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Mirrors And Lenses Chapter 23

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Introduction Images can be formed by plane or spherical mirrors and by lenses. Images can be formed by plane or spherical mirrors and by lenses. –Ray diagrams will be used

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Plane and Curved Mirrors Important terms: Important terms: –Object distance (p) –Image »Formed where light rays actually intersect or where they appear to originate –Image distance (q)

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Two Types of Images Real image Real image –Light rays actually intersect and pass through the image point. –May be formed on a screen

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Virtual Image Virtual Image –Light rays only appear to come from the image point. –Cannot be formed on a screen »Example: images in flat mirrors

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Flat Mirrors The image distance (q) always equals the object distance (p). The image distance (q) always equals the object distance (p). 23.1, 29.1

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The image height (h’) always equals the object height (h). The image height (h’) always equals the object height (h).23.2

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Images are left-right reversed. Images are left-right reversed.

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Images are always virtual. Images are always virtual.186

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Images are always upright. Images are always upright.

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Magnification (M) is always 1. Magnification (M) is always 1.

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Flat Mirrors Summary The image distance always equals the object distance. The image distance always equals the object distance. The image height (h’) always equals the object height (h). The image height (h’) always equals the object height (h). Images are left-right reversed. Images are left-right reversed. Images are always virtual. Images are always virtual. Images are always upright. Images are always upright. Lateral magnification (M) is always 1. Lateral magnification (M) is always 1.

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Applications of Flat Mirrors Rearview mirrors in cars Rearview mirrors in cars Dressing room mirrors Dressing room mirrors Bathroom mirrors Bathroom mirrors 242, 29.2

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Concave Mirrors Concave mirrors are a part of a sphere. Concave mirrors are a part of a sphere. 236, 380

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Light reflects from the inner surface. Light reflects from the inner surface.

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Images formed may be real or virtual. Images formed may be real or virtual. –The type of image depends upon the object location.

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Images may be upright or inverted. Images may be upright or inverted.

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Concave mirrors are sometimes called converging mirrors. Concave mirrors are sometimes called converging mirrors.

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The focal length is positive. The focal length is positive.

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Concave Mirrors Summary Are a part of a sphere Are a part of a sphere Light reflects from the inner surface. Light reflects from the inner surface. Images formed may be real or virtual. Images formed may be real or virtual. –Depends upon object location Images may be upright or inverted. Images may be upright or inverted. Sometimes called converging mirrors Sometimes called converging mirrors Focal length is positive. Focal length is positive.

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Important Terms Principal axis Principal axis Image point Image point Image distance (q) Image distance (q) Object distance (p) Object distance (p) Center of curvature C Center of curvature C Radius of curvature R Radius of curvature R Focal point (F) Focal point (F) Focal length (f) Focal length (f)23.9

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Spherical Aberration Spherical aberration is an undesirable characteristic that is present in all spherical mirrors Spherical aberration is an undesirable characteristic that is present in all spherical mirrors »It may be eliminated by using parabolic mirrors.

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Parabolic Mirror Applications Satellite dishes Satellite dishes Car headlights Car headlights Flashlights Flashlights Projector bulbs Projector bulbs Astronomical telescopes Astronomical telescopes

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Ray Diagrams Front side and back side of the mirror Front side and back side of the mirror –Light rays are always in front of the mirror. »This is taken to be the left side.

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Three Important Rays The intersection of any two rays will locate the image. The intersection of any two rays will locate the image. Parallel rays that come from infinity always pass through the focal point Parallel rays that come from infinity always pass through the focal point –When the object is at infinity, the image is at the focal point 382, 188, 382, 383

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The paths of light rays are reversible. The paths of light rays are reversible.238

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Equations for Concave Mirrors Magnification equation: Magnification equation: The mirror equation The mirror equation

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Applications of Concave Mirrors Shaving mirrors Shaving mirrors Makeup mirrors Makeup mirrors Solar cookers Solar cookers

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Convex Mirrors Convex mirrors are a part of a sphere. Convex mirrors are a part of a sphere.380

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Light reflects from the outer surface. Light reflects from the outer surface.

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Images formed are always virtual. Images formed are always virtual. –They always lie behind the mirror.

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Images are always upright. Images are always upright.

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Convex mirrors are sometimes called diverging mirrors. Convex mirrors are sometimes called diverging mirrors.

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The focal length is negative. The focal length is negative.

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Convex Mirrors Summary Are a part of a sphere Are a part of a sphere Light reflects from the outer surface Light reflects from the outer surface Images formed are always virtual Images formed are always virtual –They always lie behind the mirror. Images are always upright Images are always upright Sometimes called diverging mirrors Sometimes called diverging mirrors Focal length is negative Focal length is negative

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Ray Diagrams for Convex Mirrors Front side and back side of the mirror Front side and back side of the mirror –Light rays are always in front of the mirror.

