Lesson 1: Reflection and its Importance Light and Reflection Lesson 1: Reflection and its Importance

The Facts of Light What is light? Light is the range of frequencies of electromagnetic waves that stimulates the retina of the eye.

The Facts of Light The entire range of the spectrum is often broken into specific regions. The subdividing of the entire spectrum into smaller spectra is done mostly on the basis of how each region of electromagnetic waves interacts with matter. Although there are lines between the types of waves there is really no distinction. In reality the spectrum is continuous.

The Role of Light to Sight The visual ability of humans and other animals is the result of the complex interaction of light, eyes and brain. We are able to see because light from an object can move through space and reach our eyes. Once light reaches our eyes, signals are sent to our brain, and our brain deciphers the information in order to detect the appearance, location and movement of the objects we are sighting at.

The Role of Light to Sight The objects which we see can be placed into one of two categories: luminous objects and illuminated objects. Luminous objects are objects which generate their own light. Illuminated objects are objects which are capable of reflecting light to our eyes.

The Role of Light to Sight The sun is an example of a luminous object, while the moon is an illuminated object. During the day, the sun generates sufficient light to illuminate objects on Earth. Everything we see are all seen as a result of light from the sun (the luminous object) reflecting off the illuminated objects and traveling to our eyes.

The Role of Light to Sight None of us are light-generating objects. We are not brilliant objects like the sun; rather, we are illuminated objects like the moon. We make our presence visibly known by reflecting light to the eyes of those who look our way. It is only by reflection that we, as well as most of the other objects in our physical world, can be seen.

The Law of Reflection Line of Sight In order to view an object, you must sight along a line at that object; and when you do light will come from that object to your eye along the line of sight.

The Law of Reflection Light is known to behave in a very predictable manner. If a ray of light could be observed approaching and reflecting off of a flat mirror, then the behavior of the light as it reflects would follow a predictable law known as the law of reflection

The Law of Reflection Incoming and reflected angles are equal.

The Law of Reflection As a convention, an object’s image is said to be at this location behind the mirror. Object distance and image distance are equal. The size of the object is the same size as the image. There is a right to left reversal.

The Law of Reflection Which one of the angles (A, B, C, or D) is the angle of incidence? ______ Which one of the angles is the angle of reflection? ______

The Law of Reflection A ray of light is incident towards a plane mirror at an angle of 30-degrees with the mirror surface. What is the angle of reflection?

Specular vs. Diffuse Reflection Reflection off of smooth surfaces such as mirrors or a calm body of water leads to a type of reflection known as specular reflection. Reflection off of rough surfaces such as clothing, paper, and the asphalt roadway leads to a type of reflection known as diffuse reflection.

Specular vs. Diffuse Reflection

Lesson 2: Image Formation in Plane Mirrors Light and Reflection Lesson 2: Image Formation in Plane Mirrors

Image Formation in Plane Mirrors

Image Characteristics An image location is the location in space where all the reflected light appears to diverge from. Since light from the object appears to diverge from this location, a person who sights along a line at this location will perceive a replica or likeness of the actual object

Image Characteristics In the case of plane (or flat) mirrors, the image is said to be a virtual image. Virtual images are images which are formed in locations where light does not actually reach. Light does not actually pass through the location on the other side of the mirror; it only appears to an observer as though the light is coming from this location.

Image Characteristics

Image Characteristics If you view an image of yourself in a plane mirror (perhaps a bathroom mirror), you will quickly notice that there is an apparent left-right reversal of the image.

Image Characteristics While there is an apparent left-right reversal of the orientation of the image, there is no top-bottom vertical reversal. The image is said to be upright, as opposed to inverted

Image Characteristics A third characteristic of plane mirror images pertains to the relationship between the object's distance to the mirror and the image's distance to the mirror. For plane mirrors, the object distance (often represented by the symbol do) is equal to the image distance (often represented by the symbol di).

Image Characteristics A fourth and final characteristic of plane mirror images is that the dimensions of the image are the same as the dimensions of the object. The ratio of the image dimensions to the object dimensions is termed the magnification. Plane mirrors produce images which have a magnification of 1.

Image Characteristics In conclusion, plane mirrors produce images with a number of distinguishable characteristics. Images formed by plane mirrors are Virtual Upright left-right reversed the same distance from the mirror as the object's distance, and the same size as the object.

What Portion of a Mirror is Required? The diagram shows a 6-foot tall man standing in front of a plane mirror. To see the image of his feet, he must sight along a line towards his feet; and to see the image of the top of his head, he must sight along a line towards the top of his head. The ray diagram depicts these lines of sight and the complete path of light from his extremities to the mirror and to the eye. In order to view his image, the man must look as low as point Y (to see his feet) and as high as point X (to see the tip of his head).

