NORTHERN ILLINOIS UNIVERSITY PHYSICS DEPARTMENT Physics 211 E&M and Quantum Physics Spring 2018 Lab #8: Thin Lenses Lab Writeup Due: Mon/Wed/Thu/Fri, April 2/4/5/6, 2018 Background In the previous lab (Reflection & Refraction) you experimented with light refracting through materials, where the index of refraction determine how the light ray bent as it passed through glass and plastic shapes. We ll now apply these principles to two different shaped lenses that are used in a large variety of optical devices. Ray tracing is a procedure that allows us to locate and describe an image that is formed from the light rays refracted through a lens from some object. The objective of this lab to determine and analyze the optical properties of thin lenses using the lens maker s equation. 1. Overview Light waves start out as spherical wave fronts, but as they spread out over some distance the wave fronts become essentially parallel. A good analogy is throwing a rock in the water, which generates circular waves that grow larger as they spread out and become close to parallel. Parallel light rays in geometric optics represent a parallel wave. Convex and concave lens will form images at the focal points when parallel light rays are incident on one side of the lens, this is in fact the definition of the focal point. The distance between the lens and the focal point is the focal length f. The lens is manufactured to have a specific focal length, which is determined by the refractive index of the material and the radius of curvature of the lens. The focal length is ½ the radius of curvature of the lens. If the lenses are symmetric, there are focal points on both sides of the lens. A convex, or converging lens is one that is thicker in the middle then it is at the edges (see figures below). A concave, or diverging lens is one that is thinner in the middle than at the edges.
Convex, Converging Lens Concave, Diverging Lens Lens Makers Equation Using some geometry (which we will skip) the focal length f, the object distance p and the image distance q are related by the lens makers equation, which is further simplified for thin lenses as: 1 1 1 p q f As you saw in the video (prelab), we can draw a ray diagram by following a few simple rules. 1. The principle ray connects the object, the center of the lens, and the image (ray #1 below). Note that any ray passing through the center of the lens has NO net refraction. 2. A second ray can be drawn straight from the object to the lens, in which case it must pass through the focal point on the opposite side of the lens. 3. The point at which these two rays intersect will locate the image. 4. For a convex (converging) lens example below, since the object distance is further from the lens than the focal length, an inverted real image is formed. 2
5. The magnification of the image is based on the ratio of the image to the object distance from the mirror. Note that the image height h is negative if the image is inverted. h q M h p 6. A diverging lens example is below, showing a virtual image (no actual light rays go through the image, dotted lines show inferred rays). Diverging lenses form virtual images on the same side of the lens as the object. Sign conventions for mirrors and thin lenses Quantity When Positive (+) When Negative (-) Object distance p Real object Virtual object Image distance q Real image Virtual image Focal length f Converging lens or mirror Diverging lens or mirror Magnification m Upright image Inverted image 3
2. Procedure Apparatus includes:. Optical bench. Light source. Ruler. Screen, mirror with mount. Converging, diverging lens A. Activity #1: Finding the "Approximate" Focal Length Approach A You will use a light source that will produce parallel light rays that will be focused by a converging lens on a screen at the focal length of the lens. 1. On the optical bench, mount the converging lens, white screen, and light source. 2. Remove the light source from the bench and move it a foot or so away, but in line with the lens. Move the lens towards the screen until a sharp image of the light source appears on the screen. The light source is essentially at a distance of infinity compared to the size of the lens. 3. Make the table below in your lab notebook, and record the position of the lens and screen using the values imprinted on the optical bench. 4. Move the lens and screen to a slightly different position and have another lab member find the positions that produce a sharp image of the bulb on the screen. Repeat until you have 4 measurements. B. Activity #2: Finding the Focal Length of a Lens Approach B This approach uses a mirror to reflect parallel light rays back through the converging lens and produce an image at the focal point. 4
