Lenses PDF

LENSES Lesson 1: Lens and Refraction of Light We learned in a previous lesson that light goes through a transparent material and bends depending on the indices of refraction of the materials involved. Refraction by light is governed by Snell’s Law, named after the Dutch astronomer Willebrord Snell...

LENSES Lesson 1: Lens and Refraction of Light We learned in a previous lesson that light goes through a transparent material and bends depending on the indices of refraction of the materials involved. Refraction by light is governed by Snell’s Law, named after the Dutch astronomer Willebrord Snell (1580-1626). A lens is a basic optical device that uses refraction on two surfaces to produce images. A thin lens is one whose thickness is small relative to its focal length, the radii of curvature of its two surfaces, and to the object and image distances. A lens has two surfaces, each of which may be flat, concave, or convex. Whatever the shape of the surfaces, there are two categories of lenses: Figure 1.Converging lens converging and diverging. Lenses that collect light after refraction are known as converging lenses. A converging lens, also known as a convex lens, is easily recognizable because the middle of the lens is thicker than the edges. Fig.1 shows the profiles of some converging lenses. Perhaps the most familiar of these is the biconvex (or double convex) lens, commonly used as a magnifying glass or simple magnifier. On the other hand, lenses that do the opposite are the diverging lenses or also known as concave lenses. Light goes through a diverging lens and due to the shape of the surfaces on either side of the lens, refracted light Figure 2. Diverging lens rays are directed away from the principal axis. Fig. 2 shows the profiles of some common diverging lenses. They are easily recognizable because the middle parts of the lenses are thinner than the edges. These are the lenses used for telescopes, cameras, binoculars, and eyeglasses for nearsightedness.  Important Parts of Lens Centre of curvature - The center of the sphere where the lens is formed. Since concave and convex lenses are formed by the combination of two parts of spheres, therefore they have two centers of curvature. One center of curvature is usually denoted by C1 or 2F1 (based on different references) and the second is denoted by C2 or 2F2. Principal Focus – The point at which parallel rays of light converge in a concave lens and parallel rays of light diverge from the point is called Focus or Principal Focus of the lens. Note: Convex and Concave lenses have two Foci. These are represented as F1 and F2. Principal Axis – The horizontal imaginary line that passes through the centers of curvature of a lens. Optical center - The central point of a lens is called its Optical Centre. A ray passes through the optical center of a lens without any deviation. Radius of curvature - The distance between optical center and center of curvature and is generally denoted by R. Focal Length - The distance between the optical center and principal focus. The focal length of a lens is half of the radius of curvature. Formation of Images through Lenses The characteristics and orientation of the images formed through lenses vary. They depend on the distance between the object and the lens, and the type of lens through which light passes. Here is a step-by-step method for drawing ray diagrams for lenses. Step 1: A ray from the top of the object parallel to the principal axis on one side of the lens, when refracted, passes through the F2 (ray 1).  Step 2: A ray from the top of the object passing through the lens vertex (midpoint) is refracted along the same direction (ray 2). Note: The point where the rays intersect will be the location of the image formed. Object’s Position Configuration Magnification Orientation Type of Image (Position) (Magnified or (Upright or (Real or Virtual) Reduced) Inverted) Is in 2F1 Between F2 and 2F2 Reduced Inverted Real Concave Lenses Step 1: From the tip of the object, draw a parallel line to the center of the lens. Figure 6. Step 1 Step 2: Draw a diverging line connecting from line 1 and aligned with F1. (Ray-1) Step 3: From the tip of the object, draw a line passing through the vertex. (Ray-2) Note: The point where the rays intersect will be the location of the image formed. Object’s Location Configuration Magnification Orientation Type of Image (Position) (Magnified or (Upright or (Real or Virtual) Reduced) Inverted) Between 2F1 and F1 Between F1 and V Reduced Upright Virtual Lesson 2: Properties of Lenses Applied in Optical Devices Most optical instruments are made up of an arrangement or combination of lenses. The function of the optical system is determined by the focal lengths of the lenses and their relative positions. Many devices use the visible electromagnetic waves we call light. Some of these devices create light, some detect light, and others manipulate the beams of light for some use. The Human Eye One of the most complicated optical systems is the human eye. The human eye acts like a camera. Light passes through a transparent layer called the cornea, which has a refractive index of 1.376. Most of the refraction of the light entering the eye occurs at its cornea. After light passes through the