nPhysics Laboratory 10.2: Plane, Convex, and Concave Concave Mirrors: When parallel light rays from

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  • nPhysics Laboratory 10.2: Plane, Convex, and Concave Mirrors

    Name: ____________________________________ Date: ________________________

    Lab Partners: ____________________________________________________________

    PURPOSE: The purpose of this laboratory is to present the rules for locating images

    for different types of mirrors and to illustrate their use with examples.

    EQUIPMENT: Three Mirrors (plane, convex, concave), Meter Stick, Two Milk

    Containers (one to serve as the object and the other as a reference for the images)

    THEORY: Certain optical devices (mirrors and lenses) can be used to “create” images of

    objects that our brains interpret as actual objects themselves. Mirrors accomplish this by

    reflecting light in such a manner that we “see” images in locations that are not actually

    occupied by the objects in question, while lenses accomplish this feat by virtue of how

    light changes direction when traveling between two materials in which the speed of light

    is different. In addition, certain mirrors and lenses can adjust the magnification of the

    object for clearer viewing.

    Law of Reflection: A light ray incident upon a reflective

    surface will be reflected at an angle equal to the incident

    angle. Both angles are typically measured with respect to the

    normal to the surface.

    The Law of reflection is the only thing needed to sketch every single ray diagram, though

    it seems more complicated than that given the different possibilities. In order for a mirror

    to be effective, it must be shaped properly so that the reflected rays can reach our eyes in a

    spatial arrangement that can be properly processed by our brains. The “perfect” shape for

    a curved mirror is a paraboloid, although spherical mirrors are also effective.

    Plane Mirrors: In the case of a plane mirror, the reflected rays reach our eyes in a pattern

    that results in our brain’s concluding that there is second object behind the mirror at

    precisely the same distance and size of the object being reflected by the mirror.

    Convex Mirrors: A convex mirror is a mirror that bulges in the center. As for the

    plane mirror, the image is upright (right side up) and virtual (our brains must project

    diverging reflected rays backward to create the image). Unlike the plane mirror, the

    image for a convex mirror is always reduced in size as compared to the size of the

    associated object.

    Concave Mirrors: A concave mirror is a mirror that curves forward at the edges.

    When the focal point is between the object and the mirror surface, the resulting image is

    inverted, real, and reduced. When the object is between the focal point and the mirror

    surface and the resulting image is upright, virtual, and enlarged.

  • LOCATING THE FOCAL POINT OF CURVED MIRRORS:

    Concave Mirrors: When parallel light rays

    from a distant object reach a parabolic concave

    mirror, they reflect in such a manner that they

    become focused on a single spot, called a focal

    point. A concave mirror with a spherical surface

    focuses light similarly to a parabolic mirror as

    long as the angle subtended by the spherical

    mirror section is small. A spherical mirror has a

    radius of curvature R (or center of curvature C)

    and a focal length f = R/2.

    Convex Mirrors: A convex mirror is a mirror

    that bulges in the center. As for all other

    mirrors, light rays always bounce off the

    mirrored surface such that the reflected angle is

    equal to the incident angle. When parallel light

    rays reach a parabolic convex mirror, they

    diverge from the surface such that all of the

    backward extensions of these divergent

    reflections meet at a single point … called the

    focal point. Circular mirrors provide very

    close approximations to this behavior, they are

    much easier to construct, and it is much easier

    to approximate their focal point (at a point

    midway between the center of curvature and

    the mirror itself). Accordingly, we will just

    consider circular mirrors.

    Plane Mirrors: When parallel light rays reach a plane mirror,

    they all bounce and travel in the same direction, in accordance

    with the Law of Reflection. Accordingly, plane mirrors do not

    have focal points.

    (note: all images on this page are from

    http://sciencelearn.org.nz/Contexts/Light-and-Sight/Science-Ideas-and-Concepts/Reflection-of-light)

  • Theory to Practice Demonstrations: For each of the three photographs below,

    indicate the type of mirror being used and, where appropriate, locate both the center of

    curvature and the focal point.

