The Lens Lenses are used in many different optical devices. They are found in telescopes, binoculars, cameras, camcorders and eyeglasses. Even your eye contains a lens that helps you see objects at different distances. In general, all lenses are more optically dense than the surrounding air. Refraction and The Lens Light bends when it enters the lens and light bends Figure 1: when it exits the lens. In figure 1, the following parallel rays are incident on the lens. Draw the normal for each ray. Try to predict the path of the five rays as they enter the lens. Label points a b c d e f g h i j As light enters the lens (points a b c d e), the angle of incidence is greater than the angle of refraction, as the light enters a more optically dense medium. As light exits the lens (points f g h i j), the angle of incidence is less than the angle of refraction, as light enters a medium that is less optically dense. This lens causes light to __________ to a common point, hence is called a ____________ lens. The common point where the rays __________ is called the _________ ________. This lens is also sometimes called a ___________ lens. Thin Lens For lenses that are thin, we define several key characteristics. The principal axis and vertical axis are shown in the figure. The _________ ___________ is the point of intersection between the __________ and _________ axis. F is called the __________ _________ and the focal length is the distance between the _________ ________ and the _________ point. Note that to simplify the diagram, the bending of the rays is drawn only at the vertical axis. Label the optic centre, the vertical and principal axis. Draw the refracted rays and label the focal length. . Focal point Draw the refracted rays for the thin lens and the thick lens with the same optical density/index of refraction. Assume that the focal length for the thin lens is 3 cm. Estimate the focal length for the thicker lens. Draw the refracted rays for the thin lens with index of refraction of 1.2 (assume focal length is 2.5 cm) and index of refraction of 2.2. Estimate the focal length for the lens with an index of refraction of 2.2. Example 1: The following lenses have the same focal length (place the focal point 2 cm from the optic centre for each lens) and draw the refracted rays. Which lens has the higher index of refraction (is more optically dense)? Example 2: Draw the refracted rays for this lens. Does this lens have a focal point? Lens and Image Formation Lenses can be used to create images of objects. The image formed by the lens is called a ___________ _________ as it can be projected on a screen or formed on a sheet of paper. The lens can be larger or smaller than the image or the object. For thin lenses, ____________ are used to Figure 2: learn more about the properties of the images. The focal point is labeled f. 2f is twice the distance of the focal length. The distance between the object and the lens is called the __________ ______________ (do). The distance between the image and the lens is called the __________ ______________ (di). . . For figure 2, label do, di, f and 2f. Also label the optic centre and the image. Answer the following questions: 1) To create an image smaller than the object, where does the object have to be? 2) To create an image larger than the object, where does the object have to be? 3) Describe the characteristics of the image when the screen is not placed at the optimal image distance? Include a diagram. For images to be in focus on a screen, the distance between the lens and the screen (di) depends on two factors: 1) The ____________________ of the lens 2) The __________________________ is from the lens As focal length increases, for the same object distance (same do), image size ___________ and image distance (di) __________. Reflection of Light Revisited Previously, we discovered that when light is incident on a shiny smooth surface (figure 3), the reflected ray has the same angle as the incident ray. However, most surfaces are not smooth at the microscopic level. In figure 4, the pencil reflects light at many different angles. In fact, every point on the pencil reflects light in all directions. Draw the reflected rays of light. Figure 3: Figure 4: Image Distance and Ray Diagrams Ray diagrams can be used to determine the distance between the screen and the lens for which the image will appear in focus. Recall that when light reflects off of a rough surface (most surfaces), rays reflect at all angles. We will use 3 of those rays to determine the appropriate distance between the screen and lens so that the image is in focus. To determine the location of an image, Step 1. Place the object so that its bottom is on the ___________ ________. Step 2. Draw each of the three rays for the ______ _______ of the object only. If the 3 rays do not __________, re-draw until they do. Step 3. Draw the image, so that its _________ is on the ____________ _________ and its top is where the 3 rays ____________. Situation 1: The object is at a distance greater than 2f from the optic centre (let f = 3 cm, object position is 7 cm from optic centre, object height is 1 cm) . . Image distance = Image height = Image Characteristics: ___________, ____________, ______________, ____________ Phun Phact Did you know a “35 mm” camera typically has a lens with a focal length of 50 mm (35 mm is the size of the film)? Situation 2: The object is at a distance less than 2f but greater than f from the optic centre (let f = 25 mm, object position is 4 cm from optic centre, object height is 1 cm) Image distance = Image height = Image Characteristics: ___________, ____________, ______________, ____________ Situation 3: Situation 4: a) f = 5 cm, object distance is 10 cm b) f = 2 cm, object distance = 12 cm The Camera For a camera, the object is the person or landscape that you take a picture of. The screen is the film or the charge coupled device (digital camera) and is usually very small (for non digital cameras, the film is 35 mm in width). The focal length for a traditional camera is in the range of 50 mm. For a camera, the screen does not move nor does the landscape, therefore to focus an image on the film or CCD, the lens moves back and forth. Diagram: Draw an object, a lens, an image and the film. Label object distance, image distance, the lens, film and image. As the lens moves to the correct position, the image becomes focused. Question: What physical properties of a lens and a camera changes when you want to capture images that are magnified/larger? Thin Lens Equations The following equations can be used to determine the optimal distance (di) to place a screen so that an image is in focus. 1) At a movie theatre, the image projected on the screen is magnified by a factor of 80 (-80). The image distance between the lens and the screen is 30 meters. Calculate the distance between the lens and the object (film). Sketch a diagram. What does a negative magnification mean? 2) At a movie theatre, the image projected on the screen is magnified by a factor of 60 (-60). The height of the film (object) is about 0.05 m. Calculate the height of the image on the screen. Sketch a diagram. 3) A camera (f = 50 mm) is used to take pictures of objects. Object A is 1.2 m from the lens. a) Calculate the image distance (di) between the lens and the film for object A. b) Calculate the magnification for object A. c) What does a magnification of -2 mean? What does a magnification of -1 mean? What does a magnification of -0.5 mean? 4) The same camera as in the previous question is used to take a picture of Object B, 8 m from the lens. a) Calculate the image distance (di) between the lens and the film for object B. b) Calculate the magnification for object B. c) As object distance increases, what happens to magnification? 5) A 110 mm lens is used to take pictures of objects (the case that holds the lens is typically much longer than the 50 mm lens (WHY IS THIS?)). Object B is 8 m from the lens. Calculate the magnification of the object. Compare the magnification to the previous question. As focal length increases, magnification ________ 6) An object is located 8.5 cm from the principal plane of a converging lens. The focal length of the lens is 5.5 cm. The object is 2.5 mm high. Calculate the image height and the location of the image. 7) When an object of 1 cm high is placed in front of the lens, an inverted image is produced that is 4 cm high. The object is 26 cm from the lens. Determine the focal length for this lens.