Ch. 23 Mirrors and lenses. Conceptual questons #13, 15 Problems# 5, 7, 13, 15, 21, 25, 27, 29, 31, 37, 39, 41

Transcription

1 Ch. 23 Mirrors and lenses Conceptual questons #13, 15 Problems# 5, 7, 13, 15, 21, 25, 27, 29, 31, 37, 39, 41

2 Images appear in mirrors where rays of light actually intersect or where they appear to originate. 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. See pictures on page 755. The images are virtual.

3 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. The image is unmagnified (M=1), virtual and upright (not flipped upside down)

4 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.

5 Spherical Mirrors Spherical mirrors have the shape of a segment of a sphere. Concave mirror - the reflective surface is on the inner side of the mirror. see picture on page 757

6 The principle axis is a line drawn through the center of the mirror. Use approximation that we only use light rays that make small angles with the principle axis. Rays that make large angle with principle axis have effect called spherical aberration. Produces blurred image because the rays are not reflected to the exact same place.

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 Mirror equation becomes; 1/p + 1/q = 1/f M = h /h = -q/p Example of flat mirror. For flat mirror, R = infinity So 1/f = 0 Thus p = q Convex mirror: Silvered so the light is reflected from the outer side of the mirror. Also called diverging mirror. Mirror equation is true for these also.

9 Sign conventions for mirrors See page 760. 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.

10 Ray diagrams for mirrors Rules for drawing ray diagrams. These are all products of the rule of angle of incidence is equal to angle of reflection. 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.

11 See pictures of ray diagrams and images on page 761. Work example 23.2 more examples: or/applets/welcome.html /prb4.html

12 Images can be formed by refraction Consider two mediums with different indices of refraction. Rays originating from the object are refracted and converge at the image point. See figure Equation to find where the image is: n1 n2 n2 n1 p q R Magnification is still M = h /h becomes M = h /h = -(n 1 q)/(n 2 p) See sign conventions in table 23.2 do example 23.5

13 Flat refracting surface For a flat refraction surface, all you need to do is use: n1 n2 n2 n1 and set R = p q then n 1 /p = -n 2 /q q = -(n 2 /n 1 )p R do example 23.6

14 Thin Lenses Lens = piece clear material (typically glass) that is shaped so that the two refracting surfaces are either a segment of a sphere or a plane. Examples in fig Two types: Converging and diverging lenses. Converging lenses are thicker in the center than at the edge. Diverging lenses are thinner in the middle.

15 Equation for lenses is the same as equation for mirrors. Group of rays parallel to principle axis converge at the focal length after passing through the lens. The focal length is the image distance that corresponds to an infinite object length. Lenses have two focal points, one on each side.

16 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

17 Thin lenses obey the equation: 1/p + 1/q = 1/f The focal length depends on the index of refraction and the radii of the two sides of the lens. Lens maker s formula: 1 f ( n 1) 1 R 1 1 R 2

18 Ray diagrams for lenses 1) If ray comes from parallel to axis, after being refracted, it will pass through the focal point. 2) If ray is drawn through the center of the lens, it keeps going straight. 3) If ray is drawn through the focal on the same side of the object, after going through the lens, it will be parallel to the principle axis. See fig

19 opic=48 see example 23.7 and 23.8 Combinations of lenses. When you have multiple lenses, you can work each lens one at a time. The image formed by the first lens becomes the object for the second lens. Some telescopes and microscopes work this way.

20 Lens and mirror 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 exact same point, and the image is fuzzy. Two types of aberrations: spherical and chromatic

21 Spherical aberration Results from fact that the focal points of rays far from principle axis are different from the rays that are near the principle axis. Has to do with the spherical shape of the lens or mirror. See fig Cameras can take care of this by having an adjustable aperture that can reduce this problem. By narrowing the aperture, you eliminate the rays that are far from the principle axis.

22 Spherical aberration in mirrors can be reduced or eliminated by using a parabolic mirror. All rays that are parallel to the principle axis are reflected through the focal point. Good for telescopes, where the object is far enough that the rays are essentially parallel to the axis. Also used in flashlights. Put the bulb at the focus and the light is parallel beam is reflected off the parabolic surface. High quality parabolic mirrors are expensive.

23 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.