Physics 1202: Lecture 19 Today s Agenda Announcements: Team problems today Team 12: Kervell Baird, Matthew George, Derek Schultz Team 13: Paxton Stowik, Stacey Ann Burke Team 14: Gregory Desautels, Benjamin Hallisey, Kyle Mcginnis Team 15: Austin Dion, Nicholas Gandza, Paul Macgillis-Falcon Homework #9: due Friday Midterm 2: Tuesday April 10: covers Ch. 23-27. Chapter 26: Review Equation for lenses Dispersion & rainbows Chapter 27: Eye Optical instruments h o f i h 1
Converging Lens Principal Rays Object F F P.A. Image 1) Rays parallel to principal axis pass through focal point. 2) Rays through center of lens are not refracted. 3) Rays through F emerge parallel to principal axis. Image is: real, inverted and enlarged (in this case). Assumptions: monochromatic light incident on a thin lens. rays are all near the principal axis. Diverging Lens Principal Rays Object F Image F P.A. 1) Rays parallel to principal axis pass through focal point. 2) Rays through center of lens are not refracted. 3) Rays toward F emerge parallel to principal axis. Image is virtual, upright and reduced 2
26-7: The Lens Equation We have derived, in the paraxial (and thin lens) approximation, the same equations for mirrors and lenses: when the following sign conventions are used: Variable f > 0 f < 0 Mirror concave convex Lens converging diverging o > 0 o < 0 i > 0 i < 0 real (front) virtual (back) real (front) virtual (back) real (front) virtual (back) real (back) virtual (front) 3 Cases for Converging Lenses Object Image Past 2F Inverted Reduced Real This could be used in a camera. Big object on small film Object Between F & 2F Image Inverted Enlarged Real This could be used as a projector. Small slide on big screen Image Object Inside F Upright Enlarged Virtual This is a magnifying glass 3
26-8 Dispersion and the Rainbow The index of refraction n varies slightly with the frequency f of light (or wavelength l) of light in general, the higher f, the higher the index of refraction n This means that refracted light is spread out in a rainbow of colors This is known as dispersion Prisms A prism does two things, 1. Bends light the same way at both entrance and exit interfaces. 2. Splits colors due to dispersion. Index of refraction 1.54 1.52 1.50 white light frequency ultraviolet absorption bands prism 4
Prisms Entering Exiting q 1 q 3 q 4 q 2 For air/glass interface, we use n(air)=1, n(glass)=n Prisms f The index of refraction for a material usually decreases with increasing wavelength Violet light refracts more than red light when passing from air into a material 5
Lecture 19, ACT 1 White light is passed through a prism as shown. Since n(blue) > n(red), which color will end up higher on the screen??? A) BLUE B) RED 26-8 Dispersion and the Rainbow Rainbows are created by the dispersion of light as it refracts in a rain drop. 6
26-8 Dispersion and the Rainbow How does it look. 26-8 More about Rainbows As the drop falls, all the colors of the rainbow arrive at the eye. 7
LIKE SO! In second rainbow pattern is reversed Sometimes a faint secondary arc can be seen. 26-8 A second Rainbow! Two reflection + refraction Less intense because of loss due to refraction 2017 Pearson Education, Inc. 8
26-8 The two Rainbows Why? 2017 Pearson Education, Inc. 27 Optical Instruments 9
The EYE ~f o objective I 2 L I 1 ~f e eyepiece The Eye What does the eye consist of? Sphere (balloon) of water. - An aperture that controls how much light gets through the Iris/pupil - Bulge at the front the cornea - A variable focus lens behind the retina the lens - A screen that is hooked up to your brain the retina Cornea Retina Iris Lens To brain 10
27-1 The Human Eye & the Camera Light passes through the cornea is focused by the lens onto the retina The ciliary muscles change the shape of the lens so it can focus at different distances The vitreous and aqueous humors are transparent Rods and cones on the retina convert the light into electrical impulses signal travels down the optic nerve to the brain. 2017 Pearson Education, Inc. Recall: 3 Cases for Converging Lenses Object Image Past 2F Inverted Reduced Real This could be used in a camera. Big object on small film Object Between F & 2F Image Inverted Enlarged Real This could be used as a projector. Small slide on big screen Image Object Inside F Upright Enlarged Virtual This is a magnifying glass 11
27-1 The Human Eye The eye produces a real, inverted image (usually smaller) on the retina The brain adjusts the image to appear properly That s why things do not look upside down to us 27-1 The Human Eye The ciliary muscles adjust the shape of the lens to accommodate near and far vision. The near point the closest point to the eye that the lens is able to focus normal vision ~ 25 cm from the eye it increases with age as the lens becomes less flexible The far point farthest point at which the eye can focus it is infinitely far away, if vision is normal 12
