Learning Goal: To learn the quantitative use of the lens equation, as well as how to Part J determine qualitative properties of solutions. n working with lenses, there are three important quantities to consider: Is the lens converging or diverging? The object distance s is the distance along the axis of the lens to the object. The image distance s' is the distance along the axis of the lens to the image. The focal length f is an intrinsic property of the lens. O converging These three quantities are related through the equation diverging Note that this equation is valid only for thin, spherical lenses. Unless Submit Previous Answers otherwise specified, a lens problem always assumes that you are using thin, spherical lenses. Correct The equation above allows you to calculate the locations of images You can solve the lens equation for s' in terms of s and f. If you do this and then substitute your result into the magnification equation, you will see that the and objects. Frequently, you will also be interested in the size of the only way to obtain an image of a real object that is larger than the object itself is with a converging lens image or object, particularly if you are considering a magnifying glass or microscope. The ratio of the size of an image to the size of the object is called the magnification. It is given by m = y Part K where y' is the height of the image and y is the height of the object. Find the focal length of the lens. The second equality allows you to find the size of the image (or object) with the information provided by the thin lens equation. Express your answer in centimeters, as a fraction or to three significant figures. All of the quantities in the above equations can take both positive and negative values. Positive distances correspond to real images or objects, while negative distances correspond to virtual images or O ( = ] ? objects. Positive heights correspond to upright images or objects, while negative heights correspond to inverted images or objects. The following table summarizes these properties: f = 6.67 cm positive negative S virtual Submit Previous Answers Request Answer s' real virtual y upright inverted * Incorrect; Try Again; 5 attempts remaining y' upright inverted The focal length f can also be positive or negative. A positive focal length corresponds to a converging lens, while a negative focal length corresponds to a diverging lens. Provide Feedback Next > PearsonConsider an object with s = 12 cm that produces an image with s' = 15 cm. Note that whenever you are working with a physical object, the object distance will be Learning Goal: positive (in multiple optics setups, you will encounter "objects" that are actually images, but that is not a possibility in this problem). A positive image distance means that To learn the quantitative use of the lens equation, as well as how to the image is formed on the side of the lens from which the light emerges. determine qualitative properties of solutions. In working with lenses, there are three important quantities to consider: The object distance s is the distance along the axis of the lens to the Part A object. The image distance s' is the distance along the axis of the lens to the image. The focal length f is an intrinsic property of the lens. These three quantities are related through the equation Find the focal length of the lens that produces the image described in the problem introduction using the thin lens equation. Express your answer in centimeters, as a fraction or to three significant figures. Note that this equation is valid only for thin, spherical lenses. Unless f = 6.67 cm otherwise specified, a lens problem always assumes that you are using thin, spherical lenses Submit Previous Answers The equation above allows you to calculate the locations of images and objects. Frequently, you will also be interested in the size of the image or object, particularly if you are considering a magnifying glass Correct or microscope. The ratio of the size of an image to the size of the object is called the magnification. It is given by y V Part B where y' is the height of the image and y is the height of the object. v The second equality allows you to find the size of the image (or object) Considering the sign of f, is the lens converging or diverging? with the information provided by the thin lens equation. All of the quantities in the above equations can take both positive and converging negative values. Positive distances correspond to real images or objects, while negative distances correspond to virtual images or diverging objects. Positive heights correspond to upright images or objects, while negative heights correspond to inverted images or objects. The following table summarizes these properties: Submit Previous Answers positive negative S virtual Correct s real virtual y upright inverted y' upright inverted V Part C The focal length f can also be positive or negative. A positive focal length corresponds to a converging lens, while a negative focal length corresponds to a diverging lens. What is the magnification m of the lens