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Applied Optics

by: Guido Casper IV

Applied Optics PHYS 3190

Guido Casper IV
Weber State University
GPA 3.7

John Sohl

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John Sohl
Class Notes
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This 7 page Class Notes was uploaded by Guido Casper IV on Wednesday October 28, 2015. The Class Notes belongs to PHYS 3190 at Weber State University taught by John Sohl in Fall. Since its upload, it has received 13 views. For similar materials see /class/230789/phys-3190-weber-state-university in Physics 2 at Weber State University.

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Date Created: 10/28/15
Department of Physics Weber State University PHSX 3190 Applied Optics Lab Experiment 2 Thin Lenses Revised 9108 Introduction and Overview In this lab you ll find the focal length of lenses by various methods including a technique called autocollimation You will also work with the thin lens equation ie Gaussian optics Equipment Optical rail and mounts Screen for seeing images Positive lenses fl 25 to 300 mm Object card to go in front of lamp Negative lens fl 75 mm Two needles for exploring virtual images First surface mirror on optical mount Ruler for measuring objects and images RGB Light Source on optical mount Warning and Handling Notes Always handle optical components by the edges These lenses are research quality lenses although they are not coated Handle them with respect You will be using a rst surface mirror today under no circumstances should you touch the re ective surface Glass rod used as Procedure cylindrical lens Rotation Stage oriented Part 1 Explore refraction and measure the hOHZO taHY index of refraction Shine the laser beam into the rhombus the rectangle etc Don t worry about taking notes just 3113 play for a while to get a feel for it Try to get total internal re ection Top View Place the laser glass rod and rhombus on a piece of stiff paper on the rotation stage as shown Side View in Figure 1 If you set the rotation stage to zero Diode i def332 degrees and adjust the rhombus so that the ray Laser hitting the rst surface re ects directly back to the laser then you ll know you have the incident angle Figure 1 Setting up the system for the at zero Try to have the point of contact laser 0n measurement of the index of refraction It is rhombus exactly above the center of the rotation probably easiest to mount 311 this on the stage Rotate the rhombus a and observe the triangular optical ra s mounts 2008 John E Sohl Page 1 of 7 PHYS 3190 Experiment 2 Thin Lenses sln mg pnsmnn ef the exllmg my1t mm eut thet when yen Iefmcl throng twe pemnel stdes the extttng my wtn be pemnel to the tnettlent a my See thtue z This essuntes thet the tnttm1 h mse Just thet emu ntg yety careful net to nnute et mesh t bump the shffpnpex and mesh the ntettlent end J T exllmg mys end the two pemnel edges nfthe thembns the ymlxselfplemy ef teem bemuse met you wtn use e pmlnclm et Ingmmmel e at delen mlle he nemml to e sutfeee the ntettlent a gure 2 Geemeoy fa o my pesstng Ihmllgh 1e end the ntteunt of nffsel between the e mspnxenl plete mg ntettlent my end the exllmg my You wtzzwm to tesults m h ntettlent engle e Fr ebteet tn en the tesu1t ts mu 6 whete 115 the offset n ts the tt g Question 1 thet Value7 Include e elem tome wtth ym tepen Part 111ota1 Internal Re em nn t the Iefmcled my ts yety nearly 90 nm the netme11gtey e1ese ettentten to the engttness nfthe re ected my the moment the xefncled my teeehes 90 This ts mnetl Tm Total Lntenml Re eetten teEmetten Question 2 o 2008 Iahn E Sam Pig 2 a 7 pays 1 90 Expcnmcm fl Thm Lenses use error rather than a difference in values which is fairly meaningless usually As for the index of refraction typically the comparisons are done for nl rather than for n alone Exit paint Reflected Ray 154 152 Rhombus n 1507 Entrance oint 39 p total Internal 13948 Reflection 7 39 39 Fused Quartz 1 46 Figure 3 Obtaining the index of refraction 4 V Y 7 from total internal re ection Drawing taken 100 300 400 500 600 700 from the Pasco optics manual 7quot n m Figure 4 Index of refraction for various F S 11 L h th t mm HE S aw we can S 0W a materials at UV and visible wavelengths sin 80 1 n In Figure 3 you can see the geometry for measuring the index of refraction This is for the case where 9 6C is the critical angle vis a vis the point at which the refracted beam just barely disappears as it hits 90 Questions 3 How does the relative brightness of the the re ected and refracted rays change as you rotate the ray table