Basic Physics III Lecture 14
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Title 
Basic Physics III Lecture 14

Title of Series  
Part Number 
14

Number of Parts 
27

Author 

License 
CC Attribution  ShareAlike 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal and noncommercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor and the work or content is shared also in adapted form only under the conditions of this license. 
DOI  
Publisher 
University of California Irvine (UCI)

Release Date 
2013

Language 
English

Content Metadata
Subject Area 
00:00
Lugger
January
Accretion (astrophysics)
Thin film
Cosmic distance ladder
Airliner
Astronaut
Measuring cup
Atmosphere of Earth
Speckle imaging
Optometry
Refractive index
Sunday
Pair production
Focus (optics)
Cartridge (firearms)
Plane (tool)
Willo'thewisp
Dud
Sunlight
Mir
Camera lens
Suitcase
Curved mirror
Rotating radio transient
Monday
Superheterodyne receiver
Dumpy level
Measuring instrument
Glass
Negation
June
Antiparticle
Typesetting
Kontraktion
Pooltype reactor
Camera lens
Stationery
Light pollution
Suitcase
Heat
Glass
Focal length
Angle of attack
Forging
Caliber
Optics
Week
Last
05:16
Transmission line
Geokorona
Optical amplifier
Year
Particle physics
Camera lens
Relative articulation
Cosmic distance ladder
Reflexionskoeffizient
Curved mirror
Dipole
Gedeckter Güterwagen
Roll forming
Fox
Automobile
Cardinal direction
Rain
Array data structure
Regentropfen
Speckle imaging
Cylinder head
Camera lens
Tracing paper
Refractive index
FACTS (newspaper)
Concentrator
Focal length
Focus (optics)
Angle of attack
Series and parallel circuits
Cartridge (firearms)
Gradient
Miner
Atmosphere of Earth
De Havilland Venom
09:47
Cardboard (paper product)
Superheterodyne receiver
Speckle imaging
WeizenbierBrauerei J. Bayer
Hot working
Camera lens
Visiting card
Book cover
Camera lens
Cogeneration
10:59
Nut (hardware)
Photography
Auger electron spectroscopy
Radar
Relative articulation
Cosmic distance ladder
Light
Gradient
Roll forming
Wear
Joint
Cylinder block
Speckle imaging
Combined cycle
Cocktail party effect
Evening
Light
Pair production
Scale (map)
Focus (optics)
Autumn
Cartridge (firearms)
Electronic media
Flight information region
Willo'thewisp
Sewing
Year
Camera lens
Map
Cell (biology)
Rotating radio transient
Superheterodyne receiver
Cougar
Focus (optics)
Band gap
Dumpy level
Ship class
Spare part
Negation
Array data structure
Camera lens
Intensity (physics)
Centre Party (Germany)
Pen
Hue
Finger protocol
Focal length
Sizing
Visiting card
Plant (control theory)
Magnetic resonance imaging
Gamma ray
Caliber
18:11
Impact event
Lugger
Drehmasse
Effects unit
Photography
Hull (watercraft)
Multiplexed Analogue Components
Minute
Relative articulation
Cosmic distance ladder
Light
Brightness
Stardust (novel)
Limiter
Diaphragm (optics)
Plane (tool)
Astronaut
Atmosphere of Earth
Measurement
Cylinder block
Divergence
Speckle imaging
Optometry
Transmission line
Combined cycle
Sound
Thin film
Photodetector
Light
Pair production
Contactor
Focus (optics)
Gedeckter Güterwagen
Series and parallel circuits
Perturbation theory
Hochseeschlepper
Cartridge (firearms)
Diaphragm (optics)
Automobile
Shutter (photography)
Book design
Dual inline package
Screen printing
Sensor
Hot working
Switchgear
Transmission line
Day
Year
Camera lens
Energy level
Singing
Weather front
Superheterodyne receiver
Sharpening
Apparent magnitude
Focus (optics)
Band gap
June
Controller (control theory)
Focal length
Tin can
Cosmic distance ladder
Camera lens
Intensity (physics)
Yarn
Cogeneration
Finger protocol
Focal length
Moon
Sizing
Brightness
Standard cell
30:01
Chemical substance
Analog signal
Quality (business)
Photography
Light
Casting defect
Gedeckter Güterwagen
Roll forming
Colorfulness
Tool
Color code
Atmosphere of Earth
Speckle imaging
Funk
Transmission line
Sensor
Refractive index
Evening
Casting defect
Light
Crystallization
Polrad
Focus (optics)
Flight
Density
Glasfluss
Astronomer
Diaphragm (optics)
Swimming (sport)
Shutter (photography)
Electric charge
Sensor
Chargecoupled device
Hot working
Refractive index
Year
Camera lens
Hilt
Weather front
Superheterodyne receiver
Silvering
Focus (optics)
Band gap
Concentrated solar power
Spare part
June
Shutter (photography)
Electric charge
Truck
Focal length
Ramjet
Stress (mechanics)
Camera lens
Intensity (physics)
SEED
Engine knocking
Chemical substance
Chargecoupled device
Cogeneration
Refraction
Concentrator
Focal length
Metre
Finger protocol
Forging
Digital television
Caliber
Electricity
Workshop
35:40
Weapon
Mechanical fan
Transmission line
Zylinderlinse
Year
Force
Camera lens
Cosmic distance ladder
Paint
Roll forming
Power (physics)
Glass
Negative feedback
Institut für Raumfahrtsysteme
Near field communication
Atmosphere of Earth
Focal length
Divergence
Speckle imaging
Car tuning
Cosmic distance ladder
Camera lens
Crystallographic defect
Power (physics)
Evening
Contactor
Cogeneration
Focus (optics)
Glass
Metre
Bügeleisen
Direct current
Cartridge (firearms)
Shot peening
Caliber
Workshop
Last
00:05
below yeah we last new chapter last week and this is a
00:13
border lenses and general and were also optical instruments
00:19