cornea, it goes to the pupil which is found at the center of the colored part of the eyes called the iris. The pupil is an opening that changes in diameter to regulate the amount of light that enters the eye. The light then travels to the aqueous humor, and then to the lens. The lens focuses on the light that enters the eye. Just like the lens used in the camera, the focal length of our lens changes depending on the distance from the source of light. The light then travels to the retina, where the image is formed. The retina has photocells called rods and cones. The rods are responsive to brightness, while the cones are responsive to the colors. These photocells transport the image to the brain via the optic nerves. The human eye is limited to a certain range. This range includes the near point and far point of the eye. The 25 cm to infinity sight is the ideal range. In reality, many people’s eyes cannot accommodate this range, due to eye defects. These defects can be corrected using lenses or can be treated using laser eye surgery. Some eye defects and how they can be corrected or treated are listed in the following table. Table 1. Human Eye Defects and their Proposed Medication Eye Defect Cause and Description Proposed Medication Myopia or The patient cannot focus on distant objects. Use eyeglasses that have diverging/concave nearsightedness lenses. Hyperopia or The patient cannot focus on objects that are Use eyeglasses that have converging/convex farsightedness nearby. The eyeballs are short, or the corneas lenses. are not sufficiently curved. Astigmatism The patient’s vision is blurred. The corneas Use glasses with cylindrical lenses. are irregularly shaped. The Camera The camera is a boxlike device for taking pictures modeled after the eye. The opening is covered by a lens or a combination of lenses that act like the crystalline lens of the eye. The shutter, which opens and closes, corresponds to the eyelid of the eye. The film corresponds to the retina where the image is formed. The diaphragm regulates the amount of light that enters the camera through its aperture, just as the iris permits the proper amount of light that enters the eye through the pupil. The Magnifying Glass To be able to examine an object in detail, you just simply bring it near the eye to increase the size of the retinal image. However, there is a limit to this increase in size because the rays will always diverge. There is a need now to use a single convex lens known as the magnifying glass that will add convergence to the visual system. A convex lens can be used as a magnifying glass. It gives a magnified upright image of an object placed within its focal length. With a magnifying glass, an object results in a much larger retinal image when Figure 14. Magnifying glass examined. Trivia time! The convex lens in the magnifying glass causes things to burn. The double convex lens in the magnifying glass focuses the beam of heat rays at one single point. Concentrating the energy at a single point causes a flammable object to set fire.  The Microscope We have seen that a convex lens can form a magnified image. For better magnification, it is necessary to use a microscope. A microscope is made up of two converging lenses. The first lens is called the objective lens and is of short focal length. It forms the real magnified image of the object. The second lens is called an eyepiece, and the image of the objective lens becomes the object of the eyepiece lens. The eyepiece lens is a magnifying glass that looks at and enlarges the image created by the objective lens. A light source below illuminates the object. Figure 15. Microscope The Telescope The telescope is a device used to see very far or distant objects. It makes use of two lenses. The objective lens with its big diameter allows it to collect more light. The image formed by the objective lens appears to be smaller than the object because the object’s distance is more than twice the focal length. The eyepiece magnifies the image formed by the objective lens. Refracting telescopes use a lens to collect and focus rays of light. Reflecting telescopes use a large concave mirror instead of a lens for the same purpose. Figure 16. Telescope  The Binoculars Being long, having an inverted image makes the telescope cumbersome. This difficulty is overcome in the so-called prism binoculars or modern opera glasses. Binoculars produce an erect image and increase the magnification of an image through its system of prism and lenses. In binoculars, the image experiences four inversions by the reflection of the beam of light through a series of four reflecting prisms. The result is an erect image. Figure 17. Binocular The Projector The projector has a concave mirror that reflects light from an intense source back into a pair of condenser lenses. The condenser lenses direct very bright light through the slide to the projection lenses. These lenses are mounted in a sliding tube so that they can be moved forward or backward for a sharp image to be focused on the screen. If you want a smaller, closer picture, you have to move the lens away from the slide. The projection lenses put a real inverted image of the slide on the screen. To get upright, you have to mount the slide upside down. Figure 18. Projector