of incidence, θi, to be the angle between the incident ray and a line perpendicular to the surface called the “normal”.

The angle of reflection, θr, is the angle between the normal and the reflected ray.

Law of Reflection All types of waves follow the Law of Reflection as

found by ancient Greeks:

The angle of incidence equals the angle of reflection.

We can confirm this with a flashlight beam and a mirror.

Diffuse vs Specular Reflection When light strikes a “rough” surface, it is reflected in

many different directions. This is called diffuse reflection.

When light strikes a “smooth” surface, it is reflected more as one “beam”.

Each individual ray still follows the Law of reflection.

Image formation Objects seen in a mirror appear as images that

represent the object. Images are formed in plane mirrors by a combination between our brain and eyes.

Light reflected off objects striking a mirror is sent to our eyes producing an image; but our brain thinks light travels in straight lines, so we “project” the image to a location “behind” or “inside” the mirror.

Plane Mirror Images

The image produced by a plane mirror appears very much like the object. Due to the Law of Reflection, the image will appear the same distance, di, “behind” the mirror as the object is, do, in front of the mirror.

Is it live or is it Memorex? Because light rays do not actually cross or pass through

the image location itself, the image seems as if the rays appear there because our brain tells us light travels in straight lines. However we cannot project the image we see onto a screen or paper. This is a virtual image.

When light rays actually DO cross at the image, we form a REAL image which CAN be projected onto a screen or paper.

Lenses and mirrors can form real and virtual images.

Mirror, Mirror on the wall How tall must a full length mirror be (minimum) in

order to see yourself from head to toe?

(Let’s try it out!)

Spherical Mirrors

Spherical mirrors, unlike plane mirrors, are curved to form part a section of a sphere.

Convex mirrors reflect light on the outer surface and are thicker in the middle. These types are used for providing a wide field of view and make small images. They are found in stores, passenger car mirrors, hospitals.

Concave mirrors reflect light on the inner surface and are thinner in the middle (shaped like a cave). These mirrors are used to magnify images like for shaving or makeup application.

Look in a spoon.

Curved Mirror Images Curved mirrors can bring parallel or nearly parallel rays of

light to a central point called a focus, F. (If light waves travel very far distances, they get closer to parallel than when they travel short distances).

The focal point lies along a principal axis, straight line through the center of the mirror and perpendicular to the mirror’s center.

The focal length is ½ the radius of curvature of the spherical mirror. f=r/2

Image Location- 3 important rays

In order to locate an image in a ray diagram, a minimum of 2 rays must cross. We use 3 rays traditionally to verify size, position, and image type.

Ray 1-Leaves the object parallel to the principal axis, reflects off the mirror and emerges through the focal point. (Only for curved mirrors or lenses )

Ray 2- Leaves the object heading through F, reflects off the mirror and emerges parallel to the principal axis.

Ray 3- heads out perpendicular to the mirror, then reflects back on itself and goes through C (center of curvature).

Image is formed where rays cross.

Describing images

In a curved mirror, image distance and object distance are measured from the center of the mirror.

The height of the object, ho, and the height of the image, hi, are related by where the object is located with regard to the focal point of the mirror.

and with geometry

The mirror equation relates image distance, object distance, and focal length, f where f=r/2.

ho

hi

do

di

1

do

1

di

1

f

Magnification Comparing the height of the image formed in a mirror to

the height of the object gives us the magnification, m.

Sign conventions: hi is positive if the image is upright, and negative if inverted relative to the object (ho is always positive). do and di are positive if image and object are on the reflecting side of the mirror. But if either image or object is behind mirror, corresponding distance is negative.

Analysis and equations for concave mirrors can be applied to convex mirrors also, but quantities must be carefully defined. Read pg 695 carefully.

mhi

ho

di

do

Index of Refraction The speed of light in a vacuum is rounded off to

c = 3.00 x 108 m/s.

This speed applies to all electromagnetic waves including visible light.

In air, the speed of light is only slightly less. In other materials like glass and water, speed is always less than in a vacuum.

The ratio of the speed of light in a vacuum to its speed in another material, v, is called the Index of Refraction n, of that material. The Index of Refraction is never less than 1.

(n≥1)n

c

v

Refraction of Light

When a light ray passes from one medium into another, the ray bends due to a change in speed. This bending is called Refraction.

In a ray diagram when a wave enters a medium where the speed of light is less (slower), the ray will bend TOWARD the normal. (Like moving from air to water) If the speed of light is greater in the new medium, the ray will bend AWAY from the normal. ( Like moving from water to air).

Interactive refraction

Snell’s Law The angle of refraction depends on the speed of light

in the two media and the incident angle of the light ray.

This was discovered analytically by Willebrord Snell (1591-1626) and is known as Snell’s Law or the Law of Refraction:

Θ1 is the angle of incidence and θ2 is the angle of refraction with respect to the “normal” perpendicular to the surface between the two media. And n1 and n2

are the respective indices of refraction.

n1sin 1 n2 sin 2

Refraction Applied Why does a pencil appear “bent” in water even when it

isn’t?

