Reflection and Mirrors The Law of Reflection always applies: “The angle of reflection is equal to the angle of incidence.”

“Plane” Mirrors form virtual images. Virtual: light APPEARS to come from this location, but does not actually start there. The image is the same distance behind the mirror as the object is in front of the mirror. The image is the same size as the object.

If you wish to take a picture of your image while standing 2 meters in front of a plane mirror, for what distance should you set your camera to provide the sharpest focus? Since the image is the same distance BEHIND the mirror as the object is in front of the mirror…. Set the distance for 4 meters

How big does a mirror have to be in order for you to see your entire image?

Concave Mirrors *Form “real”, inverted images are formed UNLESS the object is inside the focal length… …Then the images are “virtual” and upright!

Convex Mirrors The image is always smaller, upright, and virtual- an SUV. Used in security cameras and rear-view mirrors in your car. Focal point

The Mirror Equation Where f is the focal length, do is the distance from the mirror to the object, and di is the distance from the mirror to the image.

Magnification The magnification provided by a mirror is given by Where hi is the height of the image and ho is the height of the object

Yep, it’s time for you to try one… A concave mirror has a radius of curvature of 15.0 cm. A 1.5 cm tall gummy bear is placed 19.0 cm from the mirror. Where will the image be formed? What is the magnification? How tall is the image? First find the focal length. f = ½ R f = 7.5 cm Now solve for di using the lens equation. di = 12.39 cm Now, get the magnification, m = -di / do m = - 0.65 it’s negative because the image is inverted. Now for the height of the image: m = hi / ho hi = -0.98 cm

Concave and Convex Lenses Light REFRACTS as it passes through lenses, forming images. Convex lenses are CONVERGING lenses Concave lenses are DIVERGING lenses Refraction: the change in direction as a wave passes from one medium into another

Measurements with lenses f - focal length do – distance from the lens to the object being observed. di – distance from the lens to where an image is formed m- magnification- compares the size of the object being observed and the image formed by the lens.

“Virtual” A “virtual” focal point- real light waves would appear to converge at that point, but they actually do not. Concave lenses have a virtual focal point. Convex lenses have a real focal point. A “virtual” image- No real image will appear on a screen. The light rays that reach your eye just behave as if they came from the image position

The “focal length” will be ½ the “radius of curvature”. Convex Lenses The “focal length” will be ½ the “radius of curvature”.

Images formed by Convex lenses If the object is beyond twice the focal length, the image is smaller, inverted, and real- if a piece of paper was placed at the image location, you would see the image on the paper. If the object is placed at exactly twice the focal length, the image will be exactly the same size as the object, inverted, and real If the object is placed exactly at the focal point, the light rays are perfectly parallel, and NO image will be formed! If the object is placed within the focal length, the image will be larger, upright, and VIRTUAL. NO image would appear on a paper screen placed at the image location!

Your Eye

Magnifying glasses Magnifying glasses are convex lenses that converge the light towards a focal point

Diverging Lenses Concave (diverging) lenses ALWAYS form smaller, upright, virtual images. SUV

People who are near-sighted can see up close but not far away. They use concave (diverging) lenses, which will make something far away look like it’s up closer. People who are far-sighted use convex (converging) lenses that make near objects look as if they are further away.

The Lens/Mirror Equation Where f is the focal length, do is the distance from the mirror or lens to the object, and di is the distance from the mirror or lens to the image.

Magnification The magnification provided by a lens or mirror Where hi is the height of the image and ho is the height of the object

Yep, it’s time for you to try one… A convex lens has a radius of curvature of 8.0 cm. A 12 cm tall troll is placed 7.0 cm from the lens. How far from the lens should a screen be placed in order to have a sharp image? What is the magnification? How tall is the image? First find the focal length. f = ½ R f = 4.0 cm Now solve for di using the lens equation. di = 9.33 cm Now, get the magnification, m = -di / do m = - 1.33 it’s negative because the image is inverted. Now for the height of the image: m = hi / ho hi = -16 cm

Using the lens equation for concave lenses The focal point is VIRTUAL, so use a negative value for the focal length. Example: if the radius of curvature of a concave lens is 10 cm, the focal length f = -5 cm.

The power (diopter) = 1 / f Optometrists and opthalmologists, instead of using the focal length to specify the strength of a lens, use a measurement called the power or diopter of a lens. The power (diopter) = 1 / f For example, a 20 cm focal length lens has a power of 1 / 0.20 = 5.0 Diopters

Cameras

Camera Settings Shutter speed: how long the shutter is open. Speeds faster than 1/100 s are normally used. Fast action requires a very small shutter speed.

Camera Settings F-stop: changes the diameter of the iris diaphragm to control the amount of light reaching the film. The SMALLER the f-stop, the LARGER the opening.

The f-stop determines “depth of field”. A larger f-stop (a smaller opening)- will produce an image where everything is in focus. A smaller f-stop (a larger opening)- will produce an image in which only the subject is in focus and everything in the foreground and background is out of focus.

A TELEPHOTO lens has a longer focal length to magnify images. A WIDE-ANGLE lens has a shorter focal length.

Telescopes Refracting telescopes have two lenses, the objective and the eyepiece. The eyepiece lens has a smaller focal length. The objective lens has a larger focal length.

