LIGHT & OPTICS Fundamentals of Physics 22 Chapter 34
Chapter 34 Images. Two Types of Images 2. Plane Mirrors 3. Spherical Mirrors 4. Images from Spherical Mirrors 5. Spherical Refracting Surfaces 6. Thin Lenses 7. Optical Instruments Magnifying Glass Microscope Telescope 8. Three Proofs Review & Summary Chapter Questions Exercises & Problems Fundamentals of Physics 22 Chapter 34 2
Two Types of Image Real Image Virtual Image Fundamentals of Physics 22 Chapter 34 3
Plane Mirrors Light Rays & the Image in a Mirror: Observer Plane mirror Virtual Image: no light actually comes from here. Fundamentals of Physics 22 Chapter 34 4
Plane Mirrors Ray Diagram Real Object Virtual Image i - p (plane mirror) Sign Convention: p > 0 (in front of the mirror) i < 0 (behind the mirror) Fundamentals of Physics 22 Chapter 34 5
Plane Mirrors Ray Diagram: object image i - p Fundamentals of Physics 22 Chapter 34 6
Plane Mirrors Object for Mirror Image of Image! Image of Object P in Mirror Object for Mirror 2 Fundamentals of Physics 22 Chapter 34 7
Spherical Mirrors Concave Mirror Real Image Convex Mirror Virtual Image Fundamentals of Physics 22 Chapter 34 8
Focal points Fundamentals of Physics 22 Chapter 34 9
Images from Spherical Mirrors Paraxial Rays - near central axis & at small angles β α + θ γ α + 2θ α + γ 2β tan α α ac / p tan β β ac / r tan γ γ ac / i p + i f f r 2 p + i 2 r Fundamentals of Physics 22 Chapter 34 0
Images from Spherical Mirrors Sign Conventions f r 2 p + i f i for a real image is positive; negative for a virtual image f and r for a concave mirror are positive; negative for a convex mirror Fundamentals of Physics 22 Chapter 34
Images from Spherical Mirrors Focal Length & Parallel Paraxial Rays p f r 2 p + i f i f Reversibility of Rays: Fundamentals of Physics 22 Chapter 34 2
Locating Images by Drawing Rays 4 Rays: 2 Parallel Rays Focal Ray Radial Ray Real Inverted Image Lateral Magnification: m h h i p Virtual Erect Image (similar triangles abc and dec above) Fundamentals of Physics 22 Chapter 34 3
Locating Images by Drawing Rays Real Inverted Image f is positive for a concave mirror p + i f i is positive for a real image f is negative for a convex mirror Virtual Erect Image m f r 2 i p i is negative for a virtual image Sign Convention: > 0 (in front of the mirror) < 0 (behind the mirror) Fundamentals of Physics 22 Chapter 34 4
Sign Conventions for Mirrors Focal Length f is positive for concave mirrors f is negative for convex mirrors Magnification m is positive for upright images m is negative for inverted images Image Distance i is positive for images in front of a mirror (real images) i is negative for images behind a mirror (virtual images) Object Distance p is positive for objects in front of a mirror (real objects) p is negative for objects behind a mirror (virtual objects) Fundamentals of Physics 22 Chapter 34 5
Imaging Characteristics of Convex and Concave Spherical Mirrors Convex Mirror Object location Image orientation Image size Image type Arbitrary Upright Reduced Virtual Concave Mirror Object location Image orientation Image size Image type Beyond C Inverted Reduced Real C Inverted Same as object Real Between F and C Inverted Enlarged Real Just beyond F Inverted Approaching infinity Real Just inside F Upright Approaching infinity Virtual Between mirror and F Upright Enlarged Virtual Fundamentals of Physics 22 Chapter 34 6
Spherical Refracting Surfaces Images Formed by refraction at a spherical surface between two media: Fundamentals of Physics 22 Chapter 34 7
Reflection & Refraction n sin θ n sin Snell s Law of Refraction: 2 2 θ v c n n is the index of refraction: n air.0003 n water.33 n glass.5-.66 n diamond 2.4 Fundamentals of Physics 22 Chapter 34 8
Spherical Refracting Surfaces p n i ( n n ) n 2 2 + r Fundamentals of Physics 22 Chapter 34 9