What Portion of a Mirror is Required? The diagram depicts some important information about plane mirrors. To view an image of yourself in a plane mirror, you will need an amount of mirror equal to one-half of your height. A 6-foot tall man needs 3-feet of mirror (positioned properly) in order to view his entire image.

Lesson 3: Concave Mirrors Light and Reflection Lesson 3: Concave Mirrors

Objectives Calculate distance and focal lengths using the mirror equation for concave and convex spherical mirrors. Draw ray diagrams to find the image distance and magnification for concave and convex spherical mirrors. Distinguish between real and virtual images.

Concave Spherical Mirrors A spherical mirror has the shape of a sphere’s surface. A spherical mirror with light reflecting from its silvered, concave surface is called a concave spherical mirror. These are used whenever a magnified image of an object is needed, like in the case of a make up mirror.

The Anatomy of a Curved Mirror Beginning a study of spherical mirrors demands that you first become acquainted with some terminology which will be periodically used. Principal axis Center of Curvature Vertex Focal Point Radius of Curvature Focal Length

The Anatomy of a Curved Mirror

Reflection of Light and Image Formation Light always follows the law of reflection, whether the reflection occurs off a curved surface or off a flat surface. For a concave mirror, the normal at the point of incidence on the mirror surface is a line which extends through the center of curvature. Once the normal is drawn the angle of incidence can be measured and the reflected ray can be drawn with the same angle.

Reflection of Light and Image Formation The image location is the location where reflected light appears to diverge from. For plane mirrors, virtual images are formed. Light does not actually pass through the virtual image location; it only appears to an observer as though the light is coming from the virtual image location.

Reflection of Light and Image Formation Concave mirrors are capable of producing real images (as well as virtual images). When a real image is formed, it appears to an observer as though light is diverging from the real image location. Only in the case of a real image, light is actually passing through the image location.

Reflection of Light and Image Formation

Reflection of Light and Image Formation

Reflection of Light and Image Formation

Reflection of Light and Image Formation

Reflection of Light and Image Formation While the same principle applies for determining the image location, a different result is obtained. When the object is located beyond the center of curvature (C), the image is located between the center of curvature (C) and the focal point (F).

Reflection of Light and Image Formation When the object is located between the center of curvature (C) and the focal point (F), the image is located beyond the center of curvature (C). Unlike plane mirrors, the object distance is not necessarily equal to the image distance. The actual relationship between object distance and image distance is dependent upon the location of the object.

Ray Diagrams - Concave Mirrors The goal of a ray diagram is to determine the location, size, orientation, and type of image which is formed by the concave mirror.

Ray Diagrams - Concave Mirrors Pick a point on the top of the object and draw two incident rays traveling towards the mirror. Using a straight edge, accurately draw one ray so that it passes exactly through the focal point on the way to the mirror. Draw the second ray such that it travels exactly parallel to the principal axis. Place arrowheads upon the rays to indicate their direction of travel

Ray Diagrams - Concave Mirrors Once these incident rays strike the mirror, reflect them according to the two rules of reflection for concave mirrors. The ray that passes through the focal point on the way to the mirror will reflect and travel parallel to the principal axis. Use a straight edge to accurately draw its path. The ray which traveled parallel to the principal axis on the way to the mirror will reflect and travel through the focal point. Place arrowheads upon the rays to indicate their direction of travel. Extend the rays past their point of intersection

Ray Diagrams - Concave Mirrors Mark the image of the top of the object. The image point of the top of the object is the point where the two reflected rays intersect. If your were to draw a third pair of incident and reflected rays, then the third reflected ray would also pass through this point. This is merely the point where all light from the top of the object would intersect upon reflecting off the mirror. Of course, the rest of the object has an image as well and it can be found by applying the same three steps to another chosen point.

Ray Diagrams - Concave Mirrors Repeat the process for the bottom of the object. Typically, this requires determining where the image of the upper and lower extreme of the object is located and then tracing the entire image. After completing the first three steps, only the image location of the top extreme of the object has been found. Thus, the process must be repeated for the point on the bottom of the object. If the bottom of the object lies upon the principal axis (as it does in this example), then the image of this point will also lie upon the principal axis and be the same distance from the mirror as the image of the top of the object. At this point the entire image can be filled in.

Ray Diagrams - Concave Mirrors Mirror equation: Image location can be predicted with the mirror equation

Ray Diagrams - Concave Mirrors Magnification related image and object sizes. Equation for magnification:

Images formed by Concave Mirrors When you place an object beyond the center of curvature, the image that is produced will be real, inverted and smaller than the object.