Microscopes Microscopes also have two lenses, the eyepiece and the objective. The eyepiece lens has the longer focal length. The objective has the smaller focal length.

Fresnel Lens The weight and bulk of a large diameter lens can be reduced by constructing the lens from small wedged segments that follow the curvature of the original lens and collapse down to a thin layer.

Augustin Fresnel Fresnel invented this type of lens in 1822.

Fresnel lenses can take a small diverging light source and change it into a powerful straight beam of light.

Small plastic Fresnel lenses are sold at office supply stores as “Magnifying Lenses” Fresnel Lenses are also used in overhead projectors

Large glass lenses that have Fresnel surfaces surrounding a small light source have provided an invaluable contribution to coastline areas for more than 150 years. These lenses are used in…..

Lighthouses

Tests showed that while an open flame lost nearly 97% of its light, and a flame with reflectors behind it still lost 83% of its light, the fresnel lens was able to capture all but 17% of its light. Because of its amazing efficiency, a fresnel lens could easily throw its light 20 or more miles to the horizon.

Refraction When waves enter a new medium, they change direction and speed. The change in direction is called Refraction.

The angle of reflection is ALWAYS equal to the angle of incidence. The angles of incidence, reflection, and refraction are all measured from a line drawn “normal” (perpendicular) to the surface. The angle of reflection is ALWAYS equal to the angle of incidence. That is the Law of Reflection. incidence q q reflected refracted q

The amount that the wave refracts depends on the kind of medium it is moving through. The index of refraction, “n”, of each medium determines both the refraction and the average speed. c / v = n where c is the speed of light in a vacuum and v is the average speed of light through the medium.

For example: what is the velocity of light through water with an index of refraction, n = 1.54? Rearranging c/v = n gives v = c ÷ n v = 3 x 108 ÷ 1.54 = 1.95 x 108 m/s The average speed of light slows down when it goes through water!!

Snell’s Law Snell’s Law describes refraction as light strikes the boundary between two media n1 sin q1 = n2 sin q2 The index of refraction of a pure vacuum and of air is n = 1. The index of refraction of every other substance is greater than 1. incidence reflected refracted q

What is the index of refraction of the glass? Example: Light traveling through air enters a block of glass at an angle of 30° and refracts at an angle of 22°. What is the index of refraction of the glass? incidence reflected refracted q

(ok, actually violet refracts the most…) Different frequencies (colors) refract slightly different amounts. This means that the index of refraction, “n”, for blue light is slightly different than “n” for red light. This results in a dispersions of colors as seen in a prism or a rainbow. Blue Bends Best! (ok, actually violet refracts the most…)

Rainbows! Sunlight refracts as it enters a raindrop. Different colors refract different amounts. This spreads out the colors. The light reflects off the back of the raindrop. The light refracts again, spreading out the colors even more. We see the rainbow!

The Critical Angle and Total Internal Reflection When light passes from a material that is MORE dense to one that is LESS dense, its refracts AWAY from the Normal line. As the angle of incidence increase, the angle of refraction also increases. q refracted incidence

The Critical Angle and Total Internal Reflection At some Critical Angle of incidence, the angle of refraction is 90°. There is no light that is refracted! All of the light is reflected back into the original medium. This is called Total Internal Reflection n2 reflected incidence qcritical n1

The most useful application of the phenomenon of Total Internal Reflection is in Fiber Optics

When wavefronts pass through a narrow slit they spread out When wavefronts pass through a narrow slit they spread out. This effect is called diffraction.

The amount of diffraction depends upon the size of the slit. If the slit is comparable in size to the wavelength of the wave then maximum diffraction occurs.

The number of slit openings also determines what the diffraction pattern looks like.

Thomas Young, in1801, first established the wave theory of light by demonstrating that light diffracted. He also provided the first measurement of the wavelength of light.

Thomas Young’s Double-Slit Experiment He allowed sunlight to fall on two slits. He knew that if light was a wave, it would diffract as it passed through the slits. The diffracted waves would have areas of both constructive and destructive interference. This interference would produce bright and dark areas on a screen.

The pattern of bright and dark fringes did appear on a screen. The brightest area, in the center, he called the “central bright spot”. He was able to mathematically determine the wavelength by measuring the distance from the central bright spot to each fringe.

ml = d(x ÷ L) = dsinq m- “order” (m = 0 is the central bright spot) l- wavelength of light d- distance between the slits x- distance from central bright spot to another bright fringe L- distance from the slits to the screen q- the angle between the line to the central bright spot and the observed bright fringe.

The more slits there are, the narrower the fringes become. The fringes on top are from two slits. The fringes on bottom are from eight slits. A “diffraction grating” has hundreds of slits per millimeter.

Optical diffraction effects can be seen with eye - in fact most of us when children have noticed it, but ignored it when becoming adults. Look through a narrow slit between your fingers. If you look carefully you should see the objects behind are distorted and that blackish bands parallel to the slit appear in the gap. The bands are diffraction patterns.

In the atmosphere, diffracted light is actually bent around atmospheric particles -- most commonly, the atmospheric particles are tiny water droplets found in clouds. An optical effect that results from the diffraction of light is the silver lining sometimes found around the edges of clouds