The focal lengths of converging and diverging lenses are determined.https://nsuworks.nova.edu/physics_labs/1019/thumbnail.jp

Castano, Diego

Castro, Victor

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Nova Southeastern University NSUWorks Physics Lab Experiments with Simulated Data for Remote Delivery Department of Chemistry and Physics 3-2022 Experiment 2.10: Lenses Diego Castano Victor Castro Follow this and additional works at: https://nsuworks.nova.edu/physics_labs  Part of the Physics Commons I. EXPERIMENT 2.10: THIN LENSESA. AbstractThe thin lens equation is used to determine the focal length of a lens.B. Formulas1f=1p+1q(1)1fdoublet=1p1+1q2+ d1p1q2  1q2f1  1p1f2(2)P =1f= (n  1)1R1  1R2(3)where p is the object location, q is the image location in the single lens case, and p1 is theobject location from the rst lens, q2 is the image location from the second lens, and d isthe distance between the lenses in a doublet case. Equation (3) is the lens-makers formulawith R1;2 the radii of the two surfaces of the lens and n the lensindex of refraction.C. Description and BackgroundFIG. 1. (a) Converging and (b) diverging lenses.Thin lenses have a thickness that is small compared to their radius of curvature. Theymay be either converging or diverging. A converging lens (Fig. 1a) makes parallel rays of1light (to the optical axis) converge to a focus (a point on the axis). They have a positivefocal length (f > 0). A diverging lens (Fig. 1b) makes parallel light diverge from the opticalaxis; the focal point is now located where the diverging rays originate on the axis if extendedbehind the lens. They have a negative focal length (f < 0). The images of these lenses arealways virtual.FIG. 2. Separated doublet.The Lens equation can be derived geometrically. This equation relates the object location,p, image location, q, and focal length of a the lens, f , according to Eq. (1). For a (separated)doublet of lenses (Fig. 2), the relation is given by Eq. (2) in which where p1 is the objectlocation from the rst lens, q2 is the image location from the second lens, and d is thedistance between the lenses.2D. ProcedureFIG. 3. Optical bench used in the experiment.1. Place lens A (whose rated focal length, f A = 20 cm) on the optical bench. By adjustingits location and the location of the screen, arrive at a focused image on the screen.2. Record the location of the object (p) and of the image (q).3. Place lens B (whose rated focal length, f B = 10 cm) on the optical bench. By adjustingits location and the location of the screen, arrive at a focused image on the screen.4. Record the location of the object (p) and of the image (q).5. Place lens B and C (whose rated focal length, f C =  15 cm) on the optical benchas close together as possible. By adjusting its location and the location of the screen,arrive at a focused image on the screen.6. Record the location of the object (p1), from the rst lens, and the location of the image(q2), from the second lens.3E. Measurementslens A: f A [ cm ] =trial p [ cm ] q [ cm ]123456lens B: f B [ cm ] =trial p [ cm ] q [ cm ]123456lens C: f C [ cm ] = BC distance: d [ cm ] =trial f  lens 1 [ cm ] p1 [ cm ] from lens 1 f  lens 2 [ cm ] q2 [ cm ] from lens 21234564F. Instructions1. Use (1) to calculate the focal length in the A and B cases and (2) in BC case for alltrials.2. Calculate the average focal length and the associated standard error in each of thethree cases.3. The focal length of a separated doublet of lenses is given by1fdoublet=1f1+1f2  df1f2(4)Assume fdoublet = fBC , the focal length in the BC case in any given trial and f1 = fB,the average focal length found for lens B, then use this equation to determine f2 = fC ,the focal length of lens C:fC = fB   dfB   fBCfBC4. Calculate the percent error assuming the accepted values are f A = +20 cm, fB =+10 cm, and f C =  15 cm, and take the accepted value for the BC case to be theresult of using (4) with f1 = f B and f2 = fC .5G. Calculationslens A B BC Cfocal length (trial 1) [ cm ]focal length (trial 2) [ cm ]focal length (trial 3) [ cm ]focal length (trial 4) [ cm ]focal length (trial 5) [ cm ]focal length (trial 6) [ cm ]f [ cm ] f [ cm ]f  [ cm ]%-Err6

Experiment 2.10: Lenses

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Experiment 2.10: Lenses

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