introduced the subject of lenses finding the emerged point for thin lens where we have given the radius of curvature of Mr. office Ramos rats we found that these equation that relates object and image distance looks very much like America station if we are still in the focal length given by and glass when airliners was times the average I'll be back for the addition of the inverse curvature of the and this is also called the ELN sneakers accretion have a lens accretion for 1 0 which is just like the creation and also the magnification creation which relates image and object distance is the same as for the murder of an effete Sunday in an object distance of infinity then we have apparel raised that come in and image distances focal we focal length it's positive kid then it's a con Virginia lands and if it's negative ads that religion and diverging glands looks something like this so we have to invert curvature of all our for the lens arrived in a previous life and so area looks set out in the middle of an edge and optometrists off Tom motorists lens Powell rather than focal length and purchased just inversely related focal length and enrich them doctor and 1 by doctors want me 1 by optical lenses of focal length 1 and that we can make air various types of lenses this 1 would be double Convex of this would no contracts this 1 would be double concave and you can also a former Kansas like this In this case would be conflicts and if you have that parallel race as striking a land converging glands than their focus of the focal point of the angle to it it's still focused in the focal plane but no longer the focal point and you can use that start fires the converging Virginia land like so if you have a big enough man than Olivier optical all the sunlight is focused in 1 point and the absorbed heat is that it's enough to set would on pocket so is an example for the U.N.'s maker creation and reconsider a convex ministers limbs and it's made from glass and the glass as an index of refraction 1 . 5 and the radius of curvature the convex surfaces rented 2 . 4 sending and the other 1 is 46 point was sent to the question is what is the focal length and railroad would be image be object this place to leaders away about 40 ounce of EU was lens snake equation so we 1st need the difference the erasure of the index of refraction of glass and for various who is 1 of this ratio to subtract 1 of onehalf and then be add that the pool in most curvature of and this 1 has a minus sign because of and if you plug in the numbers we get a focal length 87 centimeters and since this number is positive lenses on marriage and if it turns out the lenders or on and all already is Ms. which this term on the side 1 that we get the same converging lens the bad light comes from the left over from the right now we can find the image distance for an object as usually do of the lens which it's 1 over the image distances focal length minus 1 would object to or 1 0 87 cents minus 1 400 sending and that gives us 154 send English but that for the 1st confirmation that school bag with equation that is used
05:18
if this 1 of the lens makers please rich occasionally index of a fraction and took give me an imbecile the focal solely can form a rate diagrams that for lenses as well as we do for and so grossly ahead that parallel raised a dead reflected in the focal raised focal raised it reflected parallel raise the central rate is reflected on equal angles so it is defined as symmetric point riches are the same distance as the the object the same height these then that essential Ray will reflect that point and finally Yukon centigrade 1 that goes for the center of the sphere of richest located times focal distance away from from the drop it get reflected on itself and for the lens the only difference a reflection fired off this image gets ah but on the other side and so we can sit formerly same rate is so let's loose 1 by on the start of the parallel Ray so for the rural gets reflected through the focal point for the lens it gets refracted through from the focal point than that of focal race for the Moritz reflected parallel and lends it is refracted peril than the central that's reflected through the symmetric point and for the year lens it's actually quite easy this is simply a line that goes through the center of the trod also goes through that symmetry point purchase in this case located on the other side of the but it's very easy to draw each set holiday for the lens because it goes a little of the lands it is just a straight line and final leader for the year concentric grade is the easiest for the spherical Europe because just reflects on itself in the case of the lens it is the way that goes from to miners double the focal length and refracted back so that it goes to double the focal if and then of course once we have those full raised you you can find the image which in the case of the rural on on the same side of the car and the case of the lenses on the other side of the and in this case it's a it's real image for both Morales and so if
08:11