27-1 The Camera The simplest camera: a lens & film in a light-tight box The camera lens cannot change shape it moves closer to or farther away from the film in order to focus The f-number characterizes the size of the aperture The combination of f-number and shutter speed determines the amount of light that reaches the film Convergent Lens: The Lens Equation h o f i h 13
27-2 Lenses in Combination & Corrective Optics In a two-lens system, the image produced by the first lens serves as the object for the second lens. 27-2 Lenses in Combination & Corrective Optics To find the image formed by a combination of lenses, consider each lens in turn, starting with the one closest to the object. The total magnification is the product of the magnifications of each lens. 14
Multiple Lenses We determine the effect of a system of lenses by considering the image of one lens to be the object for the next lens. -1 0 +1 +2 +3 +4 +5 +6 f = +1 f = -4 For the first lens: o 1 = +1.5, f 1 = +1 \ For the second lens: o 2 = +1, f 2 = -4 \ Multiple Lenses Objects of the second lens can be virtual. Let s move the second lens closer to the first lens (in fact, to its focus): -1 0 +1 +2 +3 +4 +5 +6 f = +1 f = -4 For the first lens: o 1 = +1.5, f 1 = +1 \ For the second lens: o 2 = -2, f 2 = -4 \ Note the negative object distance for the 2nd lens. 15
Multiple Lenses If the two lenses are thin, they can be touching i.e. in the same position. We can treat as one lens. f total =??? For the first lens: o=o 1, i 1 and f 1 For the second lens: o 2 = -i 1, i 2 =i, f 2 Adding, As long as, 27-2 Corrective Optics & Human Eye A nearsighted person: far point at a finite distance objects farther away will appear blurry: lens focus too strong so the image is formed in front of the retina. Use diverging lens f chosen for a distant object to form image at the far point Strength of corrective lenses: 2017 Pearson Education, Inc. 16
27-2 Corrective Optics & Human Eye A farsighted person: see distant objects clearly but cannot focus on close objects the near point is too far away lens not strong enough: image focus is behind the retina. Use a converging lens Augment the converging power of the eye The final image is past the near point 2017 Pearson Education, Inc. 27-3 The Magnifying Glass A simple convex lens makes objects appear bigger by making them appear closer Similar to a corrective lens for farsightedness it brings the near point closer to the eye Angular size of an object angle it subtends on the retina, and depends both on the size of the object and its distance from the eye assuming it is small 17
27-3 The Magnifying Glass If object is moved closer to the eye, its angular size increases. If it is placed at the near point, its size is: Now, place a converging lens very close to the eye with f less than N place object at the focal the object has a larger angular size 27-4 The Compound Microscope In its simplest form, made of two converging lenses One, the eyepiece, is close to the eye The other, the objective, is close to the object 18
Compound Microscope Objective (f ob < 1cm) L Eyepiece (f eye ~5cm) o 1 f ob i 1 f eye h I 1 O h 1 h 2 I 2 Magnification: 27-5 Telescopes Similar to microscopes: an objective + an eyepiece However, objects are at infinity, so the light will be focused at the focal point of the objective The image formed by the objective is at the focal point of the eyepiece. 19
Refracting Telescope Objective (f ob ~ 250cm) Eyepiece (f eye ~5cm) Star f ob i 1 f eye q o q o q h 1 q I 1 h 2 I 2 Angular Magnification: 27-5 Telescopes Objective of a telescope as large as possible so that it may collect as much light as possible. Each doubling of its diameter gives four times more light Very large lenses are difficult to handle Large telescopes are made as reflectors objective is a mirror rather than a lens The mirror has only one surface, can be made very thin, and reflects almost all the light that hits it. 20
27-6 Lens Aberrations Spherical aberration: light striking the lens far from the axis does not focus properly. can be fixed by grinding the lens to a precision, non-spherical shape. Chromatic aberration occurs when different colors of light focus at different points. 27-6 Lens Aberrations Chromatic aberration can be improved by combining two or more lenses that tend to cancel each other s aberrations This only works perfectly for a single wavelength, however. 2017 Pearson Education, Inc. 21
Recap of Today s Topic : Announcements: Team problems today Team 12: Kervell Baird, Matthew George, Derek Schultz Team 13: Paxton Stowik, Stacey Ann Burke Team 14: Gregory Desautels, Benjamin Hallisey, Kyle Mcginnis Team 15: Austin Dion, Nicholas Gandza, Paul Macgillis-Falcon Homework #9: due Friday Midterm 2: Tuesday April 10: covers Ch. 23-27. Chapter 26: Review Equation for lenses Dispersion & rainbows Chapter 27: Eye Optical instruments 22