CH. 23 Mirrors and Lenses HW# 6, 7, 9, 11, 13, 21, 25, 31, 33, 35

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1 CH. 23 Mirrors and Lenses HW# 6, 7, 9, 11, 13, 21, 25, 31, 33, 35

2 Mirrors Rays of light reflect off of mirrors, and where the reflected rays either intersect or appear to originate from, will be the location of the image. Real image light actually passes through the image point. Virtual image light appears to come from the image point. Different situations will yield real or virtual images.

3 Mirrors are commonly made of a piece of glass with a thin reflective metal coating on the back side. (sometimes a layer of silver) If you scratch away the metal coating you just have piece of glass. Some light reflects off the front surface of the glass. The rest of the light passes through the glass before reflecting off the metal and going back through the mirror. See how a rearview mirror works with a day and night setting. fig. 23.5

4 For a flat mirror: Magnification: M = image height/object height = h /h M = 1 The image appears as far behind the mirror as the object is in front. Image distance/object distance = Image height/object height The image is unmagnified (M=1), virtual and upright (not flipped upside down) fig. 23.2

5 Spherical Mirrors Spherical mirrors have the shape of a segment of a sphere. In 2-D we will treat them as a segment of a circle. Concave mirror the reflective surface is on the inner side of the mirror. Figure 23.7 Convex mirror the reflective surface is on the outer side of the mirror.

6 Spherical mirrors have an axis of symmetry. The principle axis is a line drawn through this line of symmetry, through the center of the mirror. We will use an approximation where we only use rays of light that make small angles with the principle axis. Rays that make large angles with the principle axis produce an effect called spherical aberration. Produce a blurry image because the rays are not reflected to the exact same location. figure 23.8

7 Spherical Mirrors M = h /h = -q/p (q = image length p = object length) Mirror equation 1/p + 1/q = 2/R R = radius of curvature of mirror When p is very large(approaches infinity) 1/p =0 Then the image is at q = R/2 The incoming rays are essentially parallel and are focused at the image location. (fig ) This point is called the focal point, f f= R/2

8

9 Convex mirror: Silvered so the light is reflected from the outer side of the mirror. Also called a diverging mirror. Mirror equation is still true for convex mirrors. fig For a convex mirror, the center of the circle, and thus the focal point, are both behind the mirror. (Opposite side of mirrors from the object)

10 Table 23.1 Sign Conventions for Mirrors If p, q, and f are in front of the mirror, they are positive. If in back, negative. If the image is upright, positive image height. If image is inverted, negative image height. The big difference between concave and convex mirrors is that concave mirrors have a positive focal length. Convex mirrors have a negative focal length.

11 Ray Diagrams for Mirrors Rules for drawing ray diagrams. These are all the product of the law that the angle of reflection is equal to the angle of incidence. 1)Rays drawn parallel to principle axis are reflected through the focal point. 2)Rays drawn through focal point are reflected parallel to principle axis. 3)Ray drawn through center of curvature (point C) get reflected back on itself. 4)Also can see that a ray incident at the center of the mirror is reflected at an equal angle.

12 See figure Work example 23.2 This was done in the ray tracing for mirrors lab. Make these drawing neat and to scale. These drawing can be used to determine image positions and image heights if drawn correctly.

13 Images can also be formed by Refraction

14

15

16 The equation for lenses is the same as the equation for mirrors. Rays parallel to the principle axis of a lens will converge at the focal length after passing through the lens. The focal length is the image distance that corresponds to an infinite object distance. Key difference between lenses and mirrors: Lenses have two focal points, one on each side.

17 Converging lenses cause parallel rays to converge. Diverging lenses cause parallel rays to diverge (spread out) see fig again M = h /h = -q/p Table 23.3 has sign conventions for lenses. Converging lens has + focal length Diverging lens has focal length

18

19 Ray Diagrams for Lenses 1) If a ray comes from parallel to the principle axis, after being refracted, it will pass through the focal point behind the lens. 2) If a ray drawn through the center of the lens, it keeps going straight. 3) If a ray is drawn through the focal point in front of the lens, after going through the lens, it will refract so that it is parallel to the principle axis. Figure 23.25

20 See examples 23.7 and 23.8 Combinations of lenses. When you have multiple lenses, you can work out each lens, one at a time. The image formed by the first lens, becomes the object for the second lens. This is how some telescopes and microscopes work.

21 Lens and Mirrors Aberrations We used assumptions that the incoming rays make small angles with the principle axis. This is not always true in life. When the angles are large, the rays are not focused to the same point. Image is fuzzy. Two types of aberrations: spherical and chromatic

22 Spherical Aberration Results from the fact that the focal points of rays that are far from the principle axis are different from the focal point of rays that are near the principle axis. Has to do with the spherical shape of the lens or mirror. Figure When taking a picture, your camera can reduce this problem by having an adjustable aperture. By narrowing the aperture, you eliminate the rays that are far from the principle axis.

23 Spherical aberration in mirrors can be reduced or eliminated by using a parabolic mirror instead of a spherical mirror. All rays that are parallel to the principle axis will be reflected through the focal point. Good for telescopes, since the object is far enough away that all the rays are essentially parallel to the axis. Can be used in flashlights. Put the bulb at the focus. Then the rays are reflected off the parabolic mirror and will be parallel to the axis. Problem: High quality parabolic mirrors are expensive.

24 Chromatic Aberration White light is made up of light of different colors (wavelengths). In chapter 22 we saw that index of refraction depends on wavelength. Therefore, when different colors pass through a lens, they are focused to different points. See fig Chromatic aberration can be reduced by using the right combination of converging and diverging lenses. Takes some effort. Mirrors don t have chromatic aberration, since the law of reflection does not depend on wavelength.

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