have a diverging lens of convex mirror and kind form this at the same enology Soviet head of the parallel Ray right and it gets reflected so as if it came from the focal point and for the lens for the garbage and lens it gets refracted as if came from the focal point in gross the focal rave have raid that that seems to be the focal point its parallel to and sing for the um diverging lands the raid aimed the focal point that's it's a fact of how leader West Central race that's the same as for bees converging in the case of the murder on Kosovo's status symmetry find in the case of a lens this just a straight line we can't centigrade sell out for the year for these where are the same as for the concave Marie gets reflected on itself and for a lens you 18 array that twice the focal length and it gets refracted as if it came from twice so that's rain on before and the again kind of performance image rich it is on the other side of the room and on the same side will be watching them
09:48
so Ray tracing works just like it did for from so what happens is to the image of an object the top half of lends discovered a piece of cardboard that's kind of the reality so here I
10:07
actually ahead of us of Plano convex lens I think a that um makes an image the real image that is upside down to see the ad the object you and image Bayer and the questionnaires now what happens is like cover half of top half of the lands and step away then you can see that the images is not affected also to cover the bottom half even if I cover most of the lens the image images still there if all that happens gets and so the
11:01
at so for why that is is that if block some of the Rays that doesn't mean that there emerged of former just means where there's less light intensity because raise goes to every part of the year let him as long as there's any part of it's still and written there will be an image depending on what to use for blocking you may find the told of focus emerged of the blockage for example if I lose my hand you can sort of see OK there something like fingers it is really in focus and the close I moved to the band the Of that will have let we make a point that was already late for the Air Force rural our eyes are built so that they can make images of a distant objects which have almost parallel races all close objects which are averaging but it cannot focus on converging raise and so the area of the eye is closer to the limbs image image will become brewery just like it was this circle of virtual images can always be seen since there on the other side that's also like are like photo sold lends problems please use the same procedure solving moral problems we always draw a diagram even if there's an analytic calculations on applied lens a Croatian and the magnification and pay attention to the sign of the distances and heights and the object distance is bigger than 0 if the object is placed on the side of the lens with light is coming and the image distance is bigger than 0 if it's on the the opposite side of the object and up this positive and on his negative image rights and at the end of a check these analytic solution with the rate diagram whether it makes sense so
13:20
let's do an example and the examples look exactly like the examples for the bureau let's assume you have given an object in this case leave the displaced 1 meter away from media that is based on need away from the lens of the object distance 100 natives and the question is where is image and public isn't going to be leaf is 7 . 6 centimeters high please use the ad class so that we use the Lenza creation plant in 5 sending leaders for focal length of the land and 100 sending leaders for the object distance and find that the image of 5 . 6 centimeters and since that's a positive number it means that the images on the other side of the land and it is a real image cell we now use the magnification equation which tells us that the magnification is given by minus the image distance of the object so that the 5 . 6 centimeters 170 and so the magnification a 0 . 0 5 2 6 and if we then multiply that if I to get the image height as minus . 4 sending because magnification is negative that means that the images let's make another example let's have an object that is placed 10 centimeters From over 15 cm. focal length are converging glands so close of them focal length and a problem is to determine the image position and size is both on other deeply and with the radar for the analytical calculations just plug in the numbers before and Figueroa image distance of minus 30 centimeters and because its negative that means the images on the same side as the object and the images virtual for the magnification adenomyosis saying equation get 30 centimeters divided by 10 centimeters the ramifications and that means that the images of a virtual up right let's now look at the yeah the rate diagram that looks like so in theory have all shirt and we have the parallel array which gets refractive go through the focal point and we imagine that this race is continued like this and then these focal race which seems to come from focal point is refract parallel and that the central race is unaffected and those ghostly raise if we continue them back need we have emerged emerges as the analytical solution said is bigger than the original object is a virtual image and so be it seems like the analytical calculation we can do the same thing for diverging lenses in this case the problem is should replace small insect is about 25 cm. focal length diverging lenses to form a virtual image 20 centimeters from the lens on the same side as the object in this case we have to use negative focal length for from rats life a minus sign appeal the fall and of course he'll sold for 1 0 Woody old rather than 1 ODI and because emerge distance it's negative on the same side Sweden's theater plus sign the form joint Richard Gardiner mumbles refined that the object distance must be 100 Centre and the magnification in this case that Tandy sending a 170 0 . 2 so the image of the insect is going to be even smaller than to find out what happened with combination of lenses uh 1 applies the lens equation and magnification be creation sequentially for 1 lens at the time so the image of the 1st lends becomes the object of the 2nd lends the image of the 2nd lends becomes the object of the lands and so on and the total magnification then is the product of the individual my case so it is basically no different than finding interest uh 1 image just repeatedly used
