Physics 141 Lecture 28
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1 Physics 141 Lecture 28 Today s Concept: A) Op3cal Devices Electricity & Magne/sm Lecture 28, Slide 1
2 Executive Summary Mirrors & Lenses: S > 2f real inverted smaller f > 0 2f > S > f real inverted bigger Concave (Converging) f Converging f f > S > 0 virtual upright bigger f < 0 S > 0 virtual upright smaller Convex (diverging) f Diverging f Electricity & Magne/sm Lecture 28, Slide 3
3 It s Always the Same: You just have to keep the signs straight: sʹ is posi/ve for a real image f is posi/ve when it can produce a real image Lens sign conven3ons S: posi3ve if object is upstream of lens Sʹ : posi3ve if image is downstream of lens f: posi3ve if converging lens Mirrors sign conven3ons S: posi3ve if object is upstream of mirror Sʹ: posi3ve if image is upstream of mirror f: posi3ve if converging mirror (concave) Electricity & Magne/sm Lecture 28, Slide 4
4 System of Lenses Trace rays through lenses, beginning with most upstream lens Image from first lens Becomes object for second lens Electricity & Magne/sm Lecture 28, Slide 5
5 Virtual Objects are Possible!! System of Lenses Object Distance is Nega/ve! Image from first lens Becomes object for second lens Electricity & Magne/sm Lecture 28, Slide 6
6 Normal Eye Electricity & Magne/sm Lecture 28, Slide 7
7 Far-Sighted actual Text actual Converging Lens creates virtual image at person s actual near point Electricity & Magne/sm Lecture 28, Slide 8
8 Near-Sighted Fix with diverging lens that creates virtual image at far point. Electricity & Magne/sm Lecture 28, Slide 9
9 CheckPoint 2 A B Farsighted = Converging Lens Only Converging Lens can produce a real image! Electricity & Magne/sm Lecture 28, Slide 10
10 CheckPoint 4 A B C θ r θ i d d The image is formed an equal distance behind the mirror Therefore, if you stand a distance = ½ of your near point, the distance to the image will be the near point distance. Electricity & Magne/sm Lecture 28, Slide 11
11 CheckPoint 6 A B C D E 1. Parallel rays are transmi_ed and pass through focal point (f 1 ) 2. Those rays also pass through focal point of second lens (f 2 ) and therefore are transmi_ed parallel to the axis. 3. f 2 > f 1 implies that the width > w 1 Electricity & Magne/sm Lecture 28, Slide 12
12 Multiple Lenses Exercises Suppose we now decrease the ini/al object distance to 58 cm. Applying the lens equa/on, we find s 1 = 2.48m Lens separa3on = 2 m s 1 = 58 cm f = 47 cm s 1ʹ = 2.48 m s 2 = 0.48 m What is the nature of the final image in terms of the original object? A) REAL B) REAL C) VIRTUAL D) VIRTUAL UPRIGHT INVERTED UPRIGHT INVERTED EQUATIONS PICTURES Draw Rays as above. s 2 < 0 s 2ʹ > 0 M 2 > 0 real image M = M 1 M 2 < 0 RESULTS s 2ʹ = 0.24 m M = 2.1 inverted image Electricity & Magne/sm Lecture 28, Slide 20
13 Magnifying Glass The Magnifying Glass is just a lens which creates a virtual image!. Naked eye y θ o y θ x np f (a) o u o y x np s of focal l M u u o > Text x np f (b) u y f agnification Even though the virtual image is far away, θ is bigger and makes a y bigger image on the retina: Angular magnification y s m = y = s y θ s s FIGURE Electricity & Magne/sm Lecture 28, Slide 20
14 f = 150 mm x np =250 mm
15 Experimental Measurement of M
16 Eyepie e objective, forms a real image of the object. This image Objective he lens nearest the eye, called the eyepiece or ocular, is β o view the image formed by the objective. The eyepiece y β formed by the objective falls at the first focal point of y combina/on of twothus converging m eacha point on the object emerges lens frommakes the eyea Microscope. if it were coming from a point a great distance in front L fo fe ly called viewing the image at infinity.) (d) the distance between the In a Microscope e second focal point of the objective and the first focal two lenslength that isl.comparable to the focal at 16 cm. ed the tube The tube length is fixed Optical Instrumen length of the twopoint lens.of the objective so that an utside the first focal F I G U R E Schematic diagram o t the first focal point of the eyepiece a distance L $ fo a compound consisting of two The angular magnification of the eyepiece (from Equation 32-20) microscope is The first lens is the Objec/ve lens, the ook at very small objects at is the focal length of the objective. From Figure 32-52, o positive lenses, the objective of focal length x Optical Instruments SECTION 32-4 second one called Eyepiece converging lenses. lens ateral magnification ofthe the objective is therefore np and the eyepiece of focal length fe. The rea Me! Eyepiece image of the object formed by the objective ge of the object. This fe y" Objective L image viewed by the eyepiece, which acts as a meyepiece 32-21!#! (from the eyepiece Equation 32-20) is o d the or ocular, is fo magnifier. Theof final β and fe simple where xnpyis the near-point distance of the viewer is the focal length theimage eye- is at infi x y y the objective. The eyepiece piece. Thenpmagnifying power of the compound microscope is the product of the latme! β fe focal of ls at first point of eralthe magnification the objective and the angular magnification of the eyepiece: y hus ofemerges xeyeance the viewerfrom and fethe is npfocal length of the eyel the M! mdistance Me! " in front great ofint theacompound is the product of the lato microscope fo fe L fe and the angular magnification of the eyepiece:fo tiveinfinity.) The Compound Microscope M AG N I F Y I N G P OW E R O F A M I C RO S C O P E objective andthe the tube first length. focal L is called ube length is fixed at 16 cm. M AG N I F Y I N G Pso E R Compound O an F A M I C RO S C O PE of Example the objective that The Microscope OW Electricity & Magne/sm Lecture 28, Slide 20
17 How to Make a Big Telescope Mirror Melt it & Spin it kg of borosilicate glass when filled Electricity & Magne/sm Lecture 28, Slide 14
18 Telescope Like microscope, a (Newtonian) telescope is also made of two converging lenses. In a Microscope the distance between the two lens that is comparable to the focal length of the two lenses. Both object and image in telescope are at infinity. Objective Eyepiece tan u o y s y f o u o all-angle approximation ta tan u e y u f e e tive, indicating that M u e u o f o f e θ o θ o y θ e f o f e Electricity & Magne/sm Lecture 28, Slide 20
!"#$%&$'()(*'+,&-./,'(0' focal point! parallel rays! converging lens" image of an object in a converging lens" converging lens: 3 easy rays" !
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