Do Now. 1. A ray of light is incident towards a plane mirror at an angle of 30-degrees with the mirror surface. What will be the angle of reflection?

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1 Do Now 1. A ray of light is incident towards a plane mirror at an angle of 30-degrees with the mirror surface. What will be the angle of reflection? 2. If Suzie stands 3 feet in front of a plane mirror, how far from the person will her image be located?

2 23.3 Formation of Images by Spherical Mirrors Spherical mirrors are shaped like sections of a sphere, and may be reflective on either the inside (concave) or outside (convex).

3 23.3 Formation of Images by Spherical Mirrors Rays coming from a faraway object are effectively parallel.

4 23.3 Formation of Images by Spherical Mirrors Parallel rays striking a spherical mirror do not all converge at exactly the same place if the curvature of the mirror is large; this is called spherical aberration.

5 23.3 Formation of Images by Spherical Mirrors If the curvature is small, the focus is much more precise; the focal point is where the rays converge.

6 Terms The point in the center of the sphere from which the mirror was sliced is known as the center of curvature and is denoted by the letter C The point on the mirror's surface where the principal axis meets the mirror is known as the vertex and is denoted by the letter A

7 Terms The vertex is the geometric center of the mirror. Midway between the vertex and the center of curvature is a point known as the focal point; the focal point is denoted by the letter F. The distance from the vertex to the center of curvature is known as the radius of curvature (represented by R). The radius of curvature is the radius of the sphere from which the mirror was cut.

8 Terms the distance from the mirror to the focal point is known as the focal length (represented by f). Since the focal point is the midpoint of the line segment adjoining the vertex and the center of curvature, the focal length would be one-half the radius of curvature.

9 23.3 Formation of Images by Spherical Mirrors Using geometry, we find that the focal length is half the radius of curvature: (23-1) Spherical aberration can be avoided by using a parabolic reflector; these are more difficult and expensive to make, and so are used only when necessary, such as in research telescopes.

10 1.Check Your Understanding: The surface of a concave mirror is pointed towards the sun. Light from the sun hits the mirror and converges to a point. How far is this converging point from the mirror's surface if the radius of curvature (R) of the mirror is 150 cm? Answer: 75 cm If the radius of curvature is 150 cm. then the focal length is 75 cm. The light will converge at the focal point, which is a distance of 75 cm from the mirror surface.

11 2. Check Your Understanding: It's the early stages of a concave mirror lab. Your teacher hands your lab group a concave mirror and asks you to find the focal point. What procedure would you use to do this? You will need to measure the distance from the vertex to the focal point. But first you must find the focal point. The trick involves focusing light from a distant source (the sun is ideal) upon a sheet of paper. Once you find the focal point, make your focal length measurement.

12 Formation of Image Upon reflecting, the light will converge at a point. At the point where the light from the object converges, a replica, likeness or reproduction of the actual object is created. This replica is known as the image.

13 23.3 Formation of Images by Spherical Mirrors We use ray diagrams to determine where an image will be. For mirrors, we use three key rays, all of which begin on the object: 1. A ray parallel to the axis; after reflection it passes through the focal point 2. A ray through the focal point; after reflection it is parallel to the axis 3. A ray perpendicular to the mirror; it reflects back on itself

14 23.3 Formation of Images by Spherical Mirrors

15 23.3 Formation of Images by Spherical Mirrors The intersection of these three rays gives the position of the image of that point on the object. To get a full image, we can do the same with other points (two points suffice for many purposes).

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17 Object Located Beyond Center of Curvature

18 Object Located at the center of Curvature

19 Object is Located Between Center of Curvature and Focal Point

20 Object is Located in Front of Focal Point

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23 Do Now If a concave mirror produces a real image, is the image necessary inverted? Explain.

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25 23.3 Formation of Images by Spherical Mirrors If an object is outside the center of curvature of a concave mirror, its image will be inverted, smaller, and real.

26 23.3 Formation of Images by Spherical Mirrors If an object is inside the focal point, its image will be upright, larger, and virtual.

27 Image Characteristics for Concave Mirrors L location O orientation S relative size T - type 1) Between C and F, inverted, reduced, real

28 2) At C, inverted, same size, real 3) Beyond C, inverted, magnified, real 4) No image 5) Beyond mirror, upright, magnified, virtual

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30 Convex Mirror A convex mirror is sometimes referred to as a diverging mirror due to the fact that incident light originating from the same point and will reflect off the mirror surface and diverge.

31 23.3 Formation of Images by Spherical Mirrors For a convex mirror, the image is always virtual, upright, and smaller.

32 Image Characteristics for Convex Mirrors Convex mirrors always produce virtual upright reduced in size images. The location of the object does not affect the characteristics of the image.

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34 23.3 Formation of Images by Spherical Mirrors Geometrically, we can derive an equation that relates the object distance, image distance, and focal length of the mirror: (23-2)

35 23.3 Formation of Images by Spherical Mirrors We can also find the magnification (ratio of image height to object height). (23-3) The negative sign indicates that the image is inverted. This object is between the center of curvature and the focal point, and its image is larger, inverted, and real.

36 The +/- Sign Conventions The sign conventions for the given quantities in the mirror equation and magnification equations are as follows: f is + if the mirror is a concave mirror f is - if the mirror is a convex mirror d i is + if the image is a real image and located on the object's side of the mirror. d i is - if the image is a virtual image and located behind the mirror. h i is + if the image is an upright image (and therefore, also virtual) h i is - if the image an inverted image (and therefore, also real)

37 23.3 Formation of Images by Spherical Mirrors Problem Solving: Spherical Mirrors 1. Draw a ray diagram; the image is where the rays intersect. 2. Apply the mirror and magnification equations. 3. Sign conventions: if the object, image, or focal point is on the reflective side of the mirror, its distance is positive, and negative otherwise. Magnification is positive if image is upright, negative otherwise. 4. Check that your solution agrees with the ray diagram.