Geometric Optics. This equation is known as the mirror equation or the thin lens equation, depending on the setup.

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1 Geometric Optics Purpose (Write the purposes at the beginning of each problem.) Problem 1: find the focal length of a concave mirror to verify the mirror equation; Problem 2: find the focal length of a converging lens to verify the thin lens equation; Problem 3: build a simple refracting telescope and determine the best distance between lenses; Problem 4 (Optional): build a refracting telescope from a kit. Introduction and Theory Two types of images can be formed by a lens or mirror. A real image can be seen on a screen placed at the image position, whereas a virtual image cannot. Whether or not the image is real or virtual, the following relationship exists: f d o d i where: f is the focal length of the mirror or the lens do is the object distance, which is the distance from the object to the mirror (or the lens). di is the image distance, which is the distance from the image to the mirror (or the lens). This equation is known as the mirror equation or the thin lens equation, depending on the setup. Problem 1 Apparatus required. The Focal Length of a Small Concave Mirror Draw a labelled diagram of the apparatus (See Figure 1) and list all other apparatus Concave mirror # lamp (object) cardboard screen d0 di Figure 1 Data (All data must be recorded in proper table format) 1. If the object distance in the mirror equation is infinite, the focal length is equal to the image distance. This suggests a method of measuring the focal length. In practice, an infinite object distance will be approximated as the distance from the front of the classroom to an object (eg. a tree) outside the windows. Place the concave mirror in its holder on the metrestick. Place the screen in front of the mirror. Take this setup to the front of the classroom and obtain an image of the tree on the screen. Focus a clear image by adjusting the position of the screen. Record the positions of the mirror and the screen, together with their uncertainties. Calculate the image distance, in this case it is approximately equal to the focal length of the mirror. We will call it the reference focal length Geometric Optics - 1 Saved: November 22, 2017

2 2. Go back to your desk and set up the optical bench as shown in Figure Set the object distance do to 60.0 cm, and adjust the position of the cardboard screen until you see a clear image of the lamp filament. 4. Record the positions of the mirror, the object and the screen. The uncertainty for the image position may be large, as it may be hard to decide where the image is clearest. Calculate the object distance and the image distance, and put them in the data table as well. 5. Record the image type (real/virtual), orientation (upright/inverted), and magnification (is the image larger/smaller than the apparent size of the object) in your table. 6. Repeat steps (3) to (5) with an object distance of cm. Calculations Calculate a focal length for both object distances using the mirror equation. These two focal lengths should be approximately the same. Calculate the average focal length: this is our final result. State the final result of the concave mirror s focal length in a sentence. Calculate the percentage discrepancy between the final focal length and the reference value measured earlier. Are they in agreement considering the uncertainty? Problem 2 Apparatus required. The Focal Length of a Converging Lens Draw a labelled diagram of the apparatus (see Figure 2) and list all other apparatus Data (All data must be recorded in table format) 1. Measure the reference focal length for the lens. (Repeat step 1 from Problem 1, with the screen placed behind the lens.) 2. At your desk, set up the optical bench as shown in Figure 2. lamp (object) lens # cardboard screen d0 di Figure 2 3. Repeat steps (3) to (6) from Problem 1, using the lens this time Geometric Optics - 2 Saved: November 22, 2017

3 Calculations and (Write these separately in your report) Repeat the Calculations and from Problem 1, using the thin lens equation. Problem 3: Constructing a Simple Refracting Telescope In Problem 2, you measured the reference focal length for your converging lens. We are now going to construct a simple refracting telescope, using this lens and another one. Data (All data must be recorded in proper table format) 1. Get another converging lens from the instructor, and measure its reference focal length, using the same method from Problem 2. Do not mix it up with your other lens. 2. Mount the lens with the shorter focal length at one end of the meter stick. This lens is going to be our eyepiece lens, with focal length fe. Place the other lens (called our objective lens with focal length fo) on the meter stick as in Fig 3. Eye Objective Lens Eyepiece Lens Figure 3: Simple Telescope 3. Stand at the east side of the room and point the telescope toward the window and move the objective lens along the meter stick until you see a focused image of the tree through the eyepiece. 4. Again, you will likely find a wide range between the lenses that gives a focused image. Measure the distance between the two lenses and its uncertainty. Is the image you see in your telescope inverted or upright? Is the image larger or smaller than the apparent size of the object? Calculations Add the focal lengths of the two lenses together. Compare the distance between the lenses on your well-focused simple telescope and the sum of the focal lengths. Sketch a simple ray tracing diagram of this setup of two converging lenses to help understand this relationship. Meter Stick Write a sentence stating the relationship you observed between the sum of the focal lengths and the distance between the lenses that you measured on your well-focused simple telescope. State whether or not these two values are in agreement, as compared to your expectations Geometric Optics - 3 Saved: November 22, 2017

4 Problem 4 (Optional): Paper Tube Telescope Using the knowledge you have gained from Problem 3, you are now going to construct a homemade telescope from the parts in a kit. Before assembling the telescope Get a kit from the instructor. The parts are listed in Fig 4. Estimate the focal lengths of the objective lens and the eyepiece lens, using the reference method from Problems 2 and 3. Calculate the theoretical distance you would want between the two lenses in order to focus the telescope on an image a far distance away (see Problem 3). Record these values in your data section. Tiny cardboard Objective Lens Foam cylinder Eyepiece lens Small cardboard Large cardboard Red cap White washer Figure 4: Telescope Parts Now we will build the telescope. Instructions for building the telescope (refer to Fig 5) Take the red cap and place the white washer inside it. Place the lens with the greater diameter in next. Then place the red cap snugly over one end of the thick cardboard. Put the small lens in one end of the grey foam cylinder so that the rounded end will face outside. Place the tiny cardboard and push in behind the small lens. Place the grey foam/lens piece into one end of the thin cardboard so that the end of the foam is flush with the end of the. Slide the open end of the thin cardboard into the open end of the thicker. Well done! You now have your telescope! 1114 Geometric Optics - 4 Saved: November 22, 2017

5 Tiny cardboard Eyepiece Lens Objective Lens Red cap Grey foam Thin cardboard Thick cardboard White washer Figure 5: Homemade Telescope After assembling the telescope Stand at the east end of the lab and focus the telescope on the tree outside by sliding the thinner into/out of the thicker. Alternatively, you can go out into the hallway and focus on the far end of the hallway. Once you have a focused image, measure the distance between the two lenses (please don t write on the telescope) and record it in your data tables. State the distance between the lenses that make the best telescope. Compare this measured result to what you expected from Problem 3, and say if you think the results make sense. WHEN YOU ARE FINISHED, TAKE APART THE TELESCOPE AND PUT THE KIT BACK INTO ITS BAG. Return the kit to the front of the room Geometric Optics - 5 Saved: November 22, 2017