  • CREATING IMAGES: The four examples below illustrate the 4 cases for image types

    that correspond to the different mirrors. In each case, indicated whether the image is:

    upright or inverted, real or virtual, reduced or actual size or magnified.

    Description Physical Apparatus Ray Diagram

    Plane Mirror

    _____________

    _____________

    _____________

    Convex Mirror

    _____________

    _____________

    _____________

    Concave Mirror

    with focal point

    between object

    and mirror:

    _____________

    _____________

    _____________

    Concave Mirror

    with object

    between focal

    point and mirror

    _____________

    _____________

    _____________

  • STUDENT PRACTICE: Creating Ray Diagrams to locate images for the 4 cases

    Plane Mirrors: Show where the images of the arrows illustrated will be located for the

    two plane mirrors illustrated below.

    Convex Mirrors: Show where the images of the arrows will be located for the three

    convex mirrors shown below:

  • Concave Mirrors: Show where the images of the arrows will be located for the concave

    mirrors illustrated below:

  • CONSTRUCTION#1: FINDING THE FOCAL POINT FOR A CONCAVE

    PARABOLIC MIRROR

     Set-Up: (Note: This has already been completed on the figure below) o Draw the parabola x=4.0-0.25y2 for the range -5.0

  • CONSTRUCTION#2: FINDING THE FOCAL POINT FOR A CONCAVE

    SPHERICAL MIRROR

     Set-Up: (Note: This has already been completed on the figure below) o Draw a right semicircle of radius R=4.0 that is centered at the origin, with the

    line y=0.0 separating the upper and lower halves of the semicircle. This

    semicircle represents the mirror surface

    o Draw a set of 7 equally spaced horizontal lines, centered around the line y=0.0 and with a separation of 1.0 unit in the y-direction

     Light Ray Incident @ y=0.0, which is along the principal axis of the mirror: o Darken the line y=0.0 from the left edge of the figure until it meets the mirror

    surface, this represents the incident light ray

    o Draw the reflected ray using the law of reflection, based upon the two associated short line segments, which represent the tangent and perpendicular

    directions for the mirror at y=0.0 (Note: From the Law of Reflection, the

    reflected ray travels back along the principal axis of the mirror)

     Light Ray Incident @ y=1.0: o Darken the line y=1.0 from the left edge of the figure until it meets the mirror

    surface, this represents the incident light ray

    o Draw the reflected ray using the law of reflection, from the mirror until it crosses the principal axis. Short line segments, which represent the tangent and

    perpendicular directions for the mirror at y=1.0, have already been drawn to

    assist in the construction. (Note: You should find that the x-intercept of the

    reflected ray is very close to ½ way between the center of curvature and the

    mirror, along the principal axis. This is the focal point for a circular mirror)

     Light Rays Incident @ y=2.0, y=3.0, y=-1.0, y=-2.0, y=-3.0 o Repeat instructions above for Light Ray Incident @ y=1.0. o You should find that the incident rays father from the principal axis result in a

    reflected waves that deviate farther from the focal point. This is property of

    spherical mirrors is called spherical aberration.

  • APPENDIX: Detailed steps for creating ray diagrams

    CASE#1-PLANE MIRRORS: Creating ray diagrams for a plane mirror

     Set Up: o Draw a plane mirror and an object in front of the mirror surface. o Select a point on the object to analyze.

     Locating the Image o Draw the incident light ray (1) from the selected point that is perpendicular to

    the mirror surface. This light ray will just bounce straight back. Draw the

    reflected ray.

    o Draw an incident light ray (2) from the selected point to another point on the mirror surface. Draw the reflected ray using the Law of Reflection.

    o The intersection of the backward extensions for the (diverging) reflected rays marks the position of the image for the selected point.

     Verifying the location of the image. o Draw a third incident ray from the selected point and confirm that the backward