Why do a person’s legs look shorter when standing in waist-deep water than on land?

Why does the bottom of a pool appear to be “shallower” than it really is? (why do we think streams of water are not as shallow as they appear and why do fish seem closer to the surface?

How would you spear a fish in stream? Where would you aim?

Your turn to Practice Please do Chapter 23 Review pg 716 QUESTIONS # 1,

3, & 7.

Please do ch 23 Review pg 717 Problems # 1, 3, 9, 12, 13, 14, 27, 30, & 35.

Total Internal Reflection When light passes from 1 medium to another it bends. At

a certain incident angle, the amount of bend reaches 90°and the light skims the surface. This incident angle is called the critical angle, θc and can be found using Snell’s Law:

For any incident angle less than the critical angle, refraction will occur and even partial reflection at the surface. However, for any incident angle greater than the critical angle, all light is reflected and maintains this angle for total internal reflection . This can only occur when light strikes a boundary where the medium beyond has a lower index of refraction (n2 <n1).

1

2sinn

nc

Total internal reflection applied Fiber optics take light pipes or cables and send light

into the pipe at an angle greater than the critical angle for the fiber and can reflect light multiple times with almost NO loss! (Even if the pipe is bent into complicated shapes).

Applied T.I.R. Fiber optics and Total Internal Reflection are used in

telecommunications and medicine.

Transmit video, telephone calls, and computer signals with much less loss than electrical signals in copper wires.

Fibers must be optically insulated from each other usually by a thin coat of some material with a refractive index less than that of the fiber.

Thin Lenses A thin lens is composed of 2 (usually circular) faces

(concave, convex, or plane) secured together.

Lenses are able to form images of objects by the way they interact with light.

We typically consider parallel rays of light entering lenses made of glass or plastic. (Index of refraction is greater than that of air).

Parallel rays of light falling on a double convex lens will be focused to a point (focal point) somewhere on the focal plane.

Remember rays from a distant object are essentially parallel.

Thin lenses cont’d Focal length, f, is the distance from the focal point to the

center of the lens.

We can find the focal point of a convex lens by locating a point where the Sun’s rays are brought to a sharp image.

Light can pass through either side of a lens. The focal length is the same for the other side. Focal length is specific to each individual lens. (Like your arm length is to you, and moves with the lens).

Any lens that is thicker in the middle and thinner in the edges is a converging lens. Lenses that are thinner in the middle and thicker on the edges are diverging lenses.

Image formation in Lenses Like images in mirrors, we can locate the image formed by a

lens using 3 rays.

Ray 1: Leaves the object parallel to the principal axis, is refracted by the lens, and passes through the focal point, F on the opposite side.

Ray 2: Leaves the object heading through the near focal point, is refracted by the lens, and emerges parallel to the principal axis.

Ray 3: Heads toward the center of the 2 lens surfaces and emerges at the same angle it entered. As the lens is thin, the ray is essentially unchanged in direction.

Converging lens diagram Image formation is based on object position relative to

the focal length of the lens. Objects can be placed beyond, within, or at f.

Diverging Lens diagram The same rays are used to locate an image in a

diverging lens as before, however, they behave differently due to the shapes of the lens surfaces and refraction. Parallel rays will spread apart after passing through the lens, so all images in this lens are virtual.

Principal ray

Focal ray

Central ray

Using the lens equation Another way to locate an image is to use the derived

lens equation.

This relates image distance, object distance, and the focal length for a converging lens.

Note that if the object is at infinity, then 1/do =0, so di=f.

For a diverging lens, the equation becomes:

fdd io

111

fdd io

111

What’s your sign? What does it mean when a negative (-) sign shows up

regarding a focal length or image?

A focal length is positive for converging lenses and negativefor diverging lenses.

The object distance, do , is positive if it is on the same side of the lens from which the light is coming (which is usually the case) otherwise it is negative.

The image distance, di ,is positive if it is on the opposite side of the lens from which the light is coming. If it is on the same side, di is negative. Also, image distance is positive for real images and negative for virtual images.

The height of the image, hi , is positive for upright images and negative for images that are inverted relative to the object. Object height, ho, is always positive.

Lens Magnification Magnification in a lens is found as in a mirror.

Magnification is a comparison of the image height to the object height.

For an upright image, the magnification is positive.For an inverted image, the magnification is negative.

o

i

o

i

d

d

h

hm

Lens Power

Power of a lens or mirror is measured in diopters. Diopters are an inverse measurement of the focal length.

P = 1/f

1 D= 1m-1

Example: a 20 cm focal length lens has a diopter power of 1/0.20m = 5.0D as a Diopter is an inverse meter.

Power of a converging lens is positive and power of a diverging lens is negative.

Your turn to Practice Please do the Chapter 23 Reading questions

Please do Ch 23 Rev p 720 #s 49 & 52