A. Focal Length. 3. Lens Maker Equation. 2. Diverging Systems. f = 2 R. A. Focal Length B. Lens Law, object & image C. Optical Instruments

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1 Physics 700 Geometric Optics Geometric Optics (rough drat) A. Focal Length B. Lens Law, object & image C. Optical Instruments W. Pezzaglia Updated: 0Aug A. Focal Length 3. Converging Systems 4. Converging Lens (or Mirror). Diverging Lens (or Mirror) 3. Lens Maker Equation Converging: o o Concave mirror Convex lens Light parallel to principle axis converges at the ocal point.. Diverging Systems 5 3. Lens Maker Equation 6 Diverging: o Convex mirror o Concave lens Focal length is negative Focal length o a mirror with radius o curvature R : Focal length o a lens o index n with radius o curvature R (in air) For Lens o index n submerged in medium o index n : R = R = n R = n n

2 3. Lens Maker Equation 7 B. Lens Law 8 The more curved a lens or mirror, the shorter the ocal length.. Lens Equation. Virtual images A bigger index o reraction makes a shorter ocal length lens. 3. Lens combination A lens underwater will have a longer ocal length than above water. Hence you become arsighted underwater.. Lens Equation (Gauss) 9. Virtual Image 0 Distance to object p Distance to image q = + p q For converging lens i p< then image will be virtual and erect. [Magniying glass] I p> then image will be real and inverted. [Diverging systems only can make virtual images.] 3. Lens Combination C. Optical Instruments Two lenses (close together) act as one lens with ocal length given by: = +. The Eye. Telescopes 3. Microscopes Example: eyeglasses. Farsighted eye s lens ocal length is too long. Adding an extra lens shortens it.

3 a Structure o eye 3 b Color Perception 4 Fovea o eye has best resolution (this is what you are using to read), which only has cones (color vision) Optic nerve creates a blind spot Lens is lexible Eye has 3 types o color receptors (blue green red). Hence using just these three colors can trick eye into seeing nearly all colors (can t do violet) Peripheral part o retina is mostly rods which are black & white but can see much ainter light (more than 0x) Your computer screen has only these 3 colors! c Eye: Farsighted 5 c Eye: Nearsighted 6 Hyperopia, also known as arsightedness Cannot see clearly closer than near point Correct with a converging lens Myopia or nearsighted Cannot see clearly past ar point Correct with diverging lens (ocal length equal to negative o ar point) c Astigmatism 7 c Astigmatism 8 Focal length horizontal is not same as vertical Generically, means you can ocus on one axis, but the other is out o ocus.

4 c Astigmatism 9 d Binocular Vision 0 Two eyes see slightly dierent images (due to parallax). Brain puts it together to see 3D. Can trick brain into seeing 3D by giving each eye a dierent picture (stereographs). Modern 3D movies do it using polarization glasses. Columbian Exposition 893, stereograph, viewer d. 3D Vision d. 3D Vision e. Magnitudes and Brightness 43.Magnitude Scale: Hipparchus o Rhodes (60-7 B.C) assigns magnitudes to stars to represent brightness. The eye can see down to 6 th magnitude e Herschel Extends the Table 44 William Herschel (738-8) extended the scale in both directions

5 e Herschel-Pogson Relation 45 Herschel s measurements suggested a st magnitude star is 00x more luminous that a 6 th magnitude one. Norman Pogson (854) showed that this is because the eye s response to light is logarithmic rather than linear. m = -.5Log( r) C.3b Gemini Mag 6 g4 Mag Telescopes 7 Our new telescope! Meade 4" LX00-ACF (/0) Advanced Coma-Free w/uhtc # USD$ 6, Schmidt-Cassegrain Focus Aperture 4 inch (356 mm) Focal Length 3556 mm (/0) Resolution 0.3 a Light Gathering Power Light Gathering Power (aka Light Ampliication) is proportional to area o mirror More light, can see ainter (more distant) objects. Aperture=diameter o objective mirror (or our telescope its 4 inches=356 mm) Aperture objective LGP = Aperture eye 356 mm = 6 mm = 350 more than eye 8 b Limiting Magnitude 9 c. Basic Telescope Design 30 Consulting table, a LGP o 350 translates to more than 8.5 magnitudes. Exact calculation: m =.5Log(350) = Reractor Telescope (objective is a lens) Focal Length o Objective is big Focal Length o eyepiece is small Limiting magnitude o naked eye is +6, can see over 8000 stars. hence looking through scope we can see up to +4.8 or over 00,000,000 stars in our galaxy, and over 000 galaxies!

6 d Chromatic Aberration 4 Dierent colors are bent (reracted) at slightly dierent angles, with red light ocusing the urthest away. Diicult to get a sharp color picture. Problem with reracting telescopes e Newtonian Relecting Telescope Objective is a mirror, no chromatic problems! Focal length is approximately the length o tube Light is directed out the side or the eyepiece 3 Schmidt Cassegrain Relecting Telescope 33. Magniication Power 34 Cassegrain ocus uses olded optics so the ocal length is more than twice the length o tube The overall magniication o the angular size is given by the ratio o the ocal lengths Light path goes through hole in primary mirror Schmidt design has corrector plate in ront F Power = F objective eyepiece For our scope (F=3556 mm), with a 6 mm eyepiece, the power would be: 3556 mm Power = = 37 6mm g. Too Much Magniication? Extended objects (planets, nebulae, galaxies) when magniied more will appear ainter 35 h. Too Much Magniication? Too much magniication and you won t see it at all! Its about surace brightness! Your eye can t see below a certain amount. 36 Low Power High Power Low Power High Power

7 3. Microscopes (briely) 37 Creates a BIG virtual image 5 cm away rom the eye. D. Reerences Lick Observatory Video: Video: Mechanical Universe #40, Optics Stereographs: Stereograph: 38