Color Deficiency

Why do we see certain colors? We perceive only the reflected colors.

Color by Transmission The color of a transparent object is due to the color that it transmits The material that absorbs colored light is known as pigment.

Pigment Selectively absorbs some light frequencies while other frequencies are emitted. This process of absorbing light is known as a subtractive process

Total Reflection or Absorption White is a combination of all colors of light being reflected. Black is the absence of light, all light is being absorbed.

Transmitted VS Absorbed

Primary colors of Pigment As a child you were taught that red, yellow & blue were the primary colors, however cyan, magenta and yellow are the most useful when color mixing.

Primary Colors of Pigment Mix red, green and blue paint and the result is muddy brown. Color printing is achieved by using magenta, cyan, yellow and black ink

Subtractive Primary Colors of Pigment Pigments reflect the color they are as well as other colors to either side of them on the visible spectrum. Subtractive Primaries CMYK Cyan, Magenta and Yellow Print

Cyan is light with a wavelength between green and blue or a combination of green and blue light.  Cyan pigment will absorb the red and reflect green and blue or cyan colored light.

Lenses A thin lens consists of a piece of glass or plastic, ground so that each of its two refracting surfaces is a segment of either a sphere or a plane Lenses are commonly used to form images by refraction in optical instruments (cameras, telescopes, etc.)

Lenses - Refraction There two types of lenses - Convex and Concave

Thin Lens Shapes (Convex) converging lenses They have positive focal lengths They are thickest in the middle Produces a real image- refracted light rays do cross at the focal point

More Thin Lens Shapes (Concave) diverging lenses They have negative focal lengths They are thickest at the edges Produces a virtual image- refracted light rays do not cross

Atmospheric Refraction and Sunsets Light rays from the sun are bent as they pass into the atmosphere It is a gradual bend because the light passes through layers of the atmosphere  Each layer has a slightly different index of refraction The Sun is seen to be above the horizon even after it has fallen below it

Atmospheric Refraction and Mirages A mirage can be observed when the air above the ground is warmer than the air at higher elevations The rays in path B are directed toward the ground and then bent by refraction The observer sees both an upright and an inverted image

Eyes and Eyeglasses What type of lens do we have in our eyes? Why do we have problems seeing? What can we do to correct those problems?

SEEING LIGHT - THE EYE Cornea -does most of the focusing Iris - Pupil - has the eye color and controls light intensity Lens - the hole in the eye does remainder of focusing Retina - location of light sensors, has rods and cones Blind spot - Fovea - center of vision, predominantly cones optic nerve exit, no light sensors

Nearsightedness Also called myopia, defect of vision in which far objects appear blurred but near objects are seen clearly. The image is focused in front of the retina rather than upon it. Corrective eyeglasses with concave lenses compensate for the refractive error and help to focus the image on the retina.

Focal point Reflected light enters eye Nearsightedness

Farsightedness also known as hyperopia A condition in which far objects can be seen easily but there is difficulty in near vision. The image is focused behind the retina of the eye rather than upon it. Corrective eyeglasses with convex lenses compensate for the refractive errors.

Focal point behind retina Reflected light enters eye Farsightedness

Astigmatism…pronounced as: stigmatizm A type of faulty vision caused by a non-uniform curvature in the refractive surfaces-usually the cornea, less frequently the lens-of the eye. As a result, light rays do not all come to a single focal point on the retina. Instead, some focus on the retina while others focus in front of or behind it. Vision is blurred. A special cylindrical lens is placed in the out-of-focus axis to correct the condition.

Astigmatism

Mirrors any shiny smooth surface three types of mirrors  convex, concave, and plane

Mirror Symbols f = focal length p = distance between object and mirror q = distance between image and mirror h o = height of object h i = height of image M = magnification = h i / h o

Notations and Flat Mirror The object distance is the distance from the object to the mirror or lens  Denoted by p The image distance is the distance from the image to the mirror or lens  Denoted by q The lateral magnification of the mirror or lens is the ratio of the image height (h ’) to the object height (h)  Denoted by M (=h’/h)

Types of Images for Mirrors and Lenses A real image is one in which light actually passes through the image point  Real images can be displayed on screens A virtual image is one in which the light does not pass through the image point  The light appears to come (diverge) from that point  Virtual images cannot be displayed on screens