18:12
sustained creation so let's do it with the example let's say took on Virginia lenses a and B R focal length 20 centimeters and 25 centimeters placed 80 centimeters of hot hazardous shown and pictures an object displaced 60 centimeters in front of the 1st lens and the question is where's the position and the magnification of the final image that this fall and so we 1st concentrated on that lends aid workers from Seoul for lenders aII we calculate the image distance in image I want all of its focal length minus 1 its object distance so the object distances 60 centimeters that gives us an image distance foreign aid so descended so since image distance positive needs on the other side of the bands and they can find our borders object distance for the 2nd day of vintage for days here barely know all that 30 centimeters we know that this this is 80 cent therefore this distance must be 50 Cent and B. get Arab for the object of a 2nd glance 50 centimeters 3 rounds of the same equation again and find the image of lands be at 50 Cent and the images of real and it is up right and the reason why this up apparatus and find out that total magnification riches minus DIA over D O. a times minus D B O D O that to minus signs cancel so I IBM minus 30 over 60 times minus 50 over 50 and so the total magnification a 0 . 5 the total magnification as positive that means that images of the same orientation original as another example can use can't Virginia lanes to measure the focal length of diverging so if their broaden contact with each other as shown here In this picture we can measure will be combined a focal lengths and In this case combined focal length this 28 . 5 centimeters so the combination is upon merging lens so if can't urging lens has unknown focal length of 16 centimeters then the question is what is the focal length of divergent Hey and so on that 1st of all a sincere parallel raised coming in the object distance this infinity and these emerged because wrote Jim Lentz by itself it's just focal length and that becomes minus the object's distance of religion reason why just minuses because they are touching so in other words objects distance for the the original lenses minus 16 cents and we can now plugged it into the Croatian for forward diverging England's so um area of the diverging Newlands focal length at the beginning of the year object must be the image and if you plug in the number of minus 16 centimeters and a 28 . 5 centimeters get a beverage England's of focal length of minus is 6 . 4 8 cent how do we get that Seoul are the emerge also the corn Virginia and which is so indicated by the dashed lines near it those 2 lenses are right on top of each other so we assume they have no sickness and all of those equations are valid only Finland in their have Norfolk means this image distance is the same as the impact of the negative our object about so the reason why the image of converging that lends its minus the object's distance for the diverging trends is because their touching the reason why any image distance for converging plans is its focal length is because these raise apparel and therefore the object distance for a converging lenses infinity OK but you can also simply if you have parallel race for the converging lends them they get focused into its focal so that is the air we be critical assumption that those 2 lenses touching each and perhaps now it becomes a bit more apparent wiII be optometrists like to use in the focal length calculate Yukon 1 can think of this equation he is simply an addition off those vocal so it you have given a certain number of doctors and will add another lens with another number of doctors than the total combination as numbers that touching is the sum of the area where easy to use inverse vocal for this new method to measure the a focal length books of course only the magnitude of these a converging lens a focal length is bigger than that of the religion and focal length because otherwise if you don't find a focus point focused on will be a vote for a combination let's switch gears a little weird and talk about Cameroon's camera comes from Mount Carmel old School which means dark chamber Latin and did was usually a pinhole camera also called Magic Lantern the Pinola blocks all raise except for those passing through and images for CO if you have a pinhole here and have a projection screen they object to only only 1 race goes so therefore we have an image formed here and the images revealed and its standards upside down and the problem with this procedures that image tends to be very thin because only 1 Ray this amount past and you can fix that by making the pinhole the bigger but that instead of nice points or more than 1 race going the new get sold off circles and that means that the image will will become Bluray to fix this problem that you have did images for or you have a very images the addition of converging lens is a big improvement so at usual can run has from Virginia lends Bennett has an adjustable out of the Convergent so that 1 can change the the size of the opening and therefore can't control the brightness and the sharpness of then there's the charter to limit exposure to a certain amount of time and finally there's a light sentence of film that
