Lab8_Convex_and_Concave_lenses

Physics 203 Lab 8: Convex and Concave Lenses Name: Vini Patel Partner: Sienna Gilliam Date: 4/8/2022

Abstract: In this lab we are looking at Double Convex and Double Concave Lenses using a simulation that calculates the distance of an object and image as well as the height of object and image. Which is used to graph 1/u vs. 1/v graph and calculate focal length. Equipment: - oPhysics Simulation - Microsoft Excel Procedure: Part I – Convex Lens: 1. Choose Concave mirror in oPhysics Simulation 2. Set focal length to 4.30 cm for a double thin convex lens 3. Now, put your object at a distance (u) from mirror and record the image distance (v), shown on bottom right corner of the simulation 4. Record distances of the object at 2.00, 3.00, 3.96, 4.50, 5.50, 6.50, 7.50, 8.50, 9.50, 10.0 cm. 5. Calculate M from distance measured, whether the image is real or virtual, erect or inverted, and the size of the image 6. Calculate and graph 1/v vs. 1/u 7. Find the focal length of the lens using lens formula and the y intercept found from graphing 1/u vs 1/v 8. Calculate percent difference between the theoretical and experimental values 9. Graph a ray diagram using the object length of 2.00 and 3.96 cm Part II – Concave Lens: 1. Choose Convex mirror in oPhysics Simulation 2. Set focal length to 4.30 cm for a double concave lens 3. Now, put your object at a distance (u) from mirror and record the image distance (v), shown on bottom right corner of the simulation 4. Record distances of the object at 2.00, 3.00, 3.96, 4.50, 5.50, 6.50, 7.50, 8.50, 9.50, 10.0 cm. 5. Calculate M from distance measured, whether the image is real or virtual, erect or inverted, and the size of the image 6. Calculate and graph 1/v vs. 1/u 7. Find the focal length of the lens using lens formula and the y intercept found from graphing 1/u vs 1/v 8. Calculate percent difference between the theoretical and experimental values 9. Graph a ray diagram using the object length of 2.00 and 3.96 cm

Calculation: Part I – Double Convex Lens: 1/u (cm^-1) 1/v (cm^-1) M real / virtual erect / inverted Size 0.500 -0.268 1.865 virtual erect enlarged 0.333 -0.101 3.287 virtual erect enlarged 0.253 -0.018 13.965 virtual erect enlarged 0.222 0.010 -22.920 real inverted enlarged 0.182 0.050 -3.629 real inverted enlarged 0.154 0.078 -1.971 real inverted enlarged 0.133 0.099 -1.352 real inverted enlarged 0.118 0.114 -1.029 real inverted enlarged 0.105 0.127 -0.832 real inverted reduced 0.100 0.132 -0.758 real inverted reduced Equation for 1/v vs 1/u y = -0.9993x + 0.232 Focal Point (cm) 4.310 Part II – Double Concave Lens: 1/u (cm^-1) 1/v (cm^-1) M real / virtual erect / inverted size 0.500 -0.730 0.685 virtual erect reduced 0.333 -0.565 0.590 virtual erect reduced 0.253 -0.483 0.523 virtual erect reduced 0.222 -0.455 0.489 virtual erect reduced 0.182 -0.413 0.440 virtual erect reduced 0.154 -0.386 0.398 virtual erect reduced 0.133 -0.365 0.365 virtual erect reduced 0.118 -0.350 0.336 virtual erect reduced 0.105 -0.338 0.312 virtual erect reduced 0.100 -0.332 0.301 virtual erect reduced Equation for 1/v vs 1/u y = -0.9947x - 0.2328

Focal Point (cm) 4.296 Sample calculation for 1 u 1 u = 1 2.000 cm = 0.5000 cm − 1 Sample calculation for 1 v 1 v = 1 − 3.730 cm =− 0.268 cm − 1 (Image is virtual) The formula to calculate M (from distance measured) M = − v u Sample calculation M = −− 3.730 cm 2.000 cm M = 1.865 (Image is erect and enlarged) The formula to calculate the focal length 1 u + 1 v = 1 f 1 u = − 1 v + 1 f Thisequationresembles ¿ slopeintercept form : y = mx + c Equation for DoubleConvex Lens : y = -0.9993x + 0.232 Therefore,c = 1 f f = 1 c Sample calculation c = 0.232 cm − 1 f = 1 0.232 cm f = 4.31 cm

0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500 0.550 -0.800 -0.700 -0.600 -0.500 -0.400 -0.300 -0.200 -0.100 0.000 f(x) = − 0.99 x − 0.23 Double Concave lens (1/v vs 1/u) 1/u (1/cm) 1/v (1/cm) Uncertainty Part I – Double Convex Lens: Focal Point (cm) 4.300 ∓ .005

Part II – Double Concave Lens: Focal Point (cm) 4.300 ∓ .005 Percent Difference: Part I – Double Convex Lens: Percent Difference = | TheoreticalValue − ExperimentalValue | TheoreticalValue × 100% ¿ 4.300 − 4.310 ∨ ¿ 4.300 × 100% Percent Difference = ¿ Percent Difference = 0.23% Part II – Double Concave Lens: Percent Difference = | TheoreticalValue − ExperimentalValue | TheoreticalValue × 100% ¿ 4.300 − 4.296 ∨ ¿ 4.300 × 100% Percent Difference = ¿ Percent Difference = 0.09% Results: Mirror Theoretical Focal Point Experimental Focal point Percent Difference Double Convex Lens 4.300 cm 4.310 cm 0.23% Double Concave Lens 4.300 cm 4.296 cm 0.09% Conclusion: In this lab data was collected using an online simulation for both double convex and double concave lenses. The object distance and image distance were collected. Then inverse of both were calculated to graph 1/u vs. 1/v. Data from each lenses returned a linear graph, and the equation of the line was used to calculate focal length of the lenses. For Double Convex lens focal length was 4.310 cm and for Double Concave lens focal length was 4.296 cm which gave percent difference of 0.23% and 0.09% respectively when compared to original focal length of 4.300 cm.