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Ray Diagrams See Figure See Figure –Three important rays (see pg. 765) 23.11, 240, 384, 23.12

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Rays that come from infinity always pass through the focal point. Rays that come from infinity always pass through the focal point. –When the object is at infinity, the image is at the focal point.

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The intersection of two rays will locate the image. The intersection of two rays will locate the image.

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Equations for Convex Mirrors These equations are the same as before. These equations are the same as before. –Magnification equation –The mirror equation

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Sign Conventions for Mirrors See Table 23.1 on page 765 See Table 23.1 on page 765

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Applications of Convex Mirrors Side view mirrors on cars Side view mirrors on cars Shoplifting mirrors Shoplifting mirrors

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Questions 1 - 4, 7 Pg. 783

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Images Formed By Refraction Sign conventions Sign conventions –See Table 23.2 on page 770

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Apparent Depth Flat refracting surfaces Flat refracting surfaces –Apparent Depth (q) vs. Actual Depth (p) » n 1 is below the surface 23.16, 243

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Atmospheric Refraction The Sun is not where it appears to be. The Sun is not where it appears to be. –It can be seen even though it is below the horizon. Sun dogs and Moon dogs Sun dogs and Moon dogs –Halos on cold winter days or nights »Refraction through hexagonal ice crystals Mirages Mirages23.21

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Thin Lenses A thin lens is a piece of glass or plastic which is ground so that its surfaces are segments of either spheres or planes. A thin lens is a piece of glass or plastic which is ground so that its surfaces are segments of either spheres or planes. –A thin lens acts like two prisms.

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Refraction in Optical Instruments Thin lenses are used to form images by refraction in optical instruments Thin lenses are used to form images by refraction in optical instruments –Cameras –Projectors –Microscopes –Telescopes –Binoculars –Magnifying glasses 248, 249

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The Thin Lens Equation The lens equation is virtually identical to the mirror equation. The lens equation is virtually identical to the mirror equation.23.23

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Common Lens Shapes Converging lenses Converging lenses –Biconvex –Convex-concave –Plano-convex Diverging lenses Diverging lenses –Biconcave –Convex-concave –Plano-concave 64, 66, 67

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Convex Lenses Convex lenses form virtual images when the object is within the focal length of the lens. Convex lenses form virtual images when the object is within the focal length of the lens. –Example: a simple magnifying glass. Convex lenses form real images when the object is beyond the focal length of the lens. Convex lenses form real images when the object is beyond the focal length of the lens.250

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Concave Lenses Concave lenses never form real images. 251 Concave lenses never form real images. 251

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Thin Lens Concepts Focal point (F) Focal point (F) –Thin lenses have two. –Parallel light rays pass through the lens and converge or appear to originate here. Focal length (f) Focal length (f)68

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Magnification Equation Equation for magnification: Equation for magnification:

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Thin Lens Equation Thin-lens equation: Thin-lens equation:

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Lens Maker’s Equation R 1 is for the surface closest to the object R 1 is for the surface closest to the object

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The front of the lens The front of the lens –The side from which light approaches

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Sign Conventions Sign conventions (Table 23.3) pg. 775 Sign conventions (Table 23.3) pg. 775 –Extremely important!

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Ray Diagrams Ray diagrams (similar to mirrors) Ray diagrams (similar to mirrors) –Three important rays –Rays that come from infinity always pass through the focal point. »When the object is at infinity, the image is at or appears to be at the focal point. –The intersection of two rays will locate the image. 247, 23.25, 69, 70

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Thin Lens Combinations The image formed by the first lens serves as the “object” for the second lens. The image formed by the first lens serves as the “object” for the second lens.256

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A location diagram is definitely useful when determining p 2. A location diagram is definitely useful when determining p 2.252

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Total Magnification of Thin Lens Combinations Formula: Formula:

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Spherical Aberration Similar to that produced by mirrors Similar to that produced by mirrors –In mirrors, it can be reduced by using parabolic surfaces. »Parabolic mirrors are used in headlights, satellite dishes, searchlights, and astronomical mirrors. »Parabolic surfaces are more expensive to make

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In lenses, spherical aberration may be reduced by using a small aperture size. In lenses, spherical aberration may be reduced by using a small aperture size.

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Chromatic Aberration Chromatic aberration results because different wavelengths have different indices of refraction. Chromatic aberration results because different wavelengths have different indices of refraction. Chromatic aberration is produced by lenses but not by mirrors. Chromatic aberration is produced by lenses but not by mirrors.

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Chromatic Aberration may be reduced by using combinations of converging and diverging lenses made from different types of glass Chromatic Aberration may be reduced by using combinations of converging and diverging lenses made from different types of glass –This is expensive.

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Questions Pg. 784

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