Spherical Refracting Surfaces Sign Conventions p n i ( n n ) n 2 2 + r Real images form on the side of a refracting surface that is opposite the object; and virtual images form on the same side as the object. p is positive. When the object faces a convex refracting surface, r is positive; negative when it faces a concave surface. ( reverse of the mirror case!) i for a real image is positive; negative for a virtual image Fundamentals of Physics 22 Chapter 34 20
Spherical Refracting Surfaces p n i ( n n ) n 2 2 + r Fundamentals of Physics 22 Chapter 34 2
Spherical Refracting Surfaces Images Formed by Refraction at a spherical surface between two media: Snell s Law: n sin θ n 2 sin θ 2 For small angles: n θ n 2 θ 2 θ α + β β θ 2 + γ For small angles: tan α α ac / p tan β β ac / r p n i ( n n ) n 2 2 + r tan γ γ ac / i Fundamentals of Physics 22 Chapter 34 22
Thin Lenses Thin Lens Formula: p + i f Fundamentals of Physics 22 Chapter 34 23
A Thick Converging Lens The st surface of the lens forms a virtual image I of the object O. The virtual image I becomes the object for the 2 nd refracting surface. The 2 nd surface of the lens forms a real image I of the object O. (See HRW pp 944-946.) Fundamentals of Physics 22 Chapter 34 24
A Thin Lens A thin lens: L zero. The Lens Maker s Formula: f ( n ) r r (See HRW pp 944-946.) Fundamentals of Physics 22 Chapter 34 25
Ray Diagrams for Thin Lenses Real Inverted Image p + i f Parallel Ray Focal Ray Central Ray Virtual Erect Images m i p Thin lens applet Fundamentals of Physics 22 Chapter 34 26
Sign Conventions for Lenses Focal Length f is positive for converging (convex) lenses f is negative for diverging (concave) lenses Magnification m is positive for upright images (same orientation as object) m is negative for inverted images (opposite orientation of object) Image Distance d i is positive for real images (images on the opposite side of the lens from the object) d i is negative for virtual images (images on the same side of the lens as the object) Object Distance d o is positive for real objects (from which light diverges) d o is negative for virtual objects (toward which light converges) Fundamentals of Physics 22 Chapter 34 27
Combination of 2 Thin Lenses. Find the image distance of the st lens. 2. Use it and the distance between the lenses to find the object distance for the 2 nd lens. 3. Find the final image distance for the combined lenses. The overall magnification is the product of magnifications produced by each lens: m m m 2 Fundamentals of Physics 22 Chapter 34 28
Two Lens System f +24 cm f 2 +9 cm L0 cm p 6.0 cm i? Fundamentals of Physics 22 Chapter 34 29
Optical Instruments - Magnifying Glass Image size on the retina of the eye depends on θ Bring it closer to see it better ; but now the eye can t focus on it. Near Point of the human eye P n 25cm Place the object just inside the focal length of a converging lens near your eye. Image is now far enough away to focus on. tanθ θ m θ θ θ h f h 25 25cm f Fundamentals of Physics 22 Chapter 34 30
Optical Instruments - Compound Microscope Small Object Near F Real Image just inside F Observe an enlarged inverted virtual image Very Large Virtual Image viewed at Infinity s >> f ob M m mθ i p 25cm f eye s fob 25cm f eye Fundamentals of Physics 22 Chapter 34 3
Optical Instruments - Compound Telescope Large Distant Object Real Image at Focal Length of Eyepiece Virtual Image viewed at Infinity h θeye feye m θ θ h ob f ob f f ob eye Fundamentals of Physics 22 Chapter 34 32
Optical Instruments - Compound Telescope Faint Very Distant Object Eyepiece Very large diameter mirror to gather more light. Thin- lens and paraxial ray approximations are not exactly valid. Aberrations! Fundamentals of Physics 22 Chapter 34 33
Telescopes Reflector Refractor Fundamentals of Physics 22 Chapter 34 34
Aberrations Non-Paraxial Rays - Spherical Aberration Circle of Least Confusion Distortion Coma Astigmatism Chromatic Aberration in Lenses Parabolic Mirror Fundamentals of Physics 22 Chapter 34 35
Optical Instruments - The Eye Farsighted: Nearsighted: Fundamentals of Physics 22 Chapter 34 36