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Lab Activity: Spherical Mirrors and Thin Lenses In this lab you will use ray tracing to determine the images produced by spherical mirrors and lenses. You will use the mirror equation and the thin lens equation to determine the position of the image as well as the type of image and compare that with actual measurements you make. The mirror and lens equations will be derived in lecture. Introduction You can use any two rays starting on some point on the object and hitting the reflecting or refracting surface to help you find the image produced. However, for spherical mirrors and lenses there are three incident rays that are easier to draw than others and that we will therefore use for ray tracing. These rays are called principal rays: 1. A ray parallel to the principal axis. 2. A ray through the focal point. 3. A ray through the center of curvature (mirror) or through the optical center (thin lens). The principal rays are reflected/refracted differently depending on whether the reflecting/refracting object is a convex/concave mirror or lens. Part A: Ray Diagrams for Spherical Mirrors The three principal rays for converging (concave) mirrors: 1. Any incident ray parallel to the principal axis is reflected through the focal point (which is located at ½ R where R is the distance from the mirrors center (or vertex) to the center of curvature C. 2. Any incident ray which passes through the focal point is reflected parallel to the principal axis. 3. Any incident ray which passes through the mirror’s center of curvature C (i.e. along the radius) is reflected back upon itself. The three principal rays for diverging (convex) mirrors: 1. Any incident ray parallel to the principal axis is reflected as if it came from the focal point (which is located at ½ R behind the mirror’s surface where R is the distance from the mirror’s center (or vertex) to the center of curvature C. 2. Any incident ray which is directed towards the focal point is reflected parallel to the principal axis. 3. Any incident ray directed towards the mirror’s center of curvature C (i.e. along the radius) is reflected back upon itself. Practice drawing ray diagrams: Finish the ray diagrams for the following concave and convex mirror setups using the rules for diagramming as given above. Do this for a) an object located between C and F b) an object located beyond C c) an object located between V and F for the concave mirror and the case given for the convex mirror. 1 Lab Activity: Spherical Mirrors and Thin Lenses C F V R R/2 C F V C F V 2 Lab Activity: Spherical Mirrors and Thin Lenses V F C R R/2 Questions: For each case give your answers to the following questions in the table below: 1. Is the image larger or smaller than the object? 2. Is the image upright or inverted? 3. Is the image real or virtual? Object Image Image Image Image Exp. Mirror location location larger/smaller upright/inverted real/virtual Check between C&F (case a) beyond C Concave (case b) between V&F (case c) in front of Convex mirror A shaving mirror would be an example of a convex or a concave mirror? Where would you put your face? The spherical mirror on a car’s side mirror would be an example of a convex or concave mirror. Explain the warning: “Vehicles in mirror are closer than they appear!” Ask your instructor to show you the experimental setup for mirrors and check your findings experimentally (check box in table when you are satisfied). 3 Lab Activity: Spherical Mirrors and Thin Lenses Quantitative: concave mirror, concave mirror, concave mirror, convex mirror object between object beyond C object between C&F V&F object distance d0 (measured) image distance di (measured) focal length f (measured) object size h0 (measured) image size hi (measured) magnification M (measured) image distance hi (calculated) magnification M (calculated) image size hi (calculated) from diagram, image larger/smaller? from calculation, image larger/smaller? from diagram, image upright/inverted? from calculation, image upright/inverted? from diagram, image real/virtual? from calculation, image real/virtual? Make sure everything makes sense! Calculations and ray tracing results should be in agreement. All of the sign conventions are given at the end of this tutorial. 4 Lab Activity: Spherical Mirrors and Thin Lenses Part B: Ray Diagrams for Spherical Lenses The three principal rays for converging lenses: 1. Any incident ray parallel to the principal axis passes through the focal point on the side of the lens that the ray emerges. 2. Any incident ray which passes through the focal point and then through the lens emerges from the lens parallel to the principal axis. 3. Thin lens approximation: any incident ray which passes through the optical center of the lens passes straight through the lens unrefracted. Practice drawing ray diagrams: Finish the ray diagrams for the following bi-convex lenses using the rules for diagramming as given above. Is the image real or virtual? Is the image magnified? Is it right side up or inverted? Sketch where your eye has to be located in order to see the image. Is the location of the image closer to or farther from your eye than the actual object? Design a quick experiment to verify your answer to the question above. Does your diagram match what you can empirically determine from experiment? What will happen to the location and magnification of the image if the object is moved toward the lens? (The magnification is the ratio of image size and object size.) What will happen to the location and magnification of the image if the object is moved toward the focal point? If the object is between the lens and the focal length, what type of optical instrument would we call this in everyday language? i.e. What would you use this set-up for? 5 Lab Activity: Spherical Mirrors and Thin Lenses Is the image real or virtual? Is the image magnified? Is it right side up or inverted? Sketch where your eye has to be located in order to see the image. Is the location of the image closer to or farther from your eye than the actual object? Design a quick experiment to verify your answer to the question above. Does your diagram match what you can empirically determine from experiment? What will