through the angles surrounding the point of TIR What does this have to do with conservation of energy Part III Finding the focal length of a lens There are numerous methods for finding the focal length of a lens First of all don t believe the package Unless it is a high quality research grade lens the focal length on the package will be approximate Just how approximate depends on the quality of the lens Method 1 Quick and dirty The thin lens equation is 1 f where s is the object distance s is the image distance and f is the focal length Thus if the object is very far away say at infinity then US 0 and we see that the focal length is just the image distance tall 1 1 5 2008 John E Sohl Page 3 of 7 PHYS 3190 Experiment 2 Thin Lenses Question 4 How far is in nity le how far does your object need to be for the image distance to be fairly close to the focal length I typically use the ceiling lights and just obtain a focus on the oor The distance between the lens and the oor is a good rst guess on the focal length for most lenses You can step next door into the Electronics lab and give this a try Using nothing but a lens a meter stick and available lighting determine the focal length of several of the lenses and compare it to the value on the lens package Create a table in your lab notebook comparing the values for the lenses Question 5 How well do your measured values agree with the known values Discuss Question 6 Does this method work for negative focal length lenses Explain Method 2 Bessel s method also known as the method of conjugate foci A lens is moved along the optical rail between a xed object and a xed screen The object and screen are separated by a distance L that must be gt4X the focal length f of the lens Two positions of the lens are found for which an image is in focus on the screen magni ed in one case and reduced in the other If the two lens positions I differ by distance D the focal length is then given byf L2 D24L You will prove this as a xx homework problem for class ObJeCt in Figure 5 Bessel s method for measuring the focal length of a lens using xed positions for the object and screen By symmetry in the Gaussian equation for thin lenses there will be two lens positions with good focus Set up Bessel s method to determine the focal lengths of your Pasco lenses see Figure 5 Set up a data table in your lab notebook that has L D fmeasmd ffamyand any other data that you need to determine f Be very careful to account for any offset between the location of the optical device and the marking on the housing Clearly record your results for f and your calculations Question 7 How well does your measured value agree with the known value Discuss Question 8 Will Bessel s method work for negative focal length lenses Explain Method 3 Autocollimation This method involves the de ning feature of the focal point of a lens Rays of light diverging quotom a point located at the focal point will exit a lens as parallel rays Rays that enter a lens parallel will converge at the focal point 2008 John E Sohl Page 4 of 7 PHYS 3190 Experiment 2 Thin Lenses To do this method you must have a mirror that is very slightly tipped You also need a screen and object at the same place See Figure 6 for the light path involved T he focal length is just the distance from the objectimage screen to the lens being tested You have a white metal plate with a small hole that you can use as the screenobject Place Wag the lens at roughly the expected Obled focal length away from the object Locate the mirror about 5 to 10 cm behind the lens You should have a lzzy spot next to the object Now slide the lens back and forth and obtain the 0b U best focus of the object s Jec screen Lens Minor image back on the plate as shown in Figure 6 That s it you now have the focal length Note be care ll not to get fooled by re ections off of the lens surfaces Figure 7 The optical rail when con gured to do an autocollimation Think of a way to easily and quickly verify that you have what you want hint block the light at a key location Clearly record your results for Do this for at least two of the lenses Lens Mirror Figure 6 Autocollimation of a lens to find the focal length RGB Light Optical Rail Question 9 How well do your measured values agree with the known values Discuss Question 10 Does autocollimation work for negative focal length lenses Explain Question 11 How well do the three methods agree on the values of the focal lengths for the various lenses Which is easiest and fastest Which do you think is most accurate Paraxial optics thin lens equations Your next task now that you have