Mirror Images Real Image Image that is formed by converging light rays that can be displayed onto a screen. EX: rays of light from an overhead projector Virtual Image Image formed through reflection or refraction. Can be seen by the observer, but cannot be projected onto a screen EX: plane mirror image

More About Images To establish where an image is formed, it is always necessary to follow at least two rays of light as they reflect from the mirror. The image formed by the flat mirror is a virtual image Object distance Image distance

Flat Mirror Simplest possible mirror Properties of the image can be determined by geometry One ray starts at P, follows path PQ and reflects back on itself A second ray follows path PR and reflects according to the Law of Reflection p=q!p=q!

Properties of an Image Formed by a Flat Mirror The image is as far behind the mirror as the object is in front  p = q The image is unmagnified, M=1 The image is virtual The image is upright  It has the same orientation as the object There is an apparent left-right reversal in the image rd/reflection/reflection55.htm l

Application – Day and Night Settings on Car Mirrors With the daytime setting, the bright beam of reflected light is directed into the driver’s eyes With the nighttime setting, the dim beam (D) of reflected light is directed into the driver’s eyes, while the bright beam goes elsewhere

Spherical Mirrors A spherical mirror has the shape of a segment of a sphere A concave spherical mirror has the silvered surface of the mirror on the inner, or concave, side of the curve A convex spherical mirror has the silvered surface of the mirror on the outer, or convex, side of the curve

Concave Mirror, Notation The mirror has a radius of curvature of R Its center of curvature is the point C Point V is the center of the spherical segment A line drawn from C to V is called the principle axis of the mirror I is the image point

Image Formed by a Concave Mirror, cont.  h ’ is negative when the image is inverted with respect to the object

Focal Length Incoming rays are essentially parallel In this special case, the image point is called the focal point The distance from the mirror to the focal point is called the focal length  The focal length is ½ the radius of curvature f = R/2

Focal Point and Focal Length, cont. The focal point depends solely on the curvature of the mirror, not by the location of the object With f=R/2, the mirror equation can be expressed as

Sign Conventions for Mirrors QuantityPositive WhenNegative When Object location (d o ) Object is in front of the mirror Object is behind the mirror Image location (d i ) Image is in front of mirror (real) Image is behind of mirror (virtual) Image height (h’)Image is uprightImage is inverted Focal length (f ) and radius (R) Mirror is concaveMirror is convex Magnification (M)Image is uprightImage is inverted

Focal Length Shown by Parallel Rays

Concave Mirror The center of this mirror curves away from you. This means that with the law of reflection the reflected light rays will cross producing a real image.

Images produced with Concave Mirror d o = C : real inverted image, same size d o = F : no image is seen If object is past C: Real, inverted, reduced image is formed If object is between C and F: real, inverted, large image is produced If in front of F: virtual, upright, enlarged image is produced C F

Convex Mirrors A convex mirror is sometimes called a diverging mirror The rays from any point on the object diverge after reflection as though they were coming from some point behind the mirror The image is virtual because it lies behind the mirror at the point where the reflected rays appear to originate In general, the image formed by a convex mirror is upright, virtual, and smaller than the object

Image Formed by a Convex Mirror

Convex Mirror curves outwards in the middle produces an image that is virtual, upright and smaller than the object Reflected light rays never meet so they cannot produce a real image

Objects in mirror are closer than they appear The Mirror Equation 1/d o + 1/d i = 1/f (1) Convex: f is negative Object distances are always positive for all types of mirrors. d o is positive /d i = 1/f - 1/d o (2) = neg - pos = negative d i is negative Magnification Equation: M = -d i / d o (3) M = -(negative)/positive = positive Image is upright From (2), we see that the magnitude of 1/d i is always larger than 1/d o, so the magnitude of d i is always smaller than d o : M is always less than one for a convex mirror.

