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Chapter 26

Geometrical Optics (Lecture II)

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Outline Forming images with a plane mirror

Real world application: retroreflector Spherical mirrors

Concave mirror and convex mirror Forming images with a concave or

convex mirror Ray tracing (ray diagram) Mirror equation

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Forming Images with a Plane Mirror

Forming a mirror image: The light from an object reflects from a

mirror before it enters our eyes. To the observer, it appears that the

rays are emanating from behind the mirror.

Some properties of a plane mirror image:

It is upright, but appears reversed right to left.

It is the same distance behind the mirror as the object is in front of the mirror.

It is the same size as the object. It is a virtual but NOT a real image.

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Real World Applications Retroreflection: If the angle

between the two mirrors is 90°, the reflected beam will return to the source parallel to its original path.

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Spherical Mirrors A spherical mirror has the same

shape as a section of a sphere. Concave mirror: The inside surface

is reflecting. Convex mirror: The outside surface

is a reflecting. Center of curvature C: the

center of the sphere with radius R of which the mirror is a section.

Principal axis: a straight line drawn through the center of curvature and the midpoint of the mirror.

Focal point and focal length (see next slide)

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Focal Point and Focal Length of Convex and Concave Mirrors

Focal point F Focal length f:

For a convex mirror: f = - (1/2)R. “-” sign indicates that the focal point F lies behind the mirror.

For a concave mirror: f = (1/2)R. “+” sign indicates that the focal point is in front of the mirror. In this case, the rays of light actually pass through and converge at the focal point F.

Convex mirror

Concave mirror

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Forming Images with a Convex and Concave Mirror

Two techniques to find the orientation, size, and location of an image formed by a spherical mirror: (1) Ray tracing (ray diagram): Gives

the orientation of the image as well as qualitative information on its location and size.

(2) Mirror equation: Provides precise and quantitative information without the need for accurate scale drawing.

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Raying Tracing

Basic idea behind ray tracing:

Follow the path of representative rays of light as they reflect from a mirror and form an image.

Three representative rays: (1) Parallel ray (P ray): a ray

parallel to the principle axis of the mirror

(2) Focal-point ray (F ray): a ray that passes through (concave mirror) or moves toward (convex mirror) the focal point F

(3) Center-of-curvature ray (C ray): a ray that moves along a straight line extending from the center of curvature C

Concave mirror

Convex mirror

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Ray Diagram for a Convex Mirror

Image properties: It is a virtual image: no light actually

passes through the image. Orientation: upright (the same

orientation as the object). Size: smaller than the object. Location: between the mirror and the

focal point F.

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Ray Diagram for a Concave Mirror

Consider three situations, (a), (b) and (c)

Question: Is a makeup mirror concave or convex?

(a)

(b)

(c)

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Mirror Equation Mirror equation:

(1/do) + (1/di) = 1/f do (object distance): distance from the

mirror to the object. di (image distance): distance from the

mirror to the image. f: the focal length of the spherical mirror.

Magnification, m: m = hi/ho= - di/do

hi: height of the image ho: height of the object

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Sign Conventions for the Mirror Equation

Focal length f >0 for concave mirrors f<0 for convex mirrors

Magnification m>0 for upright images m<0 for inverted images

Image distance di >0 for images in front of a mirror (real images) di<0 for images behind a mirror (virtual images)

Object distance do>0 for objects in front of a mirror (real objects) do<0 for objects behind a mirror (virtual objects)

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Examples Exercise 26-1: The concave side of a spoon

has a focal length of 5.00 cm. Find the image distance for this “mirror” when the object distance is (a) 25.0 cm, (b) 9.00 cm, and (c) 2.00 cm. Also, is the image in each case real or virtual? Upright or inverted? Smaller or enlarged?

Exercise 26-2: The convex mirror has a 20.0-cm radius of curvature. Find the image distance for this mirror when the object distance is 6.33 cm.

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Homework #12

Chapter 26, P. 939-941, Problems: #1, 10, 18, 28, 29, 31 (Physics, Walker, 4th edition).