5. Attach the light source at one end of the optical bench with the pinhole screen attached to it (white side facing away from the bulb). Leave the same converging lens on the bench and mount a mirror on the far side of the lens. Align all the components vertically on the bench so the light coming through the pinhole is aligned with the approximate center of the lens (measure the heights of each) and strikes the mirror. 6. Move the lens and the mirror until you see a sharp image of the pinhole on the white screen. This image is from the source light rays passing through the lens, reflecting off the mirror as parallel rays and then being focused by the lens at the focal length on the screen as shown below. 7. You might also see an image of the pinhole on the screen due to a reflection off the front of the lens, so make sure your image is coming from the mirror. Make the table below in your lab notebook, and record the position of the lens and pinhole screen using the values imprinted on the optical bench. Repeat to get a total of 4 measurements. C. Activity #3: Finding the Focal Length of a Lens Approach C This approach will use the lens equation, an object and an image produced by the converging lens. 5
8. Remove the mirror and the pinhole light source. Place a light source with an attached symbol at one end of the optical bench and the white screen at the other end (the white side of the pinhole screen works best). 9. Place the converging lens about 10 cm away from the screen. Vertically align all three and tighten the clamps that hold the base to the optical bench. 10. Move the lens back & forth several cm until you see a sharply focused small image of the object on the screen. Make the table below in your lab notebook, and measure and record the object, lens, and image distance. Have another lab member repeat the measurement. 11. Do not move the screen or light source and place the lens about 10 cm from the light source. Move the lens back & forth a few cm until you see a sharply focused large image on the screen record this position of the lens in your table. Have another lab member repeat the measurement. Note whether the image is upright or inverted and if there was any magnification in your lab notebook. D. Activity #4: Finding the Focal Length of a Diverging Lens 12. Move the converging lens to a distance of about 25 cm from the object, then move the screen towards the lens until you see a sharply focused image (you may need to move the lens a few cm in either direction). Center the image on the screen. Make the table below in your lab notebook, and record the locations of the object, converging lens, and screen. 13. The image formed by the converging lens is going to become the object for the diverging lens. The location of the image produced by the converging lens (object for diverging lens) is the current location of the screen. Place the diverging lens between the converging lens and the screen. Do NOT move the object or converging lens. 6
14. Move the diverging lens towards the screen AND move the screen until you have a sharply focused image of the object on the screen. Make the table below in your lab notebook, and record the position of the diverging lens and the screen. Repeat and record 4 measurements. Note the size of the image vs. the object. Above diagram is not to scale. Original screen position, now the object for diverging lens The following ray diagram of a diverging lens can be modified to explain how the combination with the converging lens works. You just need to reverse the direction of the rays because the converging lens is producing the light rays coming from the left. By reversing the rays we are also switching the positions of the object and image! The smaller virtual (only inferred light rays converge there) object produces an image on the right side. 7
Your data section should contain all tables Your Results section should contain: o Calculations of the individual and average converging lens focal lengths for approaches A, B & C. o Ray diagram of the converging lens focal length determination from Approach C for the small image. Draw the image as upright or inverted. Show the magnification of the image vs. object. o Calculation of the focal length of the diverging lens, using the distance between the diverging lens and the original position of the screen (where the image from the converging lens formed) as p and the distance from the diverging lens to new position of the screen as q. See illustration above. o Calculation of the magnification of the image produced by the diverging lens. o Ray diagram of the diverging and converging lens setup from Step (14) above. Hint: The end result of this combination is that the diverging lens is extending the focal point of the converging lens. 4. Questions 1. Compare the converging lens focal lengths from Approaches A,B, & C. Which ones appear to match why do you think some matched (or were close) and other were outliers (think about the accuracy of the methods used)? 2. Regarding the determination of the converging lens focal length using Approach C (small image only). Was the image inverted? Was it magnified if so, by how much? Refer to your ray diagram as needed. 3. What are the results of adding the diverging lens to the converging lens in terms of focal length and magnification? Explain why. 4. Referring to your ray diagram for the determination of the focal length for the diverging lens. The real image created by the converging lens became the (virtual) object for the diverging lens. List and explain some possible applications of the combination of converging and diverging lens. 5. What are the properties that determine the focal length of a thin lens? 8