FOCAL LENGTH OF LENSES

FOCAL LENGTH OF LENSES PHYS 206L 2023 Fall Lab Number: 10 Group Member(s): Gerald Owusu Perform Date:11/10/23 OBJECTIVE  Experiment 1 (Refraction from Convex and Concave lenses) Objectives: o To explore the difference between convex and concave lenses and to determine their focal lengths.  Experiment 2 (Lensmaker’s Equation) Objectives: o To determine the focal length of a concave lens by direct measurement and by using the lensmaker’s equation.  Experiment 3 (Focal Lenth of a Thin Lens) Objectives: o To determine the focal length of a thin lens. THEORY  Experiment 1 (Refraction from Convex and Concave lenses) Theory: o Parallel rays of light passing through a thin convex lens cross at the focal point of the lens. The focal length is measured from the center of the lens to the focal point.  Experiment 2 (Lensmaker’s Equation) Theory: o The lensmaker’s equation is used to calculate the focal length of a lens based on the radii of curvature of its surfaces and the index of refraction of the lens material.

1 f =( n − 1 )( 1 R 1 − 1 R 2 ) where f is the focal length , n is the relative index of refraction of the lens material, and R 1 and R 2 are the radii of curvature of the lens surfaces  Experiment 3 (Focal Lenth of a Thin Lens) Theory: For a thin lens : 1 f =( 1 d 0 + 1 d i ) where f is focal length, d o is the distance between the object and the lens and d i is the distance between the image and the lens. See Figure 3.1 (pg.6, Lab 10). EQUIPMENT  Ray box (multiple white rays)  Convex lens  Concave lens  Metric rule  Second convex lens  Bench  Light source (object)  Screen PROCEDURE Experiment 1 (Refraction from Convex and Concave lenses) Procedures 1. Place the ray box on a white piece of paper. Using five white rays from the ray box shine the rays straight into the convex lens. See Figure 1.1 (pg.1, Lab10). Trace around the surface of the lens and trace the incident and transmitted rays. Indicate the incoming and the outgoing rays with arrows in the appropriate directions. 2.The place where the five refracted rays cross each other is the focal point of the lens. Measure the focal length from center of the convex lens to the focal point. Record the result in Table1.1. 3. Repeat the procedure for the concave lens. Note that in Step 2, the rays leaving the lens are diverging and they will not cross. Use a rule to extend the outgoing rays straight back through the lens. The focal point is where these extended rays cross. Again, be careful extrapolating these line back-take your time!!

refraction is 1.5 for the acrylic lens. Remember that a concave surface has a negative radius of curvature. f =_______________ 5.Calculate the percent difference between the two values of the focal length of the concave lens: % difference =________ Experiment 3 (Focal Lenth of a Thin Lens) Procedures Part 1: FOCAL LENGTH USING AN OBJECT AT INFINITY 1.Using one of the positive lenses focuses a distant light source on a paper. 2.Measure the distance from the lens to the paper. This is the image distance. 3.Take the limit as the object distance goes to infinity in the Thin Lens formula: Solve for the focal length f =______ : 1 f =( 1 d 0 + 1 d i ) 4.If you look at the label near the base of your lens, it gives you its focal length in mm, for example, +20mm means a 20mm focal length converging lens. A negative focal length means a diverging lens. How well does this number compare with your result in 3? Why might it be different? Part 2: FOCAL LENGTH BY PLOTTING 1/d 0 vs. 1/d i a. On the optical bench, position the lens between a light source (the object) and a screen. Be sure the object and the screen are at least 0.80 meter apart. b. Move the lens to a position where an image of the object is formed on the screen. Measure the image distance and the object distance. The image distance is the distance from the screen to the center of the lens. The object distance is the distance from the light source to the center of the lens. Record all measurements in table 3.1(pg.6, Lab 10). c. Measure the object size (on the screen of the light source) and the image size for this position of the lens. d. Move the lens to a second position where the image is in focus (Do not move the screen or Light Source). Measure the image distance and the object distance e. Measure the image size for this position also. f. Move the screen toward the object until you can no longer find two positions of the lens where the image will focus. Then move the

screen a few centimeters further away from the object. Repeat Parts b and d for this position of the screen and for 4 other intermediate positions of the screen. This will give you 6 sets of data points (a total of 12 data points). g. Plot 1/do vs. 1/di using the 12 data points. This will give a straight line and the x- and y- intercepts are each equal to 1/f. Be sure that your axis range goes all the way down to zero, or this will not work. h. Find the percentage difference between the two values of the focal length found from the intercepts. Then average these two values and find the percent difference between this average and the focal length found in Part I. REFERENCES  Loyd, D. (2007). Physics laboratory manual. Cengage Learning.  Lab 10 Focal Length of Lenses.pdf