Convex Mirror

Concave vs. Convex

Ray Diagrams A ray diagram can be used to determine the position and size of an image They are graphical constructions which tell the overall nature of the image They can also be used to check the parameters calculated from the mirror and magnification equations

Drawing A Ray Diagram To make the ray diagram, you need to know  The position of the object  The position of the center of curvature Three rays are drawn  They all start from the same position on the object The intersection of any two of the rays at a point locates the image  The third ray serves as a check of the construction

The Rays in a Ray Diagram Ray 1 is drawn parallel to the principle axis and is reflected back through the focal point, F Ray 2 is drawn through the focal point and is reflected parallel to the principle axis Ray 3 is drawn through the center of curvature and is reflected back on itself 1 3 2

Notes About the Rays The rays actually go in all directions from the object The three rays were chosen for their ease of construction The image point obtained by the ray diagram must agree with the value of q calculated from the mirror equation

Concave Mirror: object is beyond focal point

Concave: Object located at Center of Curvature

Object is between focal point & mirror

Ray Diagrams A ray diagram may help one determine the approximate location and size of the image, it will not provide numerical information about image distance and object size. The mirror equation expresses the quantitative relationship between the object distance (d o ), the image distance (d i ), and the focal length (f). Magnification equation relates the ratio of the image distance and object distance to the ratio of the image height (h i ) and object height (h o ).

Ray Diagram for Concave Mirror, d o > R The image is real The image is inverted The image is smaller than the object

Ray Diagram for a Concave Mirror, d o < f The image is virtual The image is upright The image is larger than the object

Ray Diagram for a Convex Mirror The image is virtual The image is upright The image is smaller than the object

Notes on Images With a concave mirror, the image may be either real or virtual  When the object is outside the focal point, the image is real  When the object is at the focal point, the image is infinitely far away (to the left in the previous diagrams)  When the object is between the mirror and the focal point, the image is virtual With a convex mirror, the image is always virtual and upright  As the object distance increases, the virtual image gets smaller

Practice A convex mirror has a focal length of cm. An object is placed 32.7 cm from the mirror's surface. Determine the image distance. d i = 8.1 cm Determine the focal length of a convex mirror which produces an image which is 16.0 cm behind the mirror when the object is 28.5 cm from the mirror. f = 36.6 cm

Drawing Ray Diagrams (to determine where an image appears) Law of Reflection applies 1. incident ray: drawn parallel to axis reflects: through focal point 2. incident ray: drawn through center (C) reflects: back through center of curvature 3. incident ray: passes through (or appears to) focal point reflects: parallel to axis.

Concave mirror with object beyond focal point Start from the top of the object, travel parallel to the principle axis and aim for the mirror Reflect through the focal point Start from the top of the object, pass through the focal point and aim for the mirror Reflect parallel to the the principle axis A REAL image forms where the reflected rays intersect Image formed is: Real Inverted Reduced Image formed is: Real Inverted Reduced

Image between Focal Point and Mirror

As you can see, the reflected rays do not cross. That means that no REAL image forms Concave Mirror with object between focal point and mirror Start from the top of the object, guide from the focal point and aim for the mirror Reflect parallel to the principle axis Start from the top of the object, travel parallel to the principle axis and aim for the mirror Reflect through the focal point Extend virtual lines behind the mirror from the reflected rays. A VIRTUAL image forms where the virtual rays intersect Image formed is: Virtual Upright Enlarged Image formed is: Virtual Upright Enlarged

Object in front of focal point of Concave Mirror

Concave mirror with object at focal point Start from the top of the object, travel parallel to the principle axis and aim for the mirror Reflect through the focal point The normal second ray cannot be drawn because you cannot go through the focal point and still hit the mirror Start from the top of the object and aim for the point where the principle axis meets the mirror The reflected ray follows the Law of reflection with an angle equal to the angle of incidence The reflected rays will never cross because they are parallel No image formed: Results in a complete blur No image formed: Results in a complete blur

Convex Mirror (diverging) Forms virtual, upright, and smaller image Reflected light rays never meet so they cannot produce a real image

Convex Mirror

Start from the top of the object, travel parallel to the principle axis and aim for the mirror Reflect using the focal point as a guide. The red is reflected light and the dashed green is the virtual ray that passes through the focal point. Start from the top of the object, guide from the focal point and aim for the mirror Reflect parallel to the the principle axis and draw the virtual ray behind the mirror A VIRTUAL image forms where the virtual rays intersect Image formed is: Virtual Upright Reduced Image formed is: Virtual Upright Reduced