26:36
so if you focus of camera what we mean by Aventis b disadvantage of the lenses that and images only formed at a particular distance this kind of camera works at any distance between an image and pinhole also for any distance for the object but for the year converging lenses is no longer true so if we have a very distant objects was raised from the distant objects their image in the focal while a close by object it is focused longer the distance and even those we can move this lends backandforth we can only get 1 of those 2 images shot and the other in which will produce little circles like these which also sometimes called circles of confusion and therefore either the distant object or the nearby object will overlook brewery is an example of of nearby object in the distant object focused on nearby object and focus on distant objects and 1 of them were the solution to that problem is to focus on a distances in between and therefore get a both images somewhat theory but maybe toward tolerable level and that works as long as these socalled depth of field which has a range of distances emerged this sharp enough to to be acceptable as long as this depth of field is large enough and to control list depth of field to use a smaller that lends diameter all of big events that saw smaller lenders diameter increases the depth of field but reduces the image brightness just like it did for Europe pinhole camera socalled stop all 4 cameras and adjustable Iris diaphragm uh that behind the lens partially covering it and the opening is usually given as f stops and that stop means it is the ratio of focal length Over the diameter of effective legal you make the stop lesser lights yeah you will received for the image becomes demanded well but also you depth of field is getting bigger and bigger and finally given that both Phil lend light sensors are meaning that they don't work in proportion to intensity but in proportion to intensity times exposure time the shot dead a spilled in 2 the camera to limit exposure of Pennsylvania brightness of photography this proportional Twitty exposure time a exposure time is about is often given as shoppers of cause if your object moving van there's a different kind of blurry image produced if you will shutter speed is is slow and so are fastmoving objects needs Chaudhary exposure and therefore the need big openings and have therefore less at a depth of field so let's do an
30:04
example of how far must 50 mile amid a focal length camera lens removed from its Infiniti said and was sharply focused on the object bittersweet meters away and so on so that the Infiniti setting fire means that emerges formed at the focal length of 50 mm became volumes lends equation again find the image of the object of 300 sending and that we get as amount so this is 5 . 0 8 5 % or 50 . 8 5 and therefore the lenders must be moved by 0 . 8 5 mm tool focus on on closer object to another example let's say to improve the depth of field you stop down the camera lens by 2 f stops from an oval for 2 at 8 what should do do would add to the shutter speed to maintain the same exposure and France of that observe that the amount of light that is admitted by the lenses proportional from the area that uncover and that means it's proportional to the diameter square so if we reduced diameter by a factor of tools that means that would use the light intensity by a factor of 4 for the same total among the flight to increase exposure time to 4 times as long so for example if these speed was originally 1 over 500 it now has to be 1 lets their briefly talk about how camera films like census work so rare pictures used to be taken using a chemical film and I basically a chemistry of silver halide crystal changes when exposed to light and more recently it has switched technology to use chargecoupled devices those consists out of millions of small squares called pixels and they accumulate electric charge in proportion with the light export and eventually after a photograph was taken their red out as sequentially so there red on edge of photos to include color information each pixel actually consists of 4 smaller pixels which have colorful and to all those pixels have read colorful the outlook for and that encodes color and as long as the density off those pixels Roger the year resulting image looks like a this this move image so as an example let's consider 6 Mega Pixel digital camera and 6 mega pixels means that it has 6 million pixels and this is typically a resolution of 2 thousand times 3 thousand pixels on a 16 millimeter times 24 millimetres see CDC and the