Physics 1202: Lecture 21 Today s Agenda Announcements: Team problems today Team 14: Gregory Desautels, Benjamin Hallisey, Kyle Mcginnis Team 15: Austin Dion, Nicholas Gandza, Paul Macgillis-Falcon Homework #10: due Friday next week NO HOMEWORK this week. Midterm 2: solutions in class Chapter: 27 Optical instruments Review of the eye Microscope & telescope Chapter 28: Physical Optics Interference Two-slit experiment 27 Optical Instruments 1
The Mirror/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) 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 2
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 3
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. 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 \ 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. 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. 5
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 6
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 focus 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 7
Compound Microscope o 1 Objective (f ob < 1cm) f ob L=i 1 +f eye i 1 Eyepiece (f eye ~5cm) f eye L np =N m eye =N/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. 8
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. 9
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. 10
28- Physical Optics Interference Diffraction 28-1 Superposition and Interference If two waves occupy the same space, their amplitudes add at each point. They may interfere either constructively or destructively. 11
Superposition What happens when two waves collide? They add point by point Why? Because the wave equation is linear. This is the principle of superposition. Interference Light waves interfere with each other much like mechanical waves do All interference associated with light waves arises when the electromagnetic fields that constitute the individual waves combine Constructive interference Destructive interference 12
Lecture 21 Act 1 If you added the two sinusoidal waves shown in the top plot, what would the result look like? Conditions for Interference Incoherent light beams pass through each other, with no obvious interference. Although white-light interference is observed under certain conditions, it s easier to see interference when sources are monochromatic. For sustained interference between two sources of light to be observed, there are two conditions which must be met The sources must be coherent They must maintain a constant phase with respect to each other The waves must have identical wavelengths 13
A wave through a slit Wavefronts: slit acts like point source Rays A wave through two slits (two coherent point sources) 14
Intensity What happens when two light waves are present at the same point in space and time? What will we see? Intensity! Add Amplitudes! (electric fields or magnetic fields) Brightness ~ <Amplitude 2 > ~ ½ E 0 2 Lecture 21 Act 2 Suppose laser light of wavelength l is incident on the two-slit apparatus as shown below. Which of the following statements are true? (A) There are new patterns of light and dark. (B) The light at all points on the screen is increased (compared to one slit). (C) The light at all points on the screen is decreased (compareed to two slits). 15
A wave through two slits l 1 q d q l 2 L Assume L is large, Rays are parallel Screen A wave through two slits In Phase, i.e. Maxima when DP= l 2 - l 1 = d sinq = ml Out of Phase, i.e. Minima when DP = d sinq = (m+1/2)l d q DP= l 2 -l 1 = d sinq Screen 16
A wave through two slits In Phase, i.e. Maxima when DP = d sinq = ml + Out of Phase, i.e. Minima when DP = d sinq = (m+1/2)l + Waves and Interference Note that you could derive the reflectance equation (q i =q R ) using a particle model for light. Bouncing balls. You could also derive Snell s Law for particles. n 1 sin (q i )=n 2 sin(q 2 ) The particles change speed in different media (Newton did just this) You cannot get a particle model for these interference effects. You would have to magically create particles at the bright spots and annihilate them at the dark spots. Interference effects mean that light must be made up of waves. 17
28-2 Young s Two-Slit Experiment In this experiment, the original light source need not be coherent it becomes so after passing through the first very narrow single slit Thomas Young first demonstrated interference in light waves from two sources in 1801 Light is incident on a screen with a narrow slit, S o The light waves then pass through two narrow, parallel slits, S 1 and S 2 The bright areas : constructive interference The dark areas : destructive interference 2017 Pearson Education, Inc. 28-2 Young s Two-Slit Experiment The light on the screen has alternating light and dark fringes, corresponding to constructive and destructive interference. The path difference is Therefore, the condition for bright fringes (constructive interference) is: 18
28-2 Young s Two-Slit Experiment This diagram illustrates the numbering of the fringes. The dark fringes are between the bright fringes; the condition for dark fringes is: 2017 Pearson Education, Inc. Recap of Today s Topic : Announcements: Team problems today Team 14: Gregory Desautels, Benjamin Hallisey, Kyle Mcginnis Team 15: Austin Dion, Nicholas Gandza, Paul Macgillis-Falcon Homework #10: due Friday next week NO HOMEWORK this week. Midterm 2: solutions in class Chapter: 27 Optical instruments Review of the eye Microscope & telescope Chapter 28: Physical Optics Interference Two-slit experiment 19