Images formed by Concave Mirrors If you place the object at C, the image will be real, inverted but it will appear to be the same size as the object.

Images formed by Concave Mirrors If you place the object at a distance between C and the focal point (f), the object will be real, inverted, and larger than the object.

Images formed by Concave Mirrors If you place object at the focal point, the reflection will appear as a blur. No image is formed. You can use this effect to located the focal length of a mirror.

Images formed by Concave Mirrors If you place the object between f and the surface, the image will be virtual, upright and larger than the object.

Convex and Parabolic Mirrors Light and Reflection Convex and Parabolic Mirrors

Convex Spherical Mirrors An outwardly curved, mirrored surface that is a portion of a sphere and that diverges incoming light rays.

Convex Spherical Mirrors The resulting image is always virtual and the image distance is always negative.

Convex Spherical Mirrors Note that the center of curvature and the focal point are located on the side of the mirror opposite the object - behind the mirror. Since the focal point is located behind the convex mirror, such a mirror is said to have a negative focal length value.

Convex Spherical Mirrors After reflection, the light rays diverge; subsequently they will never intersect on the object side of the mirror. For this reason, convex mirrors produce virtual images which are located somewhere behind the mirror.

Convex Spherical Mirrors They take objects in a large field of view and produce a small image. Provide a fixed observer with a complete view of a large area. Warning “objects are closer than they appear”

Ray Diagrams Pick a point on the top of the object and draw two incident rays traveling towards the mirror. Using a straight edge, accurately draw one ray so that it travels towards the focal point on the opposite side of the mirror; this ray will strike the mirror before reaching the focal point; stop the ray at the point of incidence with the mirror. Draw the second ray such that it travels exactly parallel to the principal axis. Place arrowheads upon the rays to indicate their direction of travel

Ray Diagrams Once these incident rays strike the mirror, reflect them according to the two rules of reflection for convex mirrors. The ray that travels towards the focal point will reflect and travel parallel to the principal axis. Use a straight edge to accurately draw its path. The ray which traveled parallel to the principal axis on the way to the mirror will reflect and travel in a direction such that its extension passes through the focal point. Align a straight edge with the point of incidence and the focal point, and draw the second reflected ray. Place arrowheads upon the rays to indicate their direction of travel. The two rays should be diverging upon reflection

Ray Diagrams Locate and mark the image of the top of the object. The image point of the top of the object is the point where the two reflected rays intersect. Since the two reflected rays are diverging, they must be extended behind the mirror in order to intersect. Using a straight edge, extend each of the rays using dashed lines. Draw the extensions until they intersect. The point of intersection is the image point of the top of the object. Both reflected rays would appear to diverge from this point. If your were to draw a third pair of incident and reflected rays, then the extensions of the third reflected ray would also pass through this point. This is merely the point where all light from the top of the object would appear to diverge from upon reflecting off the mirror. Of course, the rest of the object has an image as well and it can be found by applying the same three steps to another chosen point.

Ray Diagrams Repeat the process for the bottom of the object. The goal of a ray diagram is to determine the location, size, orientation, and type of image which is formed by the convex mirror. Typically, this requires determining where the image of the upper and lower extreme of the object is located and then tracing the entire image. After completing the first three steps, only the image location of the top extreme of the object has been found. Thus, the process must be repeated for the point on the bottom of the object. If the bottom of the object lies upon the principal axis (as it does in this example), then the image of this point will also lie upon the principal axis and be the same distance from the mirror as the image of the top of the object. At this point the complete image can be filled in.

Convex Spherical Mirrors As the object distance is decreased, the image distance is decreased and the image size is increased. So as an object approaches the mirror, its virtual image on the opposite side of the mirror approaches the mirror as well; and at the same time, the image is becoming larger.

Convex Spherical Mirrors

Convex Spherical Mirrors Magnification related image and object sizes. Equation for magnification:

Spherical Aberration Aberration - a departure from the expected or proper course. (Webster's Dictionary)

Spherical Aberration In the diagram we can observe a departure from the expected or proper course. The two incident rays which strike the outer edges (to and bottom) of the concave mirror fail to pass through the focal point. This is a departure from the expected or proper course.

Parabolic Mirror Parabolic mirrors eliminate spherical aberration. Usually, a parabolic mirror is substituted for a spherical mirror. The outer edges of a parabolic mirror have a significantly different shape than that of a spherical mirror. Parabolic mirrors create sharp, clear images which lack the blurriness which is common to spherical mirrors.