question Howell shop should that lens image beat to make use of of this was and plans are that question now we find out he pixel density sold 2 thousand pixels 4 of 16 millimetres means 125 pixels and the same is also true for 3 thousand pixels on a reform of the image therefore needs to be shop 2 0 1 0 0 that No. 1 overall 125 mm purchase 8 Michael and you need a very highquality lenses to actually do so in other words the camera resolution is not limited by a resolution on TCP sense but by the optical quality of the band's spite of what advertisement stress so let me finish the that talking about the human eye the cameras are built analogy to the human eye soul the cameras like the kind stuff the the Iris which is adjustable opening lends the equivalent with a CCD CDC directed not on the back of the eye let me give you the induced indices of refraction so for the air In apart Of Demetrius you will be index of refraction as 1 . 3 2 7 by the aqueous you front of the lens is 1 . 3 3 6 the lends itself as an index of refraction of 1 . 3 8 6 2 1 . 4 6 directed not has special spots before we are has the largest concentration of optical sensors and the optic nerve our forms blind spot so if we have part of the image that is located here we can't actually see so imaging wealth the human eye mostly done by the cornea corn real quick
35:34
sorties spherical for for roughly spherical surface on the top of the ideas is doing what is really doing the job of the
35:42
imaging and beat these lenders in the eye is just a providing adjustment to get a shop in image this is fine tuning is called accommodation and 110 define defying a year and a half point for the human eye so ideally the far pointers infinity meaning that we can see objects shop infinite distance and the pointers desires typically 25 centimeters but various age so why many people have just like myself the defects of the iron nearsighted people like myself suffer from myopia and that means that the far pointers is less than infinity so if I take off my and my glasses that I can't see you will sharply anymore the focus and a full farsighted people it's it's the other way around so that they're far point is bigger than infinity so the IRS to accommodate a little bit even for the air force infinite distances and that means that the yield point is a further away than the usual 25 centimeters or the phenomenon that the arms get too short and pressed field Jr a similar effective problems you can't focus on you objects and suffer from that as well but it is Pewee agerelated failure to fully accommodate and corrective lenses can fix those problems for nearsighted people I want to add a divergent lens in France and then even go out originally image was of a focus for an infinite space object it is not brought to focus by the additional land and similarly for farsighted people you add of Conde that that's another defect of the human eye and that is a form of cornea meaning that we curvature is different in 1 direction compared to the direction perpendicular to it and that's called as stigmatism suffer from that as well and you can think of that like if you have a cylindrical lens which has no coverage and 1 direction and has some courage in the other direction than a point is emerged on line rather than on and you can't was normal lenses to correct for that we can't see just a onedimensional the order but that if you use cylindrical lenses that you can correct for astigmatism so let's conclude with some examples so let's say is farsighted and appointed is 100 sending leaders and the question is what lens the need for reading glasses so that you can read the usual distance of 25 cent so that means you want and new point of 25 cm image distance of the reading glasses negative after this I assumed that the twat touching which caused reality not and in that case they had emerge distances my 100 sending the object distance ought to be 25 sending me and you can use a lens agrees to get the power of the lens 0 . 0 3 per cent or 3 per meter which corresponds we die out so here simplifying assumption that the reading glasses are sitting directly on top of me I'm so this more like contact so for the 2nd example Fournier cited
39:36
alarm but make this assumption so now we assume that eyeglasses presented meters away from from the eye and we have a yield point of 17 sending far point of 12 centimeters and the question is what kind of lens we need to focus at infinity so at infinity the lens must put it emerged at the far pointer because for the point me aside and focus on and that means that the image distance must be minus 17 of bust twothirds of which is the distance between the eyes soldiers this distance must be 17 sending this systems must 15th and then we can find same before the power of the lens minus 6 . 7 die out if they had context however the 2 lenses are touching and you would only need minus 5 . 9 . 0 minus 6 7 solid slightly different for contact lenses and last if you don't wanna know what this Leader we close point then and now we have actually given the lens and they can find out what is the point of I and for the real point of PICT images minus 10 centimeters and can then find the object distance as a 3rd sending and that object distance is that these viewpoint of the combined system so I think you're much