measured the focal length of the lens is to experiment with the imaging properties of the lens The thin lens equation is 111 Ss f Also the magni cation factor for a thin lens is 2008 John ESoh1 Page 5 of 7 PHYS 3190 Experiment 2 Thin Lenses You need to measure values for s and M and compare them with the calculated values for the 4 different cases listed below You should combine this in a single neat data table One suggestion for columns for the data table is Case s 3 calculated 3 measured error h M calculated M experimental error and image description real inverted reversed etc The four cases that you should explore are 1 3 3f 2 3 2f 3 s 23f and 4 3 2f Use the 200 mm focal length lens for all these measurements The results will be similar for any of the converging lenses this just happens to be a convenient size And it makes it easier for me to grade too Set up cases 1 and 2 Record your measured and calculated values in your lab notebook In cases 3 and 4 are a bit trickier You will need to use the auxiliary lens to either view the image or to produce the object The procedure follows Case 3 In this case the image will be virtual If you look through the lens towards the light source you will be able to see the virtual image try it however you can not project the image onto a card or other screen with the one lens you have on the optical bench The eye however is simply a lens used to project a real image on a card the retina Although it is very easy to reproduce this we won t We ll just do a few simple estimatescomparisons Ask your instructor or just give it a try if you d like to use a second lens and the screen to replicate what your eye is doing It won t take long With the object located at a distance Needle 3193144312130 3 23 f the thin lens equation predicts an image 11PM by 3 object 6 at 2 f Set up a system something like that E Stand shown in Figure 8 Use the ring stand to support an object use a needle at about the correct object distance Then look into the lens with one eye the right eye in the figure and then look at the hand held needle with the other eye the left eye in the figure In other words look through the lens with the right eye and look above the a lens with the left eye Move the hand held needle Hand held I avg336 around until both it and the image of the ring needle 39 stand needle are in about the same place and both in sharp focus Try to estimate the position of the hand held needle and thus the position of the virtual image Figure 8 Probing virtual images Case 4 For this situation a negative object distance is needed ie we need a virtual object for the main lens This can be accomplished using an auxiliary lens to project an imageobject into the negative object space of the main lens First you will need to choose an auxiliary lens with a focal length comparable to that of the main lens the 300mm lens is a good choice With the main lens removed adjust the 2008 John E Sohl Page 6 of 7 PHYS 3190 Experiment 2 Thin Lenses auxiliary lens the object and the screen for a sharp focus Measure the height of the image of the auxiliary lens for this con guration this will be the object size for the main lens Now insert the main lens The distance from the screen to the main lens is the object distance adjust the position of the main lens for this distance to satisfy the experimental conditions Object 1 Auxiliary Lens Image 1 on Screen soon 0 to be Object 2 I U U Optical Rail Maln Image 2 on Auxiliary Screen Object 1 Optical Rail Figure 9 The top gure uses a lens to create an initial image The object for the next lens is the image from the previous lens which is shown in the bottom part of this figure Readjust the position of the screen such that the image is again in sharp focus The spacing between the screen and the main lens is the image distance Measure the height of the final image The height of the image from the auxiliary lens measured above is the height of the imaginary object used by the main lens since this image and object are the same The magnification of the main lens in this configuration is just the final image size divided by the object size measured above Questions 12 About how well do your experimental observations and measurements agree with your calculated values In other words in general how well does the paraxial optics formulation the thin lens equations agree with your experimental results Would you consider it to be a good approximation of reality What are your sources of error 2008 John E Sohl Page 7 of 7 PHYS 3190 Experiment 2 Thin Lenses


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