happen to the location and magnification of the image if the object is moved toward the focal point? What will happen to the location and magnification of the image if the object is moved toward infinity? If the object is farther from the lens than the focal length, what type of optical instrument would we call this in everyday language? i.e. What would you use this set-up for? Try and use this lens to project a real image of a very distant object onto a sheet of paper. You can use the outdoors as your distant object if it is light enough outdoors. If not, use a tall light source as your object. How many centimeters from the lens must you place the paper? What does the distance between the lens and the paper tell you about the focal length of the lens? 6 Lab Activity: Spherical Mirrors and Thin Lenses The three principal rays for diverging lenses: 1. Any incident ray parallel to the principal axis appears to come from the focal point on the side of the lens that the ray is coming from. 2. Any incident ray which is directed towards the focal point on the other side of the lens emerges from the lens parallel to the principal axis. 3. Thin lens approximation: any incident ray which passes through the optical center of the lens passes straight through the lens unrefracted. Practice drawing ray diagrams: Finish the ray diagrams for the following bi-convex lenses below using the rules for diagramming as given above. Is the image real or virtual? Is the image magnified? Is it right side up or inverted? Sketch where your eye has to be located in order to see the image. Is the location of the image closer to or farther from your eye than the actual object? Design a quick experiment to verify your answer to the question above. Does your diagram match what you can empirically determine from experiment? What will happen to the location and magnification of the image if the object is moved toward the focal point? What will happen to the location and magnification of the image if the object is moved toward infinity? 7 Lab Activity: Spherical Mirrors and Thin Lenses Is the image real or virtual? Is the image magnified? Is it right side up or inverted? Sketch where your eye has to be located in order to see the image. Is the location of the image closer to or farther from your eye than the actual object? Design a quick experiment to verify your answer to the question above. Does your diagram match what you can empirically determine from experiment? What will happen to the location and magnification of the image if the object is moved toward the focal point? What will happen to the location and magnification of the image if the object is moved toward infinity? Part C: The Lens Equation You have completed ray diagrams to locate the image produced by a lens. Now you will use the lens equation to determine the position of a real image and make comparisons with actual measurements. These equations will be derived in lecture. 1 1 1 di Lens Equation: Magnification: M f do di do Equipment Needed: (blue optics boxes) optics bench light source 75mm converging lens crossed target viewing screen 3 component holders 8 Lab Activity: Spherical Mirrors and Thin Lenses Procedure: 1. Set the viewing screen 40cm from the object (a lit crossed target). Place the lens between the object and viewing screen. Slide the lens back and forth until a clear image is viewed on the screen. Record: the object distance, the image distance, the object height and the image height. 2. Slide the lens further down the bench and try and produce another clear image on the screen with a different lens location. Again record: the object distance, the image distance, the object height and the image height. Calculations: 1. Using the lens equation, the distance of 40cm from the image to the object and the focal length of the lens, calculate the two different positions of the lens which will produce an image on the screen. (You will have to solve for the roots of a quadratic equation – i.e. you will find two solutions) 2. Using the results from calculations part 1, determine the magnification of these two images. 3. Compare the calculations to the actual measurements in the chart below: measurement 1 measurement 2 solution 1 solution 2 do di M = -di/do ho XXXX XXXX hi XXXX XXXX M = -hi/ho XXXX XXXX How close are your measured values to your calculations? What is your percent error? 9 Lab Activity: Spherical Mirrors and Thin Lenses Part D: Lens Combinations For the combinations of lenses below, find the final image, using ray tracing. f1 f1 f2 f2 s Suppose the focal lengths are 2.8cm and 1.25cm for the converging and diverging lenses, and that the lenses are separated by 5.4cm. If the 1.3-cm object is placed 4.4cm in front of the converging lens, find the final image, the total magnification and the image height of the final image. Make sure you follow the sign conventions closely! Questions: 1. According to your calculations, should your image be upright/inverted? 2. Should it be real/virtual? 3. Do the calculations and ray tracing agree qualitatively? 10 Lab Activity: Spherical Mirrors and Thin Lenses Equations: Mirror Equation 1 1 1 f do di Thin Lens Equation 1 1 1 f do di Lens Maker’s Equation 1 1 1 n 1 f R1 R 2 Sign Conventions The mirror equation and the thin lens equation work for both convex and concave mirrors and lenses if you use the correct sign conventions. Mirrors Quantity Positive when Negative when Object location do object is in front of mirror object is in back of mirror (real object) (virtual object) Image location di image is in front of mirror image is in back of mirror (real image) (virtual image) Image height hi image is upright image is inverted Focal length f and radius R mirror is concave mirror is convex Magnification M image is upright image is inverted Thin Lenses Quantity Positive when Negative when Object location do object is in front of lens (real object is in back of lens object) (virtual object) Image location di image is in back of lens (real image is in front of lens image) (virtual image) Image height hi image is upright image is inverted R1 and R2 center of curvature is in back center of curvature is in front of lens of lens Focal length f